Merge branch 'next-evm-digsig' of...

Merge branch 'next-evm-digsig' of git://git.kernel.org/pub/scm/linux/kernel/git/kasatkin/linux-digsig into next

Documentation/digsig.txt

+Digital Signature Verification API
+
+CONTENTS
+
+1. Introduction
+2. API
+3. User-space utilities
+
+
+1. Introduction
+
+Digital signature verification API provides a method to verify digital signature.
+Currently digital signatures are used by the IMA/EVM integrity protection subsystem.
+
+Digital signature verification is implemented using cut-down kernel port of
+GnuPG multi-precision integers (MPI) library. The kernel port provides
+memory allocation errors handling, has been refactored according to kernel
+coding style, and checkpatch.pl reported errors and warnings have been fixed.
+
+Public key and signature consist of header and MPIs.
+
+struct pubkey_hdr {
+	uint8_t		version;	/* key format version */
+	time_t		timestamp;	/* key made, always 0 for now */
+	uint8_t		algo;
+	uint8_t		nmpi;
+	char		mpi[0];
+} __packed;
+
+struct signature_hdr {
+	uint8_t		version;	/* signature format version */
+	time_t		timestamp;	/* signature made */
+	uint8_t		algo;
+	uint8_t		hash;
+	uint8_t		keyid[8];
+	uint8_t		nmpi;
+	char		mpi[0];
+} __packed;
+
+keyid equals to SHA1[12-19] over the total key content.
+Signature header is used as an input to generate a signature.
+Such approach insures that key or signature header could not be changed.
+It protects timestamp from been changed and can be used for rollback
+protection.
+
+2. API
+
+API currently includes only 1 function:
+
+	digsig_verify() - digital signature verification with public key
+
+
+/**
+ * digsig_verify() - digital signature verification with public key
+ * @keyring:	keyring to search key in
+ * @sig:	digital signature
+ * @sigen:	length of the signature
+ * @data:	data
+ * @datalen:	length of the data
+ * @return:	0 on success, -EINVAL otherwise
+ *
+ * Verifies data integrity against digital signature.
+ * Currently only RSA is supported.
+ * Normally hash of the content is used as a data for this function.
+ *
+ */
+int digsig_verify(struct key *keyring, const char *sig, int siglen,
+						const char *data, int datalen);
+
+3. User-space utilities
+
+The signing and key management utilities evm-utils provide functionality
+to generate signatures, to load keys into the kernel keyring.
+Keys can be in PEM or converted to the kernel format.
+When the key is added to the kernel keyring, the keyid defines the name
+of the key: 5D2B05FC633EE3E8 in the example bellow.
+
+Here is example output of the keyctl utility.
+
+$ keyctl show
+Session Keyring
+       -3 --alswrv      0     0  keyring: _ses
+603976250 --alswrv      0    -1   \_ keyring: _uid.0
+817777377 --alswrv      0     0       \_ user: kmk
+891974900 --alswrv      0     0       \_ encrypted: evm-key
+170323636 --alswrv      0     0       \_ keyring: _module
+548221616 --alswrv      0     0       \_ keyring: _ima
+128198054 --alswrv      0     0       \_ keyring: _evm
+
+$ keyctl list 128198054
+1 key in keyring:
+620789745: --alswrv     0     0 user: 5D2B05FC633EE3E8
+
+
+Dmitry Kasatkin
+06.10.2011

include/linux/digsig.h

+/*
+ * Copyright (C) 2011 Nokia Corporation
+ * Copyright (C) 2011 Intel Corporation
+ *
+ * Author:
+ * Dmitry Kasatkin <dmitry.kasatkin@nokia.com>
+ *                 <dmitry.kasatkin@intel.com>
+ *
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, version 2 of the License.
+ *
+ */
+
+#ifndef _DIGSIG_H
+#define _DIGSIG_H
+
+#include <linux/key.h>
+
+enum pubkey_algo {
+	PUBKEY_ALGO_RSA,
+	PUBKEY_ALGO_MAX,
+};
+
+enum digest_algo {
+	DIGEST_ALGO_SHA1,
+	DIGEST_ALGO_SHA256,
+	DIGEST_ALGO_MAX
+};
+
+struct pubkey_hdr {
+	uint8_t		version;	/* key format version */
+	time_t		timestamp;	/* key made, always 0 for now */
+	uint8_t		algo;
+	uint8_t		nmpi;
+	char		mpi[0];
+} __packed;
+
+struct signature_hdr {
+	uint8_t		version;	/* signature format version */
+	time_t		timestamp;	/* signature made */
+	uint8_t		algo;
+	uint8_t		hash;
+	uint8_t		keyid[8];
+	uint8_t		nmpi;
+	char		mpi[0];
+} __packed;
+
+#if defined(CONFIG_DIGSIG) || defined(CONFIG_DIGSIG_MODULE)
+
+int digsig_verify(struct key *keyring, const char *sig, int siglen,
+					const char *digest, int digestlen);
+
+#else
+
+static inline int digsig_verify(struct key *keyring, const char *sig,
+				int siglen, const char *digest, int digestlen)
+{
+	return -EOPNOTSUPP;
+}
+
+#endif /* CONFIG_DIGSIG */
+
+#endif /* _DIGSIG_H */

include/linux/mpi.h

+/* mpi.h  -  Multi Precision Integers
+ *	Copyright (C) 1994, 1996, 1998, 1999,
+ *                    2000, 2001 Free Software Foundation, Inc.
+ *
+ * This file is part of GNUPG.
+ *
+ * GNUPG is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * GNUPG is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
+ *
+ * Note: This code is heavily based on the GNU MP Library.
+ *	 Actually it's the same code with only minor changes in the
+ *	 way the data is stored; this is to support the abstraction
+ *	 of an optional secure memory allocation which may be used
+ *	 to avoid revealing of sensitive data due to paging etc.
+ *	 The GNU MP Library itself is published under the LGPL;
+ *	 however I decided to publish this code under the plain GPL.
+ */
+
+#ifndef G10_MPI_H
+#define G10_MPI_H
+
+#include <linux/types.h>
+
+/* DSI defines */
+
+#define SHA1_DIGEST_LENGTH   20
+
+/*end of DSI defines */
+
+#define BYTES_PER_MPI_LIMB	(BITS_PER_LONG / 8)
+#define BITS_PER_MPI_LIMB	BITS_PER_LONG
+
+typedef unsigned long int mpi_limb_t;
+typedef signed long int mpi_limb_signed_t;
+
+struct gcry_mpi {
+	int alloced;		/* array size (# of allocated limbs) */
+	int nlimbs;		/* number of valid limbs */
+	int nbits;		/* the real number of valid bits (info only) */
+	int sign;		/* indicates a negative number */
+	unsigned flags;		/* bit 0: array must be allocated in secure memory space */
+	/* bit 1: not used */
+	/* bit 2: the limb is a pointer to some m_alloced data */
+	mpi_limb_t *d;		/* array with the limbs */
+};
+
+typedef struct gcry_mpi *MPI;
+
+#define MPI_NULL NULL
+
+#define mpi_get_nlimbs(a)     ((a)->nlimbs)
+#define mpi_is_neg(a)	      ((a)->sign)
+
+/*-- mpiutil.c --*/
+MPI mpi_alloc(unsigned nlimbs);
+MPI mpi_alloc_secure(unsigned nlimbs);
+MPI mpi_alloc_like(MPI a);
+void mpi_free(MPI a);
+int mpi_resize(MPI a, unsigned nlimbs);
+int mpi_copy(MPI *copy, const MPI a);
+void mpi_clear(MPI a);
+int mpi_set(MPI w, MPI u);
+int mpi_set_ui(MPI w, ulong u);
+MPI mpi_alloc_set_ui(unsigned long u);
+void mpi_m_check(MPI a);
+void mpi_swap(MPI a, MPI b);
+
+/*-- mpicoder.c --*/
+MPI do_encode_md(const void *sha_buffer, unsigned nbits);
+MPI mpi_read_from_buffer(const void *buffer, unsigned *ret_nread);
+int mpi_fromstr(MPI val, const char *str);
+u32 mpi_get_keyid(MPI a, u32 *keyid);
+void *mpi_get_buffer(MPI a, unsigned *nbytes, int *sign);
+void *mpi_get_secure_buffer(MPI a, unsigned *nbytes, int *sign);
+int mpi_set_buffer(MPI a, const void *buffer, unsigned nbytes, int sign);
+
+#define log_mpidump g10_log_mpidump
+
+/*-- mpi-add.c --*/
+int mpi_add_ui(MPI w, MPI u, ulong v);
+int mpi_add(MPI w, MPI u, MPI v);
+int mpi_addm(MPI w, MPI u, MPI v, MPI m);
+int mpi_sub_ui(MPI w, MPI u, ulong v);
+int mpi_sub(MPI w, MPI u, MPI v);
+int mpi_subm(MPI w, MPI u, MPI v, MPI m);
+
+/*-- mpi-mul.c --*/
+int mpi_mul_ui(MPI w, MPI u, ulong v);
+int mpi_mul_2exp(MPI w, MPI u, ulong cnt);
+int mpi_mul(MPI w, MPI u, MPI v);
+int mpi_mulm(MPI w, MPI u, MPI v, MPI m);
+
+/*-- mpi-div.c --*/
+ulong mpi_fdiv_r_ui(MPI rem, MPI dividend, ulong divisor);
+int mpi_fdiv_r(MPI rem, MPI dividend, MPI divisor);
+int mpi_fdiv_q(MPI quot, MPI dividend, MPI divisor);
+int mpi_fdiv_qr(MPI quot, MPI rem, MPI dividend, MPI divisor);
+int mpi_tdiv_r(MPI rem, MPI num, MPI den);
+int mpi_tdiv_qr(MPI quot, MPI rem, MPI num, MPI den);
+int mpi_tdiv_q_2exp(MPI w, MPI u, unsigned count);
+int mpi_divisible_ui(const MPI dividend, ulong divisor);
+
+/*-- mpi-gcd.c --*/
+int mpi_gcd(MPI g, const MPI a, const MPI b);
+
+/*-- mpi-pow.c --*/
+int mpi_pow(MPI w, MPI u, MPI v);
+int mpi_powm(MPI res, MPI base, MPI exp, MPI mod);
+
+/*-- mpi-mpow.c --*/
+int mpi_mulpowm(MPI res, MPI *basearray, MPI *exparray, MPI mod);
+
+/*-- mpi-cmp.c --*/
+int mpi_cmp_ui(MPI u, ulong v);
+int mpi_cmp(MPI u, MPI v);
+
+/*-- mpi-scan.c --*/
+int mpi_getbyte(MPI a, unsigned idx);
+void mpi_putbyte(MPI a, unsigned idx, int value);
+unsigned mpi_trailing_zeros(MPI a);
+
+/*-- mpi-bit.c --*/
+void mpi_normalize(MPI a);
+unsigned mpi_get_nbits(MPI a);
+int mpi_test_bit(MPI a, unsigned n);
+int mpi_set_bit(MPI a, unsigned n);
+int mpi_set_highbit(MPI a, unsigned n);
+void mpi_clear_highbit(MPI a, unsigned n);
+void mpi_clear_bit(MPI a, unsigned n);
+int mpi_rshift(MPI x, MPI a, unsigned n);
+
+/*-- mpi-inv.c --*/
+int mpi_invm(MPI x, MPI u, MPI v);
+
+#endif /*G10_MPI_H */

lib/Kconfig

@@ -276,4 +276,29 @@ config CORDIC
 	  so its calculations are in fixed point. Modules can select this
 	  when they require this function. Module will be called cordic.
 
+config MPILIB
+	tristate "Multiprecision maths library"
+	help
+	  Multiprecision maths library from GnuPG.
+	  It is used to implement RSA digital signature verification,
+	  which is used by IMA/EVM digital signature extension.
+
+config MPILIB_EXTRA
+	bool "Multiprecision maths library - additional sources"
+	depends on MPILIB
+	help
+	  Multiprecision maths library from GnuPG.
+	  It is used to implement RSA digital signature verification,
+	  which is used by IMA/EVM digital signature extension.
+	  This code in unnecessary for RSA digital signature verification,
+	  and can be compiled if needed.
+
+config DIGSIG
+	tristate "In-kernel signature checker"
+	depends on CRYPTO
+	select MPILIB
+	help
+	  Digital signature verification. Currently only RSA is supported.
+	  Implementation is done using GnuPG MPI library
+
 endmenu

lib/Makefile

@@ -115,6 +115,9 @@ obj-$(CONFIG_CPU_RMAP) += cpu_rmap.o
 
 obj-$(CONFIG_CORDIC) += cordic.o
 
+obj-$(CONFIG_MPILIB) += mpi/
+obj-$(CONFIG_DIGSIG) += digsig.o
+
 hostprogs-y	:= gen_crc32table
 clean-files	:= crc32table.h
 

lib/digsig.c

+/*
+ * Copyright (C) 2011 Nokia Corporation
+ * Copyright (C) 2011 Intel Corporation
+ *
+ * Author:
+ * Dmitry Kasatkin <dmitry.kasatkin@nokia.com>
+ *                 <dmitry.kasatkin@intel.com>
+ *
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, version 2 of the License.
+ *
+ * File: sign.c
+ *	implements signature (RSA) verification
+ *	pkcs decoding is based on LibTomCrypt code
+ */
+
+#define pr_fmt(fmt) KBUILD_MODNAME ": " fmt
+
+#include <linux/err.h>
+#include <linux/module.h>
+#include <linux/slab.h>
+#include <linux/key.h>
+#include <linux/crypto.h>
+#include <crypto/hash.h>
+#include <crypto/sha.h>
+#include <keys/user-type.h>
+#include <linux/mpi.h>
+#include <linux/digsig.h>
+
+static struct crypto_shash *shash;
+
+static int pkcs_1_v1_5_decode_emsa(const unsigned char *msg,
+			unsigned long  msglen,
+			unsigned long  modulus_bitlen,
+			unsigned char *out,
+			unsigned long *outlen,
+			int *is_valid)
+{
+	unsigned long modulus_len, ps_len, i;
+	int result;
+
+	/* default to invalid packet */
+	*is_valid = 0;
+
+	modulus_len = (modulus_bitlen >> 3) + (modulus_bitlen & 7 ? 1 : 0);
+
+	/* test message size */
+	if ((msglen > modulus_len) || (modulus_len < 11))
+		return -EINVAL;
+
+	/* separate encoded message */
+	if ((msg[0] != 0x00) || (msg[1] != (unsigned char)1)) {
+		result = -EINVAL;
+		goto bail;
+	}
+
+	for (i = 2; i < modulus_len - 1; i++)
+		if (msg[i] != 0xFF)
+			break;
+
+	/* separator check */
+	if (msg[i] != 0) {
+		/* There was no octet with hexadecimal value 0x00
+		to separate ps from m. */
+		result = -EINVAL;
+		goto bail;
+	}
+
+	ps_len = i - 2;
+
+	if (*outlen < (msglen - (2 + ps_len + 1))) {
+		*outlen = msglen - (2 + ps_len + 1);
+		result = -EOVERFLOW;
+		goto bail;
+	}
+
+	*outlen = (msglen - (2 + ps_len + 1));
+	memcpy(out, &msg[2 + ps_len + 1], *outlen);
+
+	/* valid packet */
+	*is_valid = 1;
+	result    = 0;
+bail:
+	return result;
+}
+
+/*
+ * RSA Signature verification with public key
+ */
+static int digsig_verify_rsa(struct key *key,
+		    const char *sig, int siglen,
+		       const char *h, int hlen)
+{
+	int err = -EINVAL;
+	unsigned long len;
+	unsigned long mlen, mblen;
+	unsigned nret, l;
+	int valid, head, i;
+	unsigned char *out1 = NULL, *out2 = NULL;
+	MPI in = NULL, res = NULL, pkey[2];
+	uint8_t *p, *datap, *endp;
+	struct user_key_payload *ukp;
+	struct pubkey_hdr *pkh;
+
+	down_read(&key->sem);
+	ukp = key->payload.data;
+	pkh = (struct pubkey_hdr *)ukp->data;
+
+	if (pkh->version != 1)
+		goto err1;
+
+	if (pkh->algo != PUBKEY_ALGO_RSA)
+		goto err1;
+
+	if (pkh->nmpi != 2)
+		goto err1;
+
+	datap = pkh->mpi;
+	endp = datap + ukp->datalen;
+
+	for (i = 0; i < pkh->nmpi; i++) {
+		unsigned int remaining = endp - datap;
+		pkey[i] = mpi_read_from_buffer(datap, &remaining);
+		datap += remaining;
+	}
+
+	mblen = mpi_get_nbits(pkey[0]);
+	mlen = (mblen + 7)/8;
+
+	err = -ENOMEM;
+
+	out1 = kzalloc(mlen, GFP_KERNEL);
+	if (!out1)
+		goto err;
+
+	out2 = kzalloc(mlen, GFP_KERNEL);
+	if (!out2)
+		goto err;
+
+	nret = siglen;
+	in = mpi_read_from_buffer(sig, &nret);
+	if (!in)
+		goto err;
+
+	res = mpi_alloc(mpi_get_nlimbs(in) * 2);
+	if (!res)
+		goto err;
+
+	err = mpi_powm(res, in, pkey[1], pkey[0]);
+	if (err)
+		goto err;
+
+	if (mpi_get_nlimbs(res) * BYTES_PER_MPI_LIMB > mlen) {
+		err = -EINVAL;
+		goto err;
+	}
+
+	p = mpi_get_buffer(res, &l, NULL);
+	if (!p) {
+		err = -EINVAL;
+		goto err;
+	}
+
+	len = mlen;
+	head = len - l;
+	memset(out1, 0, head);
+	memcpy(out1 + head, p, l);
+
+	err = -EINVAL;
+	pkcs_1_v1_5_decode_emsa(out1, len, mblen, out2, &len, &valid);
+
+	if (valid && len == hlen)
+		err = memcmp(out2, h, hlen);
+
+err:
+	mpi_free(in);
+	mpi_free(res);
+	kfree(out1);
+	kfree(out2);
+	mpi_free(pkey[0]);
+	mpi_free(pkey[1]);
+err1:
+	up_read(&key->sem);
+
+	return err;
+}
+
+/**
+ * digsig_verify() - digital signature verification with public key
+ * @keyring:	keyring to search key in
+ * @sig:	digital signature
+ * @sigen:	length of the signature
+ * @data:	data
+ * @datalen:	length of the data
+ * @return:	0 on success, -EINVAL otherwise
+ *
+ * Verifies data integrity against digital signature.
+ * Currently only RSA is supported.
+ * Normally hash of the content is used as a data for this function.
+ *
+ */
+int digsig_verify(struct key *keyring, const char *sig, int siglen,
+						const char *data, int datalen)
+{
+	int err = -ENOMEM;
+	struct signature_hdr *sh = (struct signature_hdr *)sig;
+	struct shash_desc *desc = NULL;
+	unsigned char hash[SHA1_DIGEST_SIZE];
+	struct key *key;
+	char name[20];
+
+	if (siglen < sizeof(*sh) + 2)
+		return -EINVAL;
+
+	if (sh->algo != PUBKEY_ALGO_RSA)
+		return -ENOTSUPP;
+
+	sprintf(name, "%llX", __be64_to_cpup((uint64_t *)sh->keyid));
+
+	if (keyring) {
+		/* search in specific keyring */
+		key_ref_t kref;
+		kref = keyring_search(make_key_ref(keyring, 1UL),
+						&key_type_user, name);
+		if (IS_ERR(kref))
+			key = ERR_PTR(PTR_ERR(kref));
+		else
+			key = key_ref_to_ptr(kref);
+	} else {
+		key = request_key(&key_type_user, name, NULL);
+	}
+	if (IS_ERR(key)) {
+		pr_err("key not found, id: %s\n", name);
+		return PTR_ERR(key);
+	}
+
+	desc = kzalloc(sizeof(*desc) + crypto_shash_descsize(shash),
+		       GFP_KERNEL);
+	if (!desc)
+		goto err;
+
+	desc->tfm = shash;
+	desc->flags = CRYPTO_TFM_REQ_MAY_SLEEP;
+
+	crypto_shash_init(desc);
+	crypto_shash_update(desc, data, datalen);
+	crypto_shash_update(desc, sig, sizeof(*sh));
+	crypto_shash_final(desc, hash);
+
+	kfree(desc);
+
+	/* pass signature mpis address */
+	err = digsig_verify_rsa(key, sig + sizeof(*sh), siglen - sizeof(*sh),
+			     hash, sizeof(hash));
+
+err:
+	key_put(key);
+
+	return err ? -EINVAL : 0;
+}
+EXPORT_SYMBOL_GPL(digsig_verify);
+
+static int __init digsig_init(void)
+{
+	shash = crypto_alloc_shash("sha1", 0, 0);
+	if (IS_ERR(shash)) {
+		pr_err("shash allocation failed\n");
+		return  PTR_ERR(shash);
+	}
+
+	return 0;
+
+}
+
+static void __exit digsig_cleanup(void)
+{
+	crypto_free_shash(shash);
+}
+
+module_init(digsig_init);
+module_exit(digsig_cleanup);
+
+MODULE_LICENSE("GPL");

lib/mpi/Makefile

+#
+# MPI multiprecision maths library (from gpg)
+#
+
+obj-$(CONFIG_MPILIB) = mpi.o
+
+mpi-y = \
+	generic_mpih-lshift.o		\
+	generic_mpih-mul1.o		\
+	generic_mpih-mul2.o		\
+	generic_mpih-mul3.o		\
+	generic_mpih-rshift.o		\
+	generic_mpih-sub1.o		\
+	generic_mpih-add1.o		\
+	mpicoder.o			\
+	mpi-bit.o			\
+	mpih-cmp.o			\
+	mpih-div.o			\
+	mpih-mul.o			\
+	mpi-pow.o			\
+	mpiutil.o
+
+mpi-$(CONFIG_MPILIB_EXTRA) += \
+	mpi-add.o			\
+	mpi-div.o			\
+	mpi-cmp.o			\
+	mpi-gcd.o			\
+	mpi-inline.o			\
+	mpi-inv.o			\
+	mpi-mpow.o			\
+	mpi-mul.o			\
+	mpi-scan.o

lib/mpi/generic_mpi-asm-defs.h

+/* This file defines some basic constants for the MPI machinery.  We
+ * need to define the types on a per-CPU basis, so it is done with
+ * this file here.  */
+#define BYTES_PER_MPI_LIMB  (SIZEOF_UNSIGNED_LONG)

lib/mpi/generic_mpih-add1.c

+/* mpihelp-add_1.c  -  MPI helper functions
+ * Copyright (C) 1994, 1996, 1997, 1998,
+ *               2000 Free Software Foundation, Inc.
+ *
+ * This file is part of GnuPG.
+ *
+ * GnuPG is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * GnuPG is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
+ *
+ * Note: This code is heavily based on the GNU MP Library.
+ *	 Actually it's the same code with only minor changes in the
+ *	 way the data is stored; this is to support the abstraction
+ *	 of an optional secure memory allocation which may be used
+ *	 to avoid revealing of sensitive data due to paging etc.
+ *	 The GNU MP Library itself is published under the LGPL;
+ *	 however I decided to publish this code under the plain GPL.
+ */
+
+#include "mpi-internal.h"
+#include "longlong.h"
+
+mpi_limb_t
+mpihelp_add_n(mpi_ptr_t res_ptr, mpi_ptr_t s1_ptr,
+	      mpi_ptr_t s2_ptr, mpi_size_t size)
+{
+	mpi_limb_t x, y, cy;
+	mpi_size_t j;
+
+	/* The loop counter and index J goes from -SIZE to -1.  This way
+	   the loop becomes faster.  */
+	j = -size;
+
+	/* Offset the base pointers to compensate for the negative indices. */
+	s1_ptr -= j;
+	s2_ptr -= j;
+	res_ptr -= j;
+
+	cy = 0;
+	do {
+		y = s2_ptr[j];
+		x = s1_ptr[j];
+		y += cy;	/* add previous carry to one addend */
+		cy = y < cy;	/* get out carry from that addition */
+		y += x;		/* add other addend */
+		cy += y < x;	/* get out carry from that add, combine */
+		res_ptr[j] = y;
+	} while (++j);
+
+	return cy;
+}

lib/mpi/generic_mpih-lshift.c

+/* mpihelp-lshift.c  -	MPI helper functions
+ * Copyright (C) 1994, 1996, 1998, 2001 Free Software Foundation, Inc.
+ *
+ * This file is part of GnuPG.
+ *
+ * GnuPG is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * GnuPG is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
+ *
+ * Note: This code is heavily based on the GNU MP Library.
+ *	 Actually it's the same code with only minor changes in the
+ *	 way the data is stored; this is to support the abstraction
+ *	 of an optional secure memory allocation which may be used
+ *	 to avoid revealing of sensitive data due to paging etc.
+ *	 The GNU MP Library itself is published under the LGPL;
+ *	 however I decided to publish this code under the plain GPL.
+ */
+
+#include "mpi-internal.h"
+
+/* Shift U (pointed to by UP and USIZE digits long) CNT bits to the left
+ * and store the USIZE least significant digits of the result at WP.
+ * Return the bits shifted out from the most significant digit.
+ *
+ * Argument constraints:
+ * 1. 0 < CNT < BITS_PER_MP_LIMB
+ * 2. If the result is to be written over the input, WP must be >= UP.
+ */
+
+mpi_limb_t
+mpihelp_lshift(mpi_ptr_t wp, mpi_ptr_t up, mpi_size_t usize, unsigned int cnt)
+{
+	mpi_limb_t high_limb, low_limb;
+	unsigned sh_1, sh_2;
+	mpi_size_t i;
+	mpi_limb_t retval;
+
+	sh_1 = cnt;
+	wp += 1;
+	sh_2 = BITS_PER_MPI_LIMB - sh_1;
+	i = usize - 1;
+	low_limb = up[i];
+	retval = low_limb >> sh_2;
+	high_limb = low_limb;
+	while (--i >= 0) {
+		low_limb = up[i];
+		wp[i] = (high_limb << sh_1) | (low_limb >> sh_2);
+		high_limb = low_limb;
+	}
+	wp[i] = high_limb << sh_1;
+
+	return retval;
+}

lib/mpi/generic_mpih-mul1.c

+/* mpihelp-mul_1.c  -  MPI helper functions
+ * Copyright (C) 1994, 1996, 1997, 1998, 2001 Free Software Foundation, Inc.
+ *
+ * This file is part of GnuPG.
+ *
+ * GnuPG is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * GnuPG is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
+ *
+ * Note: This code is heavily based on the GNU MP Library.
+ *	 Actually it's the same code with only minor changes in the
+ *	 way the data is stored; this is to support the abstraction
+ *	 of an optional secure memory allocation which may be used
+ *	 to avoid revealing of sensitive data due to paging etc.
+ *	 The GNU MP Library itself is published under the LGPL;
+ *	 however I decided to publish this code under the plain GPL.
+ */
+
+#include "mpi-internal.h"
+#include "longlong.h"
+
+mpi_limb_t
+mpihelp_mul_1(mpi_ptr_t res_ptr, mpi_ptr_t s1_ptr, mpi_size_t s1_size,
+	      mpi_limb_t s2_limb)
+{
+	mpi_limb_t cy_limb;
+	mpi_size_t j;
+	mpi_limb_t prod_high, prod_low;
+
+	/* The loop counter and index J goes from -S1_SIZE to -1.  This way
+	 * the loop becomes faster.  */
+	j = -s1_size;
+
+	/* Offset the base pointers to compensate for the negative indices.  */
+	s1_ptr -= j;
+	res_ptr -= j;
+
+	cy_limb = 0;
+	do {
+		umul_ppmm(prod_high, prod_low, s1_ptr[j], s2_limb);
+		prod_low += cy_limb;
+		cy_limb = (prod_low < cy_limb ? 1 : 0) + prod_high;
+		res_ptr[j] = prod_low;
+	} while (++j);
+
+	return cy_limb;
+}

lib/mpi/generic_mpih-mul2.c

+/* mpihelp-mul_2.c  -  MPI helper functions
+ * Copyright (C) 1994, 1996, 1997, 1998, 2001 Free Software Foundation, Inc.
+ *
+ * This file is part of GnuPG.
+ *
+ * GnuPG is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * GnuPG is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
+ *
+ * Note: This code is heavily based on the GNU MP Library.
+ *	 Actually it's the same code with only minor changes in the
+ *	 way the data is stored; this is to support the abstraction
+ *	 of an optional secure memory allocation which may be used
+ *	 to avoid revealing of sensitive data due to paging etc.
+ *	 The GNU MP Library itself is published under the LGPL;
+ *	 however I decided to publish this code under the plain GPL.
+ */
+
+#include "mpi-internal.h"
+#include "longlong.h"
+
+mpi_limb_t
+mpihelp_addmul_1(mpi_ptr_t res_ptr, mpi_ptr_t s1_ptr,
+		 mpi_size_t s1_size, mpi_limb_t s2_limb)
+{
+	mpi_limb_t cy_limb;
+	mpi_size_t j;
+	mpi_limb_t prod_high, prod_low;
+	mpi_limb_t x;
+
+	/* The loop counter and index J goes from -SIZE to -1.  This way
+	 * the loop becomes faster.  */
+	j = -s1_size;
+	res_ptr -= j;
+	s1_ptr -= j;
+
+	cy_limb = 0;
+	do {
+		umul_ppmm(prod_high, prod_low, s1_ptr[j], s2_limb);
+
+		prod_low += cy_limb;
+		cy_limb = (prod_low < cy_limb ? 1 : 0) + prod_high;
+
+		x = res_ptr[j];
+		prod_low = x + prod_low;
+		cy_limb += prod_low < x ? 1 : 0;
+		res_ptr[j] = prod_low;
+	} while (++j);
+	return cy_limb;
+}

lib/mpi/generic_mpih-mul3.c

+/* mpihelp-mul_3.c  -  MPI helper functions
+ * Copyright (C) 1994, 1996, 1997, 1998, 2001 Free Software Foundation, Inc.
+ *
+ * This file is part of GnuPG.
+ *
+ * GnuPG is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * GnuPG is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
+ *
+ * Note: This code is heavily based on the GNU MP Library.
+ *	 Actually it's the same code with only minor changes in the
+ *	 way the data is stored; this is to support the abstraction
+ *	 of an optional secure memory allocation which may be used
+ *	 to avoid revealing of sensitive data due to paging etc.
+ *	 The GNU MP Library itself is published under the LGPL;
+ *	 however I decided to publish this code under the plain GPL.
+ */
+
+#include "mpi-internal.h"
+#include "longlong.h"
+
+mpi_limb_t
+mpihelp_submul_1(mpi_ptr_t res_ptr, mpi_ptr_t s1_ptr,
+		 mpi_size_t s1_size, mpi_limb_t s2_limb)
+{
+	mpi_limb_t cy_limb;
+	mpi_size_t j;
+	mpi_limb_t prod_high, prod_low;
+	mpi_limb_t x;
+
+	/* The loop counter and index J goes from -SIZE to -1.  This way
+	 * the loop becomes faster.  */
+	j = -s1_size;
+	res_ptr -= j;
+	s1_ptr -= j;
+
+	cy_limb = 0;
+	do {
+		umul_ppmm(prod_high, prod_low, s1_ptr[j], s2_limb);
+
+		prod_low += cy_limb;
+		cy_limb = (prod_low < cy_limb ? 1 : 0) + prod_high;
+
+		x = res_ptr[j];
+		prod_low = x - prod_low;
+		cy_limb += prod_low > x ? 1 : 0;
+		res_ptr[j] = prod_low;
+	} while (++j);
+
+	return cy_limb;
+}

lib/mpi/generic_mpih-rshift.c

+/* mpih-rshift.c  -  MPI helper functions
+ * Copyright (C) 1994, 1996, 1998, 1999,
+ *               2000, 2001 Free Software Foundation, Inc.
+ *
+ * This file is part of GNUPG
+ *
+ * GNUPG is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * GNUPG is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
+ *
+ * Note: This code is heavily based on the GNU MP Library.
+ *	 Actually it's the same code with only minor changes in the
+ *	 way the data is stored; this is to support the abstraction
+ *	 of an optional secure memory allocation which may be used
+ *	 to avoid revealing of sensitive data due to paging etc.
+ *	 The GNU MP Library itself is published under the LGPL;
+ *	 however I decided to publish this code under the plain GPL.
+ */
+
+#include "mpi-internal.h"
+
+/* Shift U (pointed to by UP and USIZE limbs long) CNT bits to the right
+ * and store the USIZE least significant limbs of the result at WP.
+ * The bits shifted out to the right are returned.
+ *
+ * Argument constraints:
+ * 1. 0 < CNT < BITS_PER_MP_LIMB
+ * 2. If the result is to be written over the input, WP must be <= UP.
+ */
+
+mpi_limb_t
+mpihelp_rshift(mpi_ptr_t wp, mpi_ptr_t up, mpi_size_t usize, unsigned cnt)
+{
+	mpi_limb_t high_limb, low_limb;
+	unsigned sh_1, sh_2;
+	mpi_size_t i;
+	mpi_limb_t retval;
+
+	sh_1 = cnt;
+	wp -= 1;
+	sh_2 = BITS_PER_MPI_LIMB - sh_1;
+	high_limb = up[0];
+	retval = high_limb << sh_2;
+	low_limb = high_limb;
+	for (i = 1; i < usize; i++) {
+		high_limb = up[i];
+		wp[i] = (low_limb >> sh_1) | (high_limb << sh_2);
+		low_limb = high_limb;
+	}
+	wp[i] = low_limb >> sh_1;
+
+	return retval;
+}

lib/mpi/generic_mpih-sub1.c

+/* mpihelp-add_2.c  -  MPI helper functions
+ * Copyright (C) 1994, 1996, 1997, 1998, 2001 Free Software Foundation, Inc.
+ *
+ * This file is part of GnuPG.
+ *
+ * GnuPG is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * GnuPG is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
+ *
+ * Note: This code is heavily based on the GNU MP Library.
+ *	 Actually it's the same code with only minor changes in the
+ *	 way the data is stored; this is to support the abstraction
+ *	 of an optional secure memory allocation which may be used
+ *	 to avoid revealing of sensitive data due to paging etc.
+ *	 The GNU MP Library itself is published under the LGPL;
+ *	 however I decided to publish this code under the plain GPL.
+ */
+
+#include "mpi-internal.h"
+#include "longlong.h"
+
+mpi_limb_t
+mpihelp_sub_n(mpi_ptr_t res_ptr, mpi_ptr_t s1_ptr,
+	      mpi_ptr_t s2_ptr, mpi_size_t size)
+{
+	mpi_limb_t x, y, cy;
+	mpi_size_t j;
+
+	/* The loop counter and index J goes from -SIZE to -1.  This way
+	   the loop becomes faster.  */
+	j = -size;
+
+	/* Offset the base pointers to compensate for the negative indices.  */
+	s1_ptr -= j;
+	s2_ptr -= j;
+	res_ptr -= j;
+
+	cy = 0;
+	do {
+		y = s2_ptr[j];
+		x = s1_ptr[j];
+		y += cy;	/* add previous carry to subtrahend */
+		cy = y < cy;	/* get out carry from that addition */
+		y = x - y;	/* main subtract */
+		cy += y > x;	/* get out carry from the subtract, combine */
+		res_ptr[j] = y;
+	} while (++j);
+
+	return cy;
+}

lib/mpi/longlong.h

+/* longlong.h -- definitions for mixed size 32/64 bit arithmetic.
+ * Note: I added some stuff for use with gnupg
+ *
+ * Copyright (C) 1991, 1992, 1993, 1994, 1996, 1998,
+ *	2000, 2001, 2002, 2003 Free Software Foundation, Inc.
+ *
+ * This file is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU Library General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or (at your
+ * option) any later version.
+ *
+ * This file is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+ * or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Library General Public
+ * License for more details.
+ *
+ * You should have received a copy of the GNU Library General Public License
+ * along with this file; see the file COPYING.LIB.  If not, write to
+ * the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+ * MA 02111-1307, USA. */
+
+/* You have to define the following before including this file:
+ *
+ * UWtype -- An unsigned type, default type for operations (typically a "word")
+ * UHWtype -- An unsigned type, at least half the size of UWtype.
+ * UDWtype -- An unsigned type, at least twice as large a UWtype
+ * W_TYPE_SIZE -- size in bits of UWtype
+ *
+ * SItype, USItype -- Signed and unsigned 32 bit types.
+ * DItype, UDItype -- Signed and unsigned 64 bit types.
+ *
+ * On a 32 bit machine UWtype should typically be USItype;
+ * on a 64 bit machine, UWtype should typically be UDItype.
+*/
+
+#define __BITS4 (W_TYPE_SIZE / 4)
+#define __ll_B ((UWtype) 1 << (W_TYPE_SIZE / 2))
+#define __ll_lowpart(t) ((UWtype) (t) & (__ll_B - 1))
+#define __ll_highpart(t) ((UWtype) (t) >> (W_TYPE_SIZE / 2))
+
+/* This is used to make sure no undesirable sharing between different libraries
+	that use this file takes place.  */
+#ifndef __MPN
+#define __MPN(x) __##x
+#endif
+
+/* Define auxiliary asm macros.
+ *
+ * 1) umul_ppmm(high_prod, low_prod, multipler, multiplicand) multiplies two
+ * UWtype integers MULTIPLER and MULTIPLICAND, and generates a two UWtype
+ * word product in HIGH_PROD and LOW_PROD.
+ *
+ * 2) __umulsidi3(a,b) multiplies two UWtype integers A and B, and returns a
+ * UDWtype product.  This is just a variant of umul_ppmm.
+
+ * 3) udiv_qrnnd(quotient, remainder, high_numerator, low_numerator,
+ * denominator) divides a UDWtype, composed by the UWtype integers
+ * HIGH_NUMERATOR and LOW_NUMERATOR, by DENOMINATOR and places the quotient
+ * in QUOTIENT and the remainder in REMAINDER.	HIGH_NUMERATOR must be less
+ * than DENOMINATOR for correct operation.  If, in addition, the most
+ * significant bit of DENOMINATOR must be 1, then the pre-processor symbol
+ * UDIV_NEEDS_NORMALIZATION is defined to 1.
+ * 4) sdiv_qrnnd(quotient, remainder, high_numerator, low_numerator,
+ * denominator).  Like udiv_qrnnd but the numbers are signed.  The quotient
+ * is rounded towards 0.
+ *
+ * 5) count_leading_zeros(count, x) counts the number of zero-bits from the
+ * msb to the first non-zero bit in the UWtype X.  This is the number of
+ * steps X needs to be shifted left to set the msb.  Undefined for X == 0,
+ * unless the symbol COUNT_LEADING_ZEROS_0 is defined to some value.
+ *
+ * 6) count_trailing_zeros(count, x) like count_leading_zeros, but counts
+ * from the least significant end.
+ *
+ * 7) add_ssaaaa(high_sum, low_sum, high_addend_1, low_addend_1,
+ * high_addend_2, low_addend_2) adds two UWtype integers, composed by
+ * HIGH_ADDEND_1 and LOW_ADDEND_1, and HIGH_ADDEND_2 and LOW_ADDEND_2
+ * respectively.  The result is placed in HIGH_SUM and LOW_SUM.  Overflow
+ * (i.e. carry out) is not stored anywhere, and is lost.
+ *
+ * 8) sub_ddmmss(high_difference, low_difference, high_minuend, low_minuend,
+ * high_subtrahend, low_subtrahend) subtracts two two-word UWtype integers,
+ * composed by HIGH_MINUEND_1 and LOW_MINUEND_1, and HIGH_SUBTRAHEND_2 and
+ * LOW_SUBTRAHEND_2 respectively.  The result is placed in HIGH_DIFFERENCE
+ * and LOW_DIFFERENCE.	Overflow (i.e. carry out) is not stored anywhere,
+ * and is lost.
+ *
+ * If any of these macros are left undefined for a particular CPU,
+ * C macros are used.  */
+
+/* The CPUs come in alphabetical order below.
+ *
+ * Please add support for more CPUs here, or improve the current support
+ * for the CPUs below!	*/
+
+#if defined(__GNUC__) && !defined(NO_ASM)
+
+/* We sometimes need to clobber "cc" with gcc2, but that would not be
+	understood by gcc1.	Use cpp to avoid major code duplication.  */
+#if __GNUC__ < 2
+#define __CLOBBER_CC
+#define __AND_CLOBBER_CC
+#else /* __GNUC__ >= 2 */
+#define __CLOBBER_CC : "cc"
+#define __AND_CLOBBER_CC , "cc"
+#endif /* __GNUC__ < 2 */
+
+/***************************************
+	**************  A29K  *****************
+	***************************************/
+#if (defined(__a29k__) || defined(_AM29K)) && W_TYPE_SIZE == 32
+#define add_ssaaaa(sh, sl, ah, al, bh, bl) \
+	__asm__ ("add %1,%4,%5\n" \
+		"addc %0,%2,%3" \
+	: "=r" ((USItype)(sh)), \
+		"=&r" ((USItype)(sl)) \
+	: "%r" ((USItype)(ah)), \
+		"rI" ((USItype)(bh)), \
+		"%r" ((USItype)(al)), \
+		"rI" ((USItype)(bl)))
+#define sub_ddmmss(sh, sl, ah, al, bh, bl) \
+	__asm__ ("sub %1,%4,%5\n" \
+		"subc %0,%2,%3" \
+	: "=r" ((USItype)(sh)), \
+		"=&r" ((USItype)(sl)) \
+	: "r" ((USItype)(ah)), \
+		"rI" ((USItype)(bh)), \
+		"r" ((USItype)(al)), \
+		"rI" ((USItype)(bl)))
+#define umul_ppmm(xh, xl, m0, m1) \
+do { \
+		USItype __m0 = (m0), __m1 = (m1); \
+		__asm__ ("multiplu %0,%1,%2" \
+		: "=r" ((USItype)(xl)) \
+		: "r" (__m0), \
+			"r" (__m1)); \
+		__asm__ ("multmu %0,%1,%2" \
+		: "=r" ((USItype)(xh)) \
+		: "r" (__m0), \
+			"r" (__m1)); \
+} while (0)
+#define udiv_qrnnd(q, r, n1, n0, d) \
+	__asm__ ("dividu %0,%3,%4" \
+	: "=r" ((USItype)(q)), \
+		"=q" ((USItype)(r)) \
+	: "1" ((USItype)(n1)), \
+		"r" ((USItype)(n0)), \
+		"r" ((USItype)(d)))
+
+#define count_leading_zeros(count, x) \
+	__asm__ ("clz %0,%1" \
+	: "=r" ((USItype)(count)) \
+	: "r" ((USItype)(x)))
+#define COUNT_LEADING_ZEROS_0 32
+#endif /* __a29k__ */
+
+#if defined(__alpha) && W_TYPE_SIZE == 64
+#define umul_ppmm(ph, pl, m0, m1) \
+do { \
+		UDItype __m0 = (m0), __m1 = (m1); \
+		__asm__ ("umulh %r1,%2,%0" \
+		: "=r" ((UDItype) ph) \
+		: "%rJ" (__m0), \
+			"rI" (__m1)); \
+		(pl) = __m0 * __m1; \
+	} while (0)
+#define UMUL_TIME 46
+#ifndef LONGLONG_STANDALONE
+#define udiv_qrnnd(q, r, n1, n0, d) \
+do { UDItype __r; \
+	(q) = __udiv_qrnnd(&__r, (n1), (n0), (d)); \
+	(r) = __r; \
+} while (0)
+extern UDItype __udiv_qrnnd();
+#define UDIV_TIME 220
+#endif /* LONGLONG_STANDALONE */
+#endif /* __alpha */
+
+/***************************************
+	**************  ARM  ******************
+	***************************************/
+#if defined(__arm__) && W_TYPE_SIZE == 32
+#define add_ssaaaa(sh, sl, ah, al, bh, bl) \
+	__asm__ ("adds %1, %4, %5\n" \
+		"adc  %0, %2, %3" \
+	: "=r" ((USItype)(sh)), \
+		"=&r" ((USItype)(sl)) \
+	: "%r" ((USItype)(ah)), \
+		"rI" ((USItype)(bh)), \
+		"%r" ((USItype)(al)), \
+		"rI" ((USItype)(bl)))
+#define sub_ddmmss(sh, sl, ah, al, bh, bl) \
+	__asm__ ("subs %1, %4, %5\n" \
+		"sbc  %0, %2, %3" \
+	: "=r" ((USItype)(sh)), \
+		"=&r" ((USItype)(sl)) \
+	: "r" ((USItype)(ah)), \
+		"rI" ((USItype)(bh)), \
+		"r" ((USItype)(al)), \
+		"rI" ((USItype)(bl)))
+#if defined __ARM_ARCH_2__ || defined __ARM_ARCH_3__
+#define umul_ppmm(xh, xl, a, b) \
+	__asm__ ("%@ Inlined umul_ppmm\n" \
+		"mov	%|r0, %2, lsr #16		@ AAAA\n" \
+		"mov	%|r2, %3, lsr #16		@ BBBB\n" \
+		"bic	%|r1, %2, %|r0, lsl #16		@ aaaa\n" \
+		"bic	%0, %3, %|r2, lsl #16		@ bbbb\n" \
+		"mul	%1, %|r1, %|r2			@ aaaa * BBBB\n" \
+		"mul	%|r2, %|r0, %|r2		@ AAAA * BBBB\n" \
+		"mul	%|r1, %0, %|r1			@ aaaa * bbbb\n" \
+		"mul	%0, %|r0, %0			@ AAAA * bbbb\n" \
+		"adds	%|r0, %1, %0			@ central sum\n" \
+		"addcs	%|r2, %|r2, #65536\n" \
+		"adds	%1, %|r1, %|r0, lsl #16\n" \
+		"adc	%0, %|r2, %|r0, lsr #16" \
+	: "=&r" ((USItype)(xh)), \
+		"=r" ((USItype)(xl)) \
+	: "r" ((USItype)(a)), \
+		"r" ((USItype)(b)) \
+	: "r0", "r1", "r2")
+#else
+#define umul_ppmm(xh, xl, a, b) \
+	__asm__ ("%@ Inlined umul_ppmm\n" \
+		"umull %r1, %r0, %r2, %r3" \
+	: "=&r" ((USItype)(xh)), \
+			"=r" ((USItype)(xl)) \
+	: "r" ((USItype)(a)), \
+			"r" ((USItype)(b)) \
+	: "r0", "r1")
+#endif
+#define UMUL_TIME 20
+#define UDIV_TIME 100
+#endif /* __arm__ */
+
+/***************************************
+	**************  CLIPPER  **************
+	***************************************/
+#if defined(__clipper__) && W_TYPE_SIZE == 32
+#define umul_ppmm(w1, w0, u, v) \
+	({union {UDItype __ll; \
+		struct {USItype __l, __h; } __i; \
+	} __xx; \
+	__asm__ ("mulwux %2,%0" \
+	: "=r" (__xx.__ll) \
+	: "%0" ((USItype)(u)), \
+		"r" ((USItype)(v))); \
+	(w1) = __xx.__i.__h; (w0) = __xx.__i.__l; })
+#define smul_ppmm(w1, w0, u, v) \
+	({union {DItype __ll; \
+		struct {SItype __l, __h; } __i; \
+	} __xx; \
+	__asm__ ("mulwx %2,%0" \
+	: "=r" (__xx.__ll) \
+	: "%0" ((SItype)(u)), \
+		"r" ((SItype)(v))); \
+	(w1) = __xx.__i.__h; (w0) = __xx.__i.__l; })
+#define __umulsidi3(u, v) \
+	({UDItype __w; \
+	__asm__ ("mulwux %2,%0" \
+	: "=r" (__w) \
+	: "%0" ((USItype)(u)), \
+		"r" ((USItype)(v))); \
+	__w; })
+#endif /* __clipper__ */
+
+/***************************************
+	**************  GMICRO  ***************
+	***************************************/
+#if defined(__gmicro__) && W_TYPE_SIZE == 32
+#define add_ssaaaa(sh, sl, ah, al, bh, bl) \
+	__asm__ ("add.w %5,%1\n" \
+		"addx %3,%0" \
+	: "=g" ((USItype)(sh)), \
+		"=&g" ((USItype)(sl)) \
+	: "%0" ((USItype)(ah)), \
+		"g" ((USItype)(bh)), \
+		"%1" ((USItype)(al)), \
+		"g" ((USItype)(bl)))
+#define sub_ddmmss(sh, sl, ah, al, bh, bl) \
+	__asm__ ("sub.w %5,%1\n" \
+		"subx %3,%0" \
+	: "=g" ((USItype)(sh)), \
+		"=&g" ((USItype)(sl)) \
+	: "0" ((USItype)(ah)), \
+		"g" ((USItype)(bh)), \
+		"1" ((USItype)(al)), \
+		"g" ((USItype)(bl)))
+#define umul_ppmm(ph, pl, m0, m1) \
+	__asm__ ("mulx %3,%0,%1" \
+	: "=g" ((USItype)(ph)), \
+		"=r" ((USItype)(pl)) \
+	: "%0" ((USItype)(m0)), \
+		"g" ((USItype)(m1)))
+#define udiv_qrnnd(q, r, nh, nl, d) \
+	__asm__ ("divx %4,%0,%1" \
+	: "=g" ((USItype)(q)), \
+		"=r" ((USItype)(r)) \
+	: "1" ((USItype)(nh)), \
+		"0" ((USItype)(nl)), \
+		"g" ((USItype)(d)))
+#define count_leading_zeros(count, x) \
+	__asm__ ("bsch/1 %1,%0" \
+	: "=g" (count) \
+	: "g" ((USItype)(x)), \
+	     "0" ((USItype)0))
+#endif
+
+/***************************************
+	**************  HPPA  *****************
+	***************************************/
+#if defined(__hppa) && W_TYPE_SIZE == 32
+#define add_ssaaaa(sh, sl, ah, al, bh, bl) \
+	__asm__ ("add %4,%5,%1\n" \
+		   "addc %2,%3,%0" \
+	: "=r" ((USItype)(sh)), \
+	     "=&r" ((USItype)(sl)) \
+	: "%rM" ((USItype)(ah)), \
+	     "rM" ((USItype)(bh)), \
+	     "%rM" ((USItype)(al)), \
+	     "rM" ((USItype)(bl)))
+#define sub_ddmmss(sh, sl, ah, al, bh, bl) \
+	__asm__ ("sub %4,%5,%1\n" \
+	   "subb %2,%3,%0" \
+	: "=r" ((USItype)(sh)), \
+	     "=&r" ((USItype)(sl)) \
+	: "rM" ((USItype)(ah)), \
+	     "rM" ((USItype)(bh)), \
+	     "rM" ((USItype)(al)), \
+	     "rM" ((USItype)(bl)))
+#if defined(_PA_RISC1_1)
+#define umul_ppmm(wh, wl, u, v) \
+do { \
+	union {UDItype __ll; \
+	struct {USItype __h, __l; } __i; \
+	} __xx; \
+	__asm__ ("xmpyu %1,%2,%0" \
+	: "=*f" (__xx.__ll) \
+	: "*f" ((USItype)(u)), \
+	       "*f" ((USItype)(v))); \
+	(wh) = __xx.__i.__h; \
+	(wl) = __xx.__i.__l; \
+} while (0)
+#define UMUL_TIME 8
+#define UDIV_TIME 60
+#else
+#define UMUL_TIME 40
+#define UDIV_TIME 80
+#endif
+#ifndef LONGLONG_STANDALONE
+#define udiv_qrnnd(q, r, n1, n0, d) \
+do { USItype __r; \
+	(q) = __udiv_qrnnd(&__r, (n1), (n0), (d)); \
+	(r) = __r; \
+} while (0)
+extern USItype __udiv_qrnnd();
+#endif /* LONGLONG_STANDALONE */
+#define count_leading_zeros(count, x) \
+do { \
+	USItype __tmp; \
+	__asm__ ( \
+	"ldi             1,%0\n" \
+	"extru,=	%1,15,16,%%r0  ; Bits 31..16 zero?\n" \
+	"extru,tr	%1,15,16,%1    ; No.  Shift down, skip add.\n" \
+	"ldo		16(%0),%0      ; Yes.	Perform add.\n" \
+	"extru,=	%1,23,8,%%r0   ; Bits 15..8 zero?\n" \
+	"extru,tr	%1,23,8,%1     ; No.  Shift down, skip add.\n" \
+	"ldo		8(%0),%0       ; Yes.	Perform add.\n" \
+	"extru,=	%1,27,4,%%r0   ; Bits 7..4 zero?\n" \
+	"extru,tr	%1,27,4,%1     ; No.  Shift down, skip add.\n" \
+	"ldo		4(%0),%0       ; Yes.	Perform add.\n" \
+	"extru,=	%1,29,2,%%r0   ; Bits 3..2 zero?\n" \
+	"extru,tr	%1,29,2,%1     ; No.  Shift down, skip add.\n" \
+	"ldo		2(%0),%0       ; Yes.	Perform add.\n" \
+	"extru		%1,30,1,%1     ; Extract bit 1.\n" \
+	"sub		%0,%1,%0       ; Subtract it.              " \
+	: "=r" (count), "=r" (__tmp) : "1" (x)); \
+} while (0)
+#endif /* hppa */
+
+/***************************************
+	**************  I370  *****************
+	***************************************/
+#if (defined(__i370__) || defined(__mvs__)) && W_TYPE_SIZE == 32
+#define umul_ppmm(xh, xl, m0, m1) \
+do { \
+	union {UDItype __ll; \
+	   struct {USItype __h, __l; } __i; \
+	} __xx; \
+	USItype __m0 = (m0), __m1 = (m1); \
+	__asm__ ("mr %0,%3" \
+	: "=r" (__xx.__i.__h), \
+	       "=r" (__xx.__i.__l) \
+	: "%1" (__m0), \
+	       "r" (__m1)); \
+	(xh) = __xx.__i.__h; (xl) = __xx.__i.__l; \
+	(xh) += ((((SItype) __m0 >> 31) & __m1) \
+	     + (((SItype) __m1 >> 31) & __m0)); \
+} while (0)
+#define smul_ppmm(xh, xl, m0, m1) \
+do { \
+	union {DItype __ll; \
+	   struct {USItype __h, __l; } __i; \
+	} __xx; \
+	__asm__ ("mr %0,%3" \
+	: "=r" (__xx.__i.__h), \
+	       "=r" (__xx.__i.__l) \
+	: "%1" (m0), \
+	       "r" (m1)); \
+	(xh) = __xx.__i.__h; (xl) = __xx.__i.__l; \
+} while (0)
+#define sdiv_qrnnd(q, r, n1, n0, d) \
+do { \
+	union {DItype __ll; \
+	   struct {USItype __h, __l; } __i; \
+	} __xx; \
+	__xx.__i.__h = n1; __xx.__i.__l = n0; \
+	__asm__ ("dr %0,%2" \
+	: "=r" (__xx.__ll) \
+	: "0" (__xx.__ll), "r" (d)); \
+	(q) = __xx.__i.__l; (r) = __xx.__i.__h; \
+} while (0)
+#endif
+
+/***************************************
+	**************  I386  *****************
+	***************************************/
+#undef __i386__
+#if (defined(__i386__) || defined(__i486__)) && W_TYPE_SIZE == 32
+#define add_ssaaaa(sh, sl, ah, al, bh, bl) \
+	__asm__ ("addl %5,%1\n" \
+	   "adcl %3,%0" \
+	: "=r" ((USItype)(sh)), \
+	     "=&r" ((USItype)(sl)) \
+	: "%0" ((USItype)(ah)), \
+	     "g" ((USItype)(bh)), \
+	     "%1" ((USItype)(al)), \
+	     "g" ((USItype)(bl)))
+#define sub_ddmmss(sh, sl, ah, al, bh, bl) \
+	__asm__ ("subl %5,%1\n" \
+	   "sbbl %3,%0" \
+	: "=r" ((USItype)(sh)), \
+	     "=&r" ((USItype)(sl)) \
+	: "0" ((USItype)(ah)), \
+	     "g" ((USItype)(bh)), \
+	     "1" ((USItype)(al)), \
+	     "g" ((USItype)(bl)))
+#define umul_ppmm(w1, w0, u, v) \
+	__asm__ ("mull %3" \
+	: "=a" ((USItype)(w0)), \
+	     "=d" ((USItype)(w1)) \
+	: "%0" ((USItype)(u)), \
+	     "rm" ((USItype)(v)))
+#define udiv_qrnnd(q, r, n1, n0, d) \
+	__asm__ ("divl %4" \
+	: "=a" ((USItype)(q)), \
+	     "=d" ((USItype)(r)) \
+	: "0" ((USItype)(n0)), \
+	     "1" ((USItype)(n1)), \
+	     "rm" ((USItype)(d)))
+#define count_leading_zeros(count, x) \
+do { \
+	USItype __cbtmp; \
+	__asm__ ("bsrl %1,%0" \
+	: "=r" (__cbtmp) : "rm" ((USItype)(x))); \
+	(count) = __cbtmp ^ 31; \
+} while (0)
+#define count_trailing_zeros(count, x) \
+	__asm__ ("bsfl %1,%0" : "=r" (count) : "rm" ((USItype)(x)))
+#ifndef UMUL_TIME
+#define UMUL_TIME 40
+#endif
+#ifndef UDIV_TIME
+#define UDIV_TIME 40
+#endif
+#endif /* 80x86 */
+
+/***************************************
+	**************  I860  *****************
+	***************************************/
+#if defined(__i860__) && W_TYPE_SIZE == 32
+#define rshift_rhlc(r, h, l, c) \
+	__asm__ ("shr %3,r0,r0\n" \
+	"shrd %1,%2,%0" \
+	   "=r" (r) : "r" (h), "r" (l), "rn" (c))
+#endif /* i860 */
+
+/***************************************
+	**************  I960  *****************
+	***************************************/
+#if defined(__i960__) && W_TYPE_SIZE == 32
+#define add_ssaaaa(sh, sl, ah, al, bh, bl) \
+	__asm__ ("cmpo 1,0\n" \
+	"addc %5,%4,%1\n" \
+	"addc %3,%2,%0" \
+	: "=r" ((USItype)(sh)), \
+	     "=&r" ((USItype)(sl)) \
+	: "%dI" ((USItype)(ah)), \
+	     "dI" ((USItype)(bh)), \
+	     "%dI" ((USItype)(al)), \
+	     "dI" ((USItype)(bl)))
+#define sub_ddmmss(sh, sl, ah, al, bh, bl) \
+	__asm__ ("cmpo 0,0\n" \
+	"subc %5,%4,%1\n" \
+	"subc %3,%2,%0" \
+	: "=r" ((USItype)(sh)), \
+	     "=&r" ((USItype)(sl)) \
+	: "dI" ((USItype)(ah)), \
+	     "dI" ((USItype)(bh)), \
+	     "dI" ((USItype)(al)), \
+	     "dI" ((USItype)(bl)))
+#define umul_ppmm(w1, w0, u, v) \
+	({union {UDItype __ll; \
+	   struct {USItype __l, __h; } __i; \
+	} __xx; \
+	__asm__ ("emul        %2,%1,%0" \
+	: "=d" (__xx.__ll) \
+	: "%dI" ((USItype)(u)), \
+	     "dI" ((USItype)(v))); \
+	(w1) = __xx.__i.__h; (w0) = __xx.__i.__l; })
+#define __umulsidi3(u, v) \
+	({UDItype __w; \
+	__asm__ ("emul      %2,%1,%0" \
+	: "=d" (__w) \
+	: "%dI" ((USItype)(u)), \
+	       "dI" ((USItype)(v))); \
+	__w; })
+#define udiv_qrnnd(q, r, nh, nl, d) \
+do { \
+	union {UDItype __ll; \
+	   struct {USItype __l, __h; } __i; \
+	} __nn; \
+	__nn.__i.__h = (nh); __nn.__i.__l = (nl); \
+	__asm__ ("ediv %d,%n,%0" \
+	: "=d" (__rq.__ll) \
+	: "dI" (__nn.__ll), \
+	     "dI" ((USItype)(d))); \
+	(r) = __rq.__i.__l; (q) = __rq.__i.__h; \
+} while (0)
+#define count_leading_zeros(count, x) \
+do { \
+	USItype __cbtmp; \
+	__asm__ ("scanbit %1,%0" \
+	: "=r" (__cbtmp) \
+	: "r" ((USItype)(x))); \
+	(count) = __cbtmp ^ 31; \
+} while (0)
+#define COUNT_LEADING_ZEROS_0 (-32)	/* sic */
+#if defined(__i960mx)		/* what is the proper symbol to test??? */
+#define rshift_rhlc(r, h, l, c) \
+do { \
+	union {UDItype __ll; \
+	   struct {USItype __l, __h; } __i; \
+	} __nn; \
+	__nn.__i.__h = (h); __nn.__i.__l = (l); \
+	__asm__ ("shre %2,%1,%0" \
+	: "=d" (r) : "dI" (__nn.__ll), "dI" (c)); \
+}
+#endif /* i960mx */
+#endif /* i960 */
+
+/***************************************
+	**************  68000	****************
+	***************************************/
+#if (defined(__mc68000__) || defined(__mc68020__) || defined(__NeXT__) || defined(mc68020)) && W_TYPE_SIZE == 32
+#define add_ssaaaa(sh, sl, ah, al, bh, bl) \
+	__asm__ ("add%.l %5,%1\n" \
+	   "addx%.l %3,%0" \
+	: "=d" ((USItype)(sh)), \
+	     "=&d" ((USItype)(sl)) \
+	: "%0" ((USItype)(ah)), \
+	     "d" ((USItype)(bh)), \
+	     "%1" ((USItype)(al)), \
+	     "g" ((USItype)(bl)))
+#define sub_ddmmss(sh, sl, ah, al, bh, bl) \
+	__asm__ ("sub%.l %5,%1\n" \
+	   "subx%.l %3,%0" \
+	: "=d" ((USItype)(sh)), \
+	     "=&d" ((USItype)(sl)) \
+	: "0" ((USItype)(ah)), \
+	     "d" ((USItype)(bh)), \
+	     "1" ((USItype)(al)), \
+	     "g" ((USItype)(bl)))
+#if (defined(__mc68020__) || defined(__NeXT__) || defined(mc68020))
+#define umul_ppmm(w1, w0, u, v) \
+	__asm__ ("mulu%.l %3,%1:%0" \
+	: "=d" ((USItype)(w0)), \
+	     "=d" ((USItype)(w1)) \
+	: "%0" ((USItype)(u)), \
+	     "dmi" ((USItype)(v)))
+#define UMUL_TIME 45
+#define udiv_qrnnd(q, r, n1, n0, d) \
+	__asm__ ("divu%.l %4,%1:%0" \
+	: "=d" ((USItype)(q)), \
+	     "=d" ((USItype)(r)) \
+	: "0" ((USItype)(n0)), \
+	     "1" ((USItype)(n1)), \
+	     "dmi" ((USItype)(d)))
+#define UDIV_TIME 90
+#define sdiv_qrnnd(q, r, n1, n0, d) \
+	__asm__ ("divs%.l %4,%1:%0" \
+	: "=d" ((USItype)(q)), \
+	     "=d" ((USItype)(r)) \
+	: "0" ((USItype)(n0)), \
+	     "1" ((USItype)(n1)), \
+	     "dmi" ((USItype)(d)))
+#define count_leading_zeros(count, x) \
+	__asm__ ("bfffo %1{%b2:%b2},%0" \
+	: "=d" ((USItype)(count)) \
+	: "od" ((USItype)(x)), "n" (0))
+#define COUNT_LEADING_ZEROS_0 32
+#else /* not mc68020 */
+#define umul_ppmm(xh, xl, a, b) \
+do { USItype __umul_tmp1, __umul_tmp2; \
+	__asm__ ("| Inlined umul_ppmm\n" \
+	"move%.l %5,%3\n" \
+	"move%.l %2,%0\n" \
+	"move%.w %3,%1\n" \
+	"swap	%3\n" \
+	"swap	%0\n" \
+	"mulu	%2,%1\n" \
+	"mulu	%3,%0\n" \
+	"mulu	%2,%3\n" \
+	"swap	%2\n" \
+	"mulu	%5,%2\n" \
+	"add%.l	%3,%2\n" \
+	"jcc	1f\n" \
+	"add%.l	%#0x10000,%0\n" \
+	"1:	move%.l %2,%3\n" \
+	"clr%.w	%2\n" \
+	"swap	%2\n" \
+	"swap	%3\n" \
+	"clr%.w	%3\n" \
+	"add%.l	%3,%1\n" \
+	"addx%.l %2,%0\n" \
+	"| End inlined umul_ppmm" \
+	: "=&d" ((USItype)(xh)), "=&d" ((USItype)(xl)), \
+		"=d" (__umul_tmp1), "=&d" (__umul_tmp2) \
+	: "%2" ((USItype)(a)), "d" ((USItype)(b))); \
+} while (0)
+#define UMUL_TIME 100
+#define UDIV_TIME 400
+#endif /* not mc68020 */
+#endif /* mc68000 */
+
+/***************************************
+	**************  88000	****************
+	***************************************/
+#if defined(__m88000__) && W_TYPE_SIZE == 32
+#define add_ssaaaa(sh, sl, ah, al, bh, bl) \
+	__asm__ ("addu.co %1,%r4,%r5\n" \
+	   "addu.ci %0,%r2,%r3" \
+	: "=r" ((USItype)(sh)), \
+	     "=&r" ((USItype)(sl)) \
+	: "%rJ" ((USItype)(ah)), \
+	     "rJ" ((USItype)(bh)), \
+	     "%rJ" ((USItype)(al)), \
+	     "rJ" ((USItype)(bl)))
+#define sub_ddmmss(sh, sl, ah, al, bh, bl) \
+	__asm__ ("subu.co %1,%r4,%r5\n" \
+	   "subu.ci %0,%r2,%r3" \
+	: "=r" ((USItype)(sh)), \
+	     "=&r" ((USItype)(sl)) \
+	: "rJ" ((USItype)(ah)), \
+	     "rJ" ((USItype)(bh)), \
+	     "rJ" ((USItype)(al)), \
+	     "rJ" ((USItype)(bl)))
+#define count_leading_zeros(count, x) \
+do { \
+	USItype __cbtmp; \
+	__asm__ ("ff1 %0,%1" \
+	: "=r" (__cbtmp) \
+	: "r" ((USItype)(x))); \
+	(count) = __cbtmp ^ 31; \
+} while (0)
+#define COUNT_LEADING_ZEROS_0 63	/* sic */
+#if defined(__m88110__)
+#define umul_ppmm(wh, wl, u, v) \
+do { \
+	union {UDItype __ll; \
+	   struct {USItype __h, __l; } __i; \
+	} __x; \
+	__asm__ ("mulu.d %0,%1,%2" : "=r" (__x.__ll) : "r" (u), "r" (v)); \
+	(wh) = __x.__i.__h; \
+	(wl) = __x.__i.__l; \
+} while (0)
+#define udiv_qrnnd(q, r, n1, n0, d) \
+	({union {UDItype __ll; \
+	   struct {USItype __h, __l; } __i; \
+	} __x, __q; \
+	__x.__i.__h = (n1); __x.__i.__l = (n0); \
+	__asm__ ("divu.d %0,%1,%2" \
+	: "=r" (__q.__ll) : "r" (__x.__ll), "r" (d)); \
+	(r) = (n0) - __q.__l * (d); (q) = __q.__l; })
+#define UMUL_TIME 5
+#define UDIV_TIME 25
+#else
+#define UMUL_TIME 17
+#define UDIV_TIME 150
+#endif /* __m88110__ */
+#endif /* __m88000__ */
+
+/***************************************
+	**************  MIPS  *****************
+	***************************************/
+#if defined(__mips__) && W_TYPE_SIZE == 32
+#if __GNUC__ > 2 || __GNUC_MINOR__ >= 7
+#define umul_ppmm(w1, w0, u, v) \
+	__asm__ ("multu %2,%3" \
+	: "=l" ((USItype)(w0)), \
+	     "=h" ((USItype)(w1)) \
+	: "d" ((USItype)(u)), \
+	     "d" ((USItype)(v)))
+#else
+#define umul_ppmm(w1, w0, u, v) \
+	__asm__ ("multu %2,%3\n" \
+	   "mflo %0\n" \
+	   "mfhi %1" \
+	: "=d" ((USItype)(w0)), \
+	     "=d" ((USItype)(w1)) \
+	: "d" ((USItype)(u)), \
+	     "d" ((USItype)(v)))
+#endif
+#define UMUL_TIME 10
+#define UDIV_TIME 100
+#endif /* __mips__ */
+
+/***************************************
+	**************  MIPS/64  **************
+	***************************************/
+#if (defined(__mips) && __mips >= 3) && W_TYPE_SIZE == 64
+#if __GNUC__ > 2 || __GNUC_MINOR__ >= 7
+#define umul_ppmm(w1, w0, u, v) \
+	__asm__ ("dmultu %2,%3" \
+	: "=l" ((UDItype)(w0)), \
+	     "=h" ((UDItype)(w1)) \
+	: "d" ((UDItype)(u)), \
+	     "d" ((UDItype)(v)))
+#else
+#define umul_ppmm(w1, w0, u, v) \
+	__asm__ ("dmultu %2,%3\n" \
+	   "mflo %0\n" \
+	   "mfhi %1" \
+	: "=d" ((UDItype)(w0)), \
+	     "=d" ((UDItype)(w1)) \
+	: "d" ((UDItype)(u)), \
+	     "d" ((UDItype)(v)))
+#endif
+#define UMUL_TIME 20
+#define UDIV_TIME 140
+#endif /* __mips__ */
+
+/***************************************
+	**************  32000	****************
+	***************************************/
+#if defined(__ns32000__) && W_TYPE_SIZE == 32
+#define umul_ppmm(w1, w0, u, v) \
+	({union {UDItype __ll; \
+	   struct {USItype __l, __h; } __i; \
+	} __xx; \
+	__asm__ ("meid %2,%0" \
+	: "=g" (__xx.__ll) \
+	: "%0" ((USItype)(u)), \
+	     "g" ((USItype)(v))); \
+	(w1) = __xx.__i.__h; (w0) = __xx.__i.__l; })
+#define __umulsidi3(u, v) \
+	({UDItype __w; \
+	__asm__ ("meid %2,%0" \
+	: "=g" (__w) \
+	: "%0" ((USItype)(u)), \
+	       "g" ((USItype)(v))); \
+	__w; })
+#define udiv_qrnnd(q, r, n1, n0, d) \
+	({union {UDItype __ll; \
+	   struct {USItype __l, __h; } __i; \
+	} __xx; \
+	__xx.__i.__h = (n1); __xx.__i.__l = (n0); \
+	__asm__ ("deid %2,%0" \
+	: "=g" (__xx.__ll) \
+	: "0" (__xx.__ll), \
+	     "g" ((USItype)(d))); \
+	(r) = __xx.__i.__l; (q) = __xx.__i.__h; })
+#define count_trailing_zeros(count, x) \
+do { \
+	__asm__("ffsd      %2,%0" \
+	: "=r"((USItype) (count)) \
+	: "0"((USItype) 0), "r"((USItype) (x))); \
+	} while (0)
+#endif /* __ns32000__ */
+
+/***************************************
+	**************  PPC  ******************
+	***************************************/
+#if (defined(_ARCH_PPC) || defined(_IBMR2)) && W_TYPE_SIZE == 32
+#define add_ssaaaa(sh, sl, ah, al, bh, bl) \
+do { \
+	if (__builtin_constant_p(bh) && (bh) == 0) \
+		__asm__ ("{a%I4|add%I4c} %1,%3,%4\n\t{aze|addze} %0,%2" \
+		: "=r" ((USItype)(sh)), \
+		"=&r" ((USItype)(sl)) \
+		: "%r" ((USItype)(ah)), \
+		"%r" ((USItype)(al)), \
+		"rI" ((USItype)(bl))); \
+	else if (__builtin_constant_p(bh) && (bh) == ~(USItype) 0) \
+		__asm__ ("{a%I4|add%I4c} %1,%3,%4\n\t{ame|addme} %0,%2" \
+		: "=r" ((USItype)(sh)), \
+		"=&r" ((USItype)(sl)) \
+		: "%r" ((USItype)(ah)), \
+		"%r" ((USItype)(al)), \
+		"rI" ((USItype)(bl))); \
+	else \
+		__asm__ ("{a%I5|add%I5c} %1,%4,%5\n\t{ae|adde} %0,%2,%3" \
+		: "=r" ((USItype)(sh)), \
+		"=&r" ((USItype)(sl)) \
+		: "%r" ((USItype)(ah)), \
+		"r" ((USItype)(bh)), \
+		"%r" ((USItype)(al)), \
+		"rI" ((USItype)(bl))); \
+} while (0)
+#define sub_ddmmss(sh, sl, ah, al, bh, bl) \
+do { \
+	if (__builtin_constant_p(ah) && (ah) == 0) \
+		__asm__ ("{sf%I3|subf%I3c} %1,%4,%3\n\t{sfze|subfze} %0,%2" \
+		: "=r" ((USItype)(sh)), \
+		"=&r" ((USItype)(sl)) \
+		: "r" ((USItype)(bh)), \
+		"rI" ((USItype)(al)), \
+		"r" ((USItype)(bl))); \
+	else if (__builtin_constant_p(ah) && (ah) == ~(USItype) 0) \
+		__asm__ ("{sf%I3|subf%I3c} %1,%4,%3\n\t{sfme|subfme} %0,%2" \
+		: "=r" ((USItype)(sh)), \
+		"=&r" ((USItype)(sl)) \
+		: "r" ((USItype)(bh)), \
+		"rI" ((USItype)(al)), \
+		"r" ((USItype)(bl))); \
+	else if (__builtin_constant_p(bh) && (bh) == 0) \
+		__asm__ ("{sf%I3|subf%I3c} %1,%4,%3\n\t{ame|addme} %0,%2" \
+		: "=r" ((USItype)(sh)), \
+		"=&r" ((USItype)(sl)) \
+		: "r" ((USItype)(ah)), \
+		"rI" ((USItype)(al)), \
+		"r" ((USItype)(bl))); \
+	else if (__builtin_constant_p(bh) && (bh) == ~(USItype) 0) \
+		__asm__ ("{sf%I3|subf%I3c} %1,%4,%3\n\t{aze|addze} %0,%2" \
+		: "=r" ((USItype)(sh)), \
+		"=&r" ((USItype)(sl)) \
+		: "r" ((USItype)(ah)), \
+		"rI" ((USItype)(al)), \
+		"r" ((USItype)(bl))); \
+	else \
+		__asm__ ("{sf%I4|subf%I4c} %1,%5,%4\n\t{sfe|subfe} %0,%3,%2" \
+		: "=r" ((USItype)(sh)), \
+		"=&r" ((USItype)(sl)) \
+		: "r" ((USItype)(ah)), \
+		"r" ((USItype)(bh)), \
+		"rI" ((USItype)(al)), \
+		"r" ((USItype)(bl))); \
+} while (0)
+#define count_leading_zeros(count, x) \
+	__asm__ ("{cntlz|cntlzw} %0,%1" \
+	: "=r" ((USItype)(count)) \
+	: "r" ((USItype)(x)))
+#define COUNT_LEADING_ZEROS_0 32
+#if defined(_ARCH_PPC)
+#define umul_ppmm(ph, pl, m0, m1) \
+do { \
+	USItype __m0 = (m0), __m1 = (m1); \
+	__asm__ ("mulhwu %0,%1,%2" \
+	: "=r" ((USItype) ph) \
+	: "%r" (__m0), \
+	"r" (__m1)); \
+	(pl) = __m0 * __m1; \
+} while (0)
+#define UMUL_TIME 15
+#define smul_ppmm(ph, pl, m0, m1) \
+do { \
+	SItype __m0 = (m0), __m1 = (m1); \
+	__asm__ ("mulhw %0,%1,%2" \
+	: "=r" ((SItype) ph) \
+	: "%r" (__m0), \
+	"r" (__m1)); \
+	(pl) = __m0 * __m1; \
+} while (0)
+#define SMUL_TIME 14
+#define UDIV_TIME 120
+#else
+#define umul_ppmm(xh, xl, m0, m1) \
+do { \
+	USItype __m0 = (m0), __m1 = (m1); \
+	__asm__ ("mul %0,%2,%3" \
+	: "=r" ((USItype)(xh)), \
+	"=q" ((USItype)(xl)) \
+	: "r" (__m0), \
+	"r" (__m1)); \
+	(xh) += ((((SItype) __m0 >> 31) & __m1) \
+	+ (((SItype) __m1 >> 31) & __m0)); \
+} while (0)
+#define UMUL_TIME 8
+#define smul_ppmm(xh, xl, m0, m1) \
+	__asm__ ("mul %0,%2,%3" \
+	: "=r" ((SItype)(xh)), \
+	"=q" ((SItype)(xl)) \
+	: "r" (m0), \
+	"r" (m1))
+#define SMUL_TIME 4
+#define sdiv_qrnnd(q, r, nh, nl, d) \
+	__asm__ ("div %0,%2,%4" \
+	: "=r" ((SItype)(q)), "=q" ((SItype)(r)) \
+	: "r" ((SItype)(nh)), "1" ((SItype)(nl)), "r" ((SItype)(d)))
+#define UDIV_TIME 100
+#endif
+#endif /* Power architecture variants.  */
+
+/***************************************
+	**************  PYR  ******************
+	***************************************/
+#if defined(__pyr__) && W_TYPE_SIZE == 32
+#define add_ssaaaa(sh, sl, ah, al, bh, bl) \
+	__asm__ ("addw        %5,%1\n" \
+	"addwc	%3,%0" \
+	: "=r" ((USItype)(sh)), \
+	"=&r" ((USItype)(sl)) \
+	: "%0" ((USItype)(ah)), \
+	"g" ((USItype)(bh)), \
+	"%1" ((USItype)(al)), \
+	"g" ((USItype)(bl)))
+#define sub_ddmmss(sh, sl, ah, al, bh, bl) \
+	__asm__ ("subw        %5,%1\n" \
+	"subwb	%3,%0" \
+	: "=r" ((USItype)(sh)), \
+	"=&r" ((USItype)(sl)) \
+	: "0" ((USItype)(ah)), \
+	"g" ((USItype)(bh)), \
+	"1" ((USItype)(al)), \
+	"g" ((USItype)(bl)))
+	/* This insn works on Pyramids with AP, XP, or MI CPUs, but not with SP.  */
+#define umul_ppmm(w1, w0, u, v) \
+	({union {UDItype __ll; \
+	struct {USItype __h, __l; } __i; \
+	} __xx; \
+	__asm__ ("movw %1,%R0\n" \
+	"uemul %2,%0" \
+	: "=&r" (__xx.__ll) \
+	: "g" ((USItype) (u)), \
+	"g" ((USItype)(v))); \
+	(w1) = __xx.__i.__h; (w0) = __xx.__i.__l; })
+#endif /* __pyr__ */
+
+/***************************************
+	**************  RT/ROMP  **************
+	***************************************/
+#if defined(__ibm032__) /* RT/ROMP */	&& W_TYPE_SIZE == 32
+#define add_ssaaaa(sh, sl, ah, al, bh, bl) \
+	__asm__ ("a %1,%5\n" \
+	"ae %0,%3" \
+	: "=r" ((USItype)(sh)), \
+	"=&r" ((USItype)(sl)) \
+	: "%0" ((USItype)(ah)), \
+	"r" ((USItype)(bh)), \
+	"%1" ((USItype)(al)), \
+	"r" ((USItype)(bl)))
+#define sub_ddmmss(sh, sl, ah, al, bh, bl) \
+	__asm__ ("s %1,%5\n" \
+	"se %0,%3" \
+	: "=r" ((USItype)(sh)), \
+	"=&r" ((USItype)(sl)) \
+	: "0" ((USItype)(ah)), \
+	"r" ((USItype)(bh)), \
+	"1" ((USItype)(al)), \
+	"r" ((USItype)(bl)))
+#define umul_ppmm(ph, pl, m0, m1) \
+do { \
+	USItype __m0 = (m0), __m1 = (m1); \
+	__asm__ ( \
+	"s       r2,r2\n" \
+	"mts	r10,%2\n" \
+	"m	r2,%3\n" \
+	"m	r2,%3\n" \
+	"m	r2,%3\n" \
+	"m	r2,%3\n" \
+	"m	r2,%3\n" \
+	"m	r2,%3\n" \
+	"m	r2,%3\n" \
+	"m	r2,%3\n" \
+	"m	r2,%3\n" \
+	"m	r2,%3\n" \
+	"m	r2,%3\n" \
+	"m	r2,%3\n" \
+	"m	r2,%3\n" \
+	"m	r2,%3\n" \
+	"m	r2,%3\n" \
+	"m	r2,%3\n" \
+	"cas	%0,r2,r0\n" \
+	"mfs	r10,%1" \
+	: "=r" ((USItype)(ph)), \
+	"=r" ((USItype)(pl)) \
+	: "%r" (__m0), \
+	"r" (__m1) \
+	: "r2"); \
+	(ph) += ((((SItype) __m0 >> 31) & __m1) \
+	+ (((SItype) __m1 >> 31) & __m0)); \
+} while (0)
+#define UMUL_TIME 20
+#define UDIV_TIME 200
+#define count_leading_zeros(count, x) \
+do { \
+	if ((x) >= 0x10000) \
+		__asm__ ("clz     %0,%1" \
+		: "=r" ((USItype)(count)) \
+		: "r" ((USItype)(x) >> 16)); \
+	else { \
+		__asm__ ("clz   %0,%1" \
+		: "=r" ((USItype)(count)) \
+		: "r" ((USItype)(x))); \
+		(count) += 16; \
+	} \
+} while (0)
+#endif /* RT/ROMP */
+
+/***************************************
+	**************  SH2  ******************
+	***************************************/
+#if (defined(__sh2__) || defined(__sh3__) || defined(__SH4__)) \
+	&& W_TYPE_SIZE == 32
+#define umul_ppmm(w1, w0, u, v) \
+	__asm__ ( \
+	"dmulu.l %2,%3\n" \
+	"sts	macl,%1\n" \
+	"sts	mach,%0" \
+	: "=r" ((USItype)(w1)), \
+	"=r" ((USItype)(w0)) \
+	: "r" ((USItype)(u)), \
+	"r" ((USItype)(v)) \
+	: "macl", "mach")
+#define UMUL_TIME 5
+#endif
+
+/***************************************
+	**************  SPARC	****************
+	***************************************/
+#if defined(__sparc__) && W_TYPE_SIZE == 32
+#define add_ssaaaa(sh, sl, ah, al, bh, bl) \
+	__asm__ ("addcc %r4,%5,%1\n" \
+	"addx %r2,%3,%0" \
+	: "=r" ((USItype)(sh)), \
+	"=&r" ((USItype)(sl)) \
+	: "%rJ" ((USItype)(ah)), \
+	"rI" ((USItype)(bh)), \
+	"%rJ" ((USItype)(al)), \
+	"rI" ((USItype)(bl)) \
+	__CLOBBER_CC)
+#define sub_ddmmss(sh, sl, ah, al, bh, bl) \
+	__asm__ ("subcc %r4,%5,%1\n" \
+	"subx %r2,%3,%0" \
+	: "=r" ((USItype)(sh)), \
+	"=&r" ((USItype)(sl)) \
+	: "rJ" ((USItype)(ah)), \
+	"rI" ((USItype)(bh)), \
+	"rJ" ((USItype)(al)), \
+	"rI" ((USItype)(bl)) \
+	__CLOBBER_CC)
+#if defined(__sparc_v8__)
+/* Don't match immediate range because, 1) it is not often useful,
+	2) the 'I' flag thinks of the range as a 13 bit signed interval,
+	while we want to match a 13 bit interval, sign extended to 32 bits,
+	but INTERPRETED AS UNSIGNED.  */
+#define umul_ppmm(w1, w0, u, v) \
+	__asm__ ("umul %2,%3,%1;rd %%y,%0" \
+	: "=r" ((USItype)(w1)), \
+	"=r" ((USItype)(w0)) \
+	: "r" ((USItype)(u)), \
+	"r" ((USItype)(v)))
+#define UMUL_TIME 5
+#ifndef SUPERSPARC		/* SuperSPARC's udiv only handles 53 bit dividends */
+#define udiv_qrnnd(q, r, n1, n0, d) \
+do { \
+	USItype __q; \
+	__asm__ ("mov %1,%%y;nop;nop;nop;udiv %2,%3,%0" \
+	: "=r" ((USItype)(__q)) \
+	: "r" ((USItype)(n1)), \
+	"r" ((USItype)(n0)), \
+	"r" ((USItype)(d))); \
+	(r) = (n0) - __q * (d); \
+	(q) = __q; \
+} while (0)
+#define UDIV_TIME 25
+#endif /* SUPERSPARC */
+#else /* ! __sparc_v8__ */
+#if defined(__sparclite__)
+/* This has hardware multiply but not divide.  It also has two additional
+	instructions scan (ffs from high bit) and divscc.  */
+#define umul_ppmm(w1, w0, u, v) \
+	__asm__ ("umul %2,%3,%1;rd %%y,%0" \
+	: "=r" ((USItype)(w1)), \
+	"=r" ((USItype)(w0)) \
+	: "r" ((USItype)(u)), \
+	"r" ((USItype)(v)))
+#define UMUL_TIME 5
+#define udiv_qrnnd(q, r, n1, n0, d) \
+	__asm__ ("! Inlined udiv_qrnnd\n" \
+	"wr	%%g0,%2,%%y	! Not a delayed write for sparclite\n" \
+	"tst	%%g0\n" \
+	"divscc	%3,%4,%%g1\n" \
+	"divscc	%%g1,%4,%%g1\n" \
+	"divscc	%%g1,%4,%%g1\n" \
+	"divscc	%%g1,%4,%%g1\n" \
+	"divscc	%%g1,%4,%%g1\n" \
+	"divscc	%%g1,%4,%%g1\n" \
+	"divscc	%%g1,%4,%%g1\n" \
+	"divscc	%%g1,%4,%%g1\n" \
+	"divscc	%%g1,%4,%%g1\n" \
+	"divscc	%%g1,%4,%%g1\n" \
+	"divscc	%%g1,%4,%%g1\n" \
+	"divscc	%%g1,%4,%%g1\n" \
+	"divscc	%%g1,%4,%%g1\n" \
+	"divscc	%%g1,%4,%%g1\n" \
+	"divscc	%%g1,%4,%%g1\n" \
+	"divscc	%%g1,%4,%%g1\n" \
+	"divscc	%%g1,%4,%%g1\n" \
+	"divscc	%%g1,%4,%%g1\n" \
+	"divscc	%%g1,%4,%%g1\n" \
+	"divscc	%%g1,%4,%%g1\n" \
+	"divscc	%%g1,%4,%%g1\n" \
+	"divscc	%%g1,%4,%%g1\n" \
+	"divscc	%%g1,%4,%%g1\n" \
+	"divscc	%%g1,%4,%%g1\n" \
+	"divscc	%%g1,%4,%%g1\n" \
+	"divscc	%%g1,%4,%%g1\n" \
+	"divscc	%%g1,%4,%%g1\n" \
+	"divscc	%%g1,%4,%%g1\n" \
+	"divscc	%%g1,%4,%%g1\n" \
+	"divscc	%%g1,%4,%%g1\n" \
+	"divscc	%%g1,%4,%%g1\n" \
+	"divscc	%%g1,%4,%0\n" \
+	"rd	%%y,%1\n" \
+	"bl,a 1f\n" \
+	"add	%1,%4,%1\n" \
+	"1:	! End of inline udiv_qrnnd" \
+	: "=r" ((USItype)(q)), \
+	"=r" ((USItype)(r)) \
+	: "r" ((USItype)(n1)), \
+	"r" ((USItype)(n0)), \
+	"rI" ((USItype)(d)) \
+	: "%g1" __AND_CLOBBER_CC)
+#define UDIV_TIME 37
+#define count_leading_zeros(count, x) \
+	__asm__ ("scan %1,0,%0" \
+	: "=r" ((USItype)(x)) \
+	: "r" ((USItype)(count)))
+/* Early sparclites return 63 for an argument of 0, but they warn that future
+	implementations might change this.  Therefore, leave COUNT_LEADING_ZEROS_0
+	undefined.  */
+#endif /* __sparclite__ */
+#endif /* __sparc_v8__ */
+	/* Default to sparc v7 versions of umul_ppmm and udiv_qrnnd.  */
+#ifndef umul_ppmm
+#define umul_ppmm(w1, w0, u, v) \
+	__asm__ ("! Inlined umul_ppmm\n" \
+	"wr	%%g0,%2,%%y	! SPARC has 0-3 delay insn after a wr\n" \
+	"sra	%3,31,%%g2	! Don't move this insn\n" \
+	"and	%2,%%g2,%%g2	! Don't move this insn\n" \
+	"andcc	%%g0,0,%%g1	! Don't move this insn\n" \
+	"mulscc	%%g1,%3,%%g1\n" \
+	"mulscc	%%g1,%3,%%g1\n" \
+	"mulscc	%%g1,%3,%%g1\n" \
+	"mulscc	%%g1,%3,%%g1\n" \
+	"mulscc	%%g1,%3,%%g1\n" \
+	"mulscc	%%g1,%3,%%g1\n" \
+	"mulscc	%%g1,%3,%%g1\n" \
+	"mulscc	%%g1,%3,%%g1\n" \
+	"mulscc	%%g1,%3,%%g1\n" \
+	"mulscc	%%g1,%3,%%g1\n" \
+	"mulscc	%%g1,%3,%%g1\n" \
+	"mulscc	%%g1,%3,%%g1\n" \
+	"mulscc	%%g1,%3,%%g1\n" \
+	"mulscc	%%g1,%3,%%g1\n" \
+	"mulscc	%%g1,%3,%%g1\n" \
+	"mulscc	%%g1,%3,%%g1\n" \
+	"mulscc	%%g1,%3,%%g1\n" \
+	"mulscc	%%g1,%3,%%g1\n" \
+	"mulscc	%%g1,%3,%%g1\n" \
+	"mulscc	%%g1,%3,%%g1\n" \
+	"mulscc	%%g1,%3,%%g1\n" \
+	"mulscc	%%g1,%3,%%g1\n" \
+	"mulscc	%%g1,%3,%%g1\n" \
+	"mulscc	%%g1,%3,%%g1\n" \
+	"mulscc	%%g1,%3,%%g1\n" \
+	"mulscc	%%g1,%3,%%g1\n" \
+	"mulscc	%%g1,%3,%%g1\n" \
+	"mulscc	%%g1,%3,%%g1\n" \
+	"mulscc	%%g1,%3,%%g1\n" \
+	"mulscc	%%g1,%3,%%g1\n" \
+	"mulscc	%%g1,%3,%%g1\n" \
+	"mulscc	%%g1,%3,%%g1\n" \
+	"mulscc	%%g1,0,%%g1\n" \
+	"add	%%g1,%%g2,%0\n" \
+	"rd	%%y,%1" \
+	: "=r" ((USItype)(w1)), \
+	"=r" ((USItype)(w0)) \
+	: "%rI" ((USItype)(u)), \
+	"r" ((USItype)(v)) \
+	: "%g1", "%g2" __AND_CLOBBER_CC)
+#define UMUL_TIME 39		/* 39 instructions */
+#endif
+#ifndef udiv_qrnnd
+#ifndef LONGLONG_STANDALONE
+#define udiv_qrnnd(q, r, n1, n0, d) \
+do { USItype __r; \
+	(q) = __udiv_qrnnd(&__r, (n1), (n0), (d)); \
+	(r) = __r; \
+} while (0)
+	extern USItype __udiv_qrnnd();
+#define UDIV_TIME 140
+#endif /* LONGLONG_STANDALONE */
+#endif /* udiv_qrnnd */
+#endif /* __sparc__ */
+
+/***************************************
+	**************  VAX  ******************
+	***************************************/
+#if defined(__vax__) && W_TYPE_SIZE == 32
+#define add_ssaaaa(sh, sl, ah, al, bh, bl) \
+	__asm__ ("addl2 %5,%1\n" \
+	"adwc %3,%0" \
+	: "=g" ((USItype)(sh)), \
+	"=&g" ((USItype)(sl)) \
+	: "%0" ((USItype)(ah)), \
+	"g" ((USItype)(bh)), \
+	"%1" ((USItype)(al)), \
+	"g" ((USItype)(bl)))
+#define sub_ddmmss(sh, sl, ah, al, bh, bl) \
+	__asm__ ("subl2 %5,%1\n" \
+	"sbwc %3,%0" \
+	: "=g" ((USItype)(sh)), \
+	"=&g" ((USItype)(sl)) \
+	: "0" ((USItype)(ah)), \
+	"g" ((USItype)(bh)), \
+	"1" ((USItype)(al)), \
+	"g" ((USItype)(bl)))
+#define umul_ppmm(xh, xl, m0, m1) \
+do { \
+	union {UDItype __ll; \
+	struct {USItype __l, __h; } __i; \
+	} __xx; \
+	USItype __m0 = (m0), __m1 = (m1); \
+	__asm__ ("emul %1,%2,$0,%0" \
+	: "=g" (__xx.__ll) \
+	: "g" (__m0), \
+	"g" (__m1)); \
+	(xh) = __xx.__i.__h; (xl) = __xx.__i.__l; \
+	(xh) += ((((SItype) __m0 >> 31) & __m1) \
+	+ (((SItype) __m1 >> 31) & __m0)); \
+} while (0)
+#define sdiv_qrnnd(q, r, n1, n0, d) \
+do { \
+	union {DItype __ll; \
+	struct {SItype __l, __h; } __i; \
+	} __xx; \
+	__xx.__i.__h = n1; __xx.__i.__l = n0; \
+	__asm__ ("ediv %3,%2,%0,%1" \
+	: "=g" (q), "=g" (r) \
+	: "g" (__xx.__ll), "g" (d)); \
+} while (0)
+#endif /* __vax__ */
+
+/***************************************
+	**************  Z8000	****************
+	***************************************/
+#if defined(__z8000__) && W_TYPE_SIZE == 16
+#define add_ssaaaa(sh, sl, ah, al, bh, bl) \
+	__asm__ ("add %H1,%H5\n\tadc  %H0,%H3" \
+	: "=r" ((unsigned int)(sh)), \
+	"=&r" ((unsigned int)(sl)) \
+	: "%0" ((unsigned int)(ah)), \
+	"r" ((unsigned int)(bh)), \
+	"%1" ((unsigned int)(al)), \
+	"rQR" ((unsigned int)(bl)))
+#define sub_ddmmss(sh, sl, ah, al, bh, bl) \
+	__asm__ ("sub %H1,%H5\n\tsbc  %H0,%H3" \
+	: "=r" ((unsigned int)(sh)), \
+	"=&r" ((unsigned int)(sl)) \
+	: "0" ((unsigned int)(ah)), \
+	"r" ((unsigned int)(bh)), \
+	"1" ((unsigned int)(al)), \
+	"rQR" ((unsigned int)(bl)))
+#define umul_ppmm(xh, xl, m0, m1) \
+do { \
+	union {long int __ll; \
+	struct {unsigned int __h, __l; } __i; \
+	} __xx; \
+	unsigned int __m0 = (m0), __m1 = (m1); \
+	__asm__ ("mult      %S0,%H3" \
+	: "=r" (__xx.__i.__h), \
+	"=r" (__xx.__i.__l) \
+	: "%1" (__m0), \
+	"rQR" (__m1)); \
+	(xh) = __xx.__i.__h; (xl) = __xx.__i.__l; \
+	(xh) += ((((signed int) __m0 >> 15) & __m1) \
+	+ (((signed int) __m1 >> 15) & __m0)); \
+} while (0)
+#endif /* __z8000__ */
+
+#endif /* __GNUC__ */
+
+/***************************************
+	***********  Generic Versions	********
+	***************************************/
+#if !defined(umul_ppmm) && defined(__umulsidi3)
+#define umul_ppmm(ph, pl, m0, m1) \
+{ \
+	UDWtype __ll = __umulsidi3(m0, m1); \
+	ph = (UWtype) (__ll >> W_TYPE_SIZE); \
+	pl = (UWtype) __ll; \
+}
+#endif
+
+#if !defined(__umulsidi3)
+#define __umulsidi3(u, v) \
+	({UWtype __hi, __lo; \
+	umul_ppmm(__hi, __lo, u, v); \
+	((UDWtype) __hi << W_TYPE_SIZE) | __lo; })
+#endif
+
+	/* If this machine has no inline assembler, use C macros.  */
+
+#if !defined(add_ssaaaa)
+#define add_ssaaaa(sh, sl, ah, al, bh, bl) \
+do { \
+	UWtype __x; \
+	__x = (al) + (bl); \
+	(sh) = (ah) + (bh) + (__x < (al)); \
+	(sl) = __x; \
+} while (0)
+#endif
+
+#if !defined(sub_ddmmss)
+#define sub_ddmmss(sh, sl, ah, al, bh, bl) \
+do { \
+	UWtype __x; \
+	__x = (al) - (bl); \
+	(sh) = (ah) - (bh) - (__x > (al)); \
+	(sl) = __x; \
+} while (0)
+#endif
+
+#if !defined(umul_ppmm)
+#define umul_ppmm(w1, w0, u, v) \
+do { \
+	UWtype __x0, __x1, __x2, __x3; \
+	UHWtype __ul, __vl, __uh, __vh; \
+	UWtype __u = (u), __v = (v); \
+	\
+	__ul = __ll_lowpart(__u); \
+	__uh = __ll_highpart(__u); \
+	__vl = __ll_lowpart(__v); \
+	__vh = __ll_highpart(__v); \
+	\
+	__x0 = (UWtype) __ul * __vl; \
+	__x1 = (UWtype) __ul * __vh; \
+	__x2 = (UWtype) __uh * __vl; \
+	__x3 = (UWtype) __uh * __vh; \
+	\
+	__x1 += __ll_highpart(__x0);/* this can't give carry */ \
+	__x1 += __x2;		/* but this indeed can */ \
+	if (__x1 < __x2)		/* did we get it? */ \
+	__x3 += __ll_B;		/* yes, add it in the proper pos. */ \
+	\
+	(w1) = __x3 + __ll_highpart(__x1); \
+	(w0) = (__ll_lowpart(__x1) << W_TYPE_SIZE/2) + __ll_lowpart(__x0); \
+} while (0)
+#endif
+
+#if !defined(umul_ppmm)
+#define smul_ppmm(w1, w0, u, v) \
+do { \
+	UWtype __w1; \
+	UWtype __m0 = (u), __m1 = (v); \
+	umul_ppmm(__w1, w0, __m0, __m1); \
+	(w1) = __w1 - (-(__m0 >> (W_TYPE_SIZE - 1)) & __m1) \
+	- (-(__m1 >> (W_TYPE_SIZE - 1)) & __m0); \
+} while (0)
+#endif
+
+	/* Define this unconditionally, so it can be used for debugging.  */
+#define __udiv_qrnnd_c(q, r, n1, n0, d) \
+do { \
+	UWtype __d1, __d0, __q1, __q0, __r1, __r0, __m; \
+	__d1 = __ll_highpart(d); \
+	__d0 = __ll_lowpart(d); \
+	\
+	__r1 = (n1) % __d1; \
+	__q1 = (n1) / __d1; \
+	__m = (UWtype) __q1 * __d0; \
+	__r1 = __r1 * __ll_B | __ll_highpart(n0); \
+	if (__r1 < __m) { \
+		__q1--, __r1 += (d); \
+		if (__r1 >= (d)) /* i.e. we didn't get carry when adding to __r1 */ \
+		if (__r1 < __m) \
+			__q1--, __r1 += (d); \
+	} \
+	__r1 -= __m; \
+	\
+	__r0 = __r1 % __d1; \
+	__q0 = __r1 / __d1; \
+	__m = (UWtype) __q0 * __d0; \
+	__r0 = __r0 * __ll_B | __ll_lowpart(n0); \
+	if (__r0 < __m) { \
+		__q0--, __r0 += (d); \
+		if (__r0 >= (d)) \
+			if (__r0 < __m) \
+				__q0--, __r0 += (d); \
+	} \
+	__r0 -= __m; \
+	\
+	(q) = (UWtype) __q1 * __ll_B | __q0; \
+	(r) = __r0; \
+} while (0)
+
+/* If the processor has no udiv_qrnnd but sdiv_qrnnd, go through
+	__udiv_w_sdiv (defined in libgcc or elsewhere).  */
+#if !defined(udiv_qrnnd) && defined(sdiv_qrnnd)
+#define udiv_qrnnd(q, r, nh, nl, d) \
+do { \
+	UWtype __r; \
+	(q) = __MPN(udiv_w_sdiv) (&__r, nh, nl, d); \
+	(r) = __r; \
+} while (0)
+#endif
+
+	/* If udiv_qrnnd was not defined for this processor, use __udiv_qrnnd_c.  */
+#if !defined(udiv_qrnnd)
+#define UDIV_NEEDS_NORMALIZATION 1
+#define udiv_qrnnd __udiv_qrnnd_c
+#endif
+
+#undef count_leading_zeros
+#if !defined(count_leading_zeros)
+	extern
+#ifdef __STDC__
+			const
+#endif
+			unsigned char __clz_tab[];
+#define count_leading_zeros(count, x) \
+do { \
+	UWtype __xr = (x); \
+	UWtype __a; \
+	\
+	if (W_TYPE_SIZE <= 32) { \
+		__a = __xr < ((UWtype) 1 << 2*__BITS4) \
+		? (__xr < ((UWtype) 1 << __BITS4) ? 0 : __BITS4) \
+		: (__xr < ((UWtype) 1 << 3*__BITS4) ?  2*__BITS4 : 3*__BITS4); \
+	} \
+	else { \
+		for (__a = W_TYPE_SIZE - 8; __a > 0; __a -= 8) \
+			if (((__xr >> __a) & 0xff) != 0) \
+				break; \
+	} \
+	\
+	(count) = W_TYPE_SIZE - (__clz_tab[__xr >> __a] + __a); \
+} while (0)
+	/* This version gives a well-defined value for zero. */
+#define COUNT_LEADING_ZEROS_0 W_TYPE_SIZE
+#endif
+
+#if !defined(count_trailing_zeros)
+/* Define count_trailing_zeros using count_leading_zeros.  The latter might be
+	defined in asm, but if it is not, the C version above is good enough.  */
+#define count_trailing_zeros(count, x) \
+do { \
+	UWtype __ctz_x = (x); \
+	UWtype __ctz_c; \
+	count_leading_zeros(__ctz_c, __ctz_x & -__ctz_x); \
+	(count) = W_TYPE_SIZE - 1 - __ctz_c; \
+} while (0)
+#endif
+
+#ifndef UDIV_NEEDS_NORMALIZATION
+#define UDIV_NEEDS_NORMALIZATION 0
+#endif

lib/mpi/mpi-add.c

+/* mpi-add.c  -  MPI functions
+ *	Copyright (C) 1998, 1999, 2000, 2001 Free Software Foundation, Inc.
+ *	Copyright (C) 1994, 1996 Free Software Foundation, Inc.
+ *
+ * This file is part of GnuPG.
+ *
+ * GnuPG is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * GnuPG is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
+ *
+ * Note: This code is heavily based on the GNU MP Library.
+ *	 Actually it's the same code with only minor changes in the
+ *	 way the data is stored; this is to support the abstraction
+ *	 of an optional secure memory allocation which may be used
+ *	 to avoid revealing of sensitive data due to paging etc.
+ *	 The GNU MP Library itself is published under the LGPL;
+ *	 however I decided to publish this code under the plain GPL.
+ */
+
+#include "mpi-internal.h"
+
+/****************
+ * Add the unsigned integer V to the mpi-integer U and store the
+ * result in W. U and V may be the same.
+ */
+int mpi_add_ui(MPI w, const MPI u, unsigned long v)
+{
+	mpi_ptr_t wp, up;
+	mpi_size_t usize, wsize;
+	int usign, wsign;
+
+	usize = u->nlimbs;
+	usign = u->sign;
+	wsign = 0;
+
+	/* If not space for W (and possible carry), increase space.  */
+	wsize = usize + 1;
+	if (w->alloced < wsize)
+		if (mpi_resize(w, wsize) < 0)
+			return -ENOMEM;
+
+	/* These must be after realloc (U may be the same as W).  */
+	up = u->d;
+	wp = w->d;
+
+	if (!usize) {		/* simple */
+		wp[0] = v;
+		wsize = v ? 1 : 0;
+	} else if (!usign) {	/* mpi is not negative */
+		mpi_limb_t cy;
+		cy = mpihelp_add_1(wp, up, usize, v);
+		wp[usize] = cy;
+		wsize = usize + cy;
+	} else {		/* The signs are different.  Need exact comparison to determine
+				 * which operand to subtract from which.  */
+		if (usize == 1 && up[0] < v) {
+			wp[0] = v - up[0];
+			wsize = 1;
+		} else {
+			mpihelp_sub_1(wp, up, usize, v);
+			/* Size can decrease with at most one limb. */
+			wsize = usize - (wp[usize - 1] == 0);
+			wsign = 1;
+		}
+	}
+
+	w->nlimbs = wsize;
+	w->sign = wsign;
+	return 0;
+}
+
+int mpi_add(MPI w, MPI u, MPI v)
+{
+	mpi_ptr_t wp, up, vp;
+	mpi_size_t usize, vsize, wsize;
+	int usign, vsign, wsign;
+
+	if (u->nlimbs < v->nlimbs) {	/* Swap U and V. */
+		usize = v->nlimbs;
+		usign = v->sign;
+		vsize = u->nlimbs;
+		vsign = u->sign;
+		wsize = usize + 1;
+		if (RESIZE_IF_NEEDED(w, wsize) < 0)
+			return -ENOMEM;
+		/* These must be after realloc (u or v may be the same as w).  */
+		up = v->d;
+		vp = u->d;
+	} else {
+		usize = u->nlimbs;
+		usign = u->sign;
+		vsize = v->nlimbs;
+		vsign = v->sign;
+		wsize = usize + 1;
+		if (RESIZE_IF_NEEDED(w, wsize) < 0)
+			return -ENOMEM;
+		/* These must be after realloc (u or v may be the same as w).  */
+		up = u->d;
+		vp = v->d;
+	}
+	wp = w->d;
+	wsign = 0;
+
+	if (!vsize) {		/* simple */
+		MPN_COPY(wp, up, usize);
+		wsize = usize;
+		wsign = usign;
+	} else if (usign != vsign) {	/* different sign */
+		/* This test is right since USIZE >= VSIZE */
+		if (usize != vsize) {
+			mpihelp_sub(wp, up, usize, vp, vsize);
+			wsize = usize;
+			MPN_NORMALIZE(wp, wsize);
+			wsign = usign;
+		} else if (mpihelp_cmp(up, vp, usize) < 0) {
+			mpihelp_sub_n(wp, vp, up, usize);
+			wsize = usize;
+			MPN_NORMALIZE(wp, wsize);
+			if (!usign)
+				wsign = 1;
+		} else {
+			mpihelp_sub_n(wp, up, vp, usize);
+			wsize = usize;
+			MPN_NORMALIZE(wp, wsize);
+			if (usign)
+				wsign = 1;
+		}
+	} else {		/* U and V have same sign. Add them. */
+		mpi_limb_t cy = mpihelp_add(wp, up, usize, vp, vsize);
+		wp[usize] = cy;
+		wsize = usize + cy;
+		if (usign)
+			wsign = 1;
+	}
+
+	w->nlimbs = wsize;
+	w->sign = wsign;
+	return 0;
+}
+
+/****************
+ * Subtract the unsigned integer V from the mpi-integer U and store the
+ * result in W.
+ */
+int mpi_sub_ui(MPI w, MPI u, unsigned long v)
+{
+	mpi_ptr_t wp, up;
+	mpi_size_t usize, wsize;
+	int usign, wsign;
+
+	usize = u->nlimbs;
+	usign = u->sign;
+	wsign = 0;
+
+	/* If not space for W (and possible carry), increase space.  */
+	wsize = usize + 1;
+	if (w->alloced < wsize)
+		if (mpi_resize(w, wsize) < 0)
+			return -ENOMEM;
+
+	/* These must be after realloc (U may be the same as W).  */
+	up = u->d;
+	wp = w->d;
+
+	if (!usize) {		/* simple */
+		wp[0] = v;
+		wsize = v ? 1 : 0;
+		wsign = 1;
+	} else if (usign) {	/* mpi and v are negative */
+		mpi_limb_t cy;
+		cy = mpihelp_add_1(wp, up, usize, v);
+		wp[usize] = cy;
+		wsize = usize + cy;
+	} else {		/* The signs are different.  Need exact comparison to determine
+				 * which operand to subtract from which.  */
+		if (usize == 1 && up[0] < v) {
+			wp[0] = v - up[0];
+			wsize = 1;
+			wsign = 1;
+		} else {
+			mpihelp_sub_1(wp, up, usize, v);
+			/* Size can decrease with at most one limb. */
+			wsize = usize - (wp[usize - 1] == 0);
+		}
+	}
+
+	w->nlimbs = wsize;
+	w->sign = wsign;
+	return 0;
+}
+
+int mpi_sub(MPI w, MPI u, MPI v)
+{
+	int rc;
+
+	if (w == v) {
+		MPI vv;
+		if (mpi_copy(&vv, v) < 0)
+			return -ENOMEM;
+		vv->sign = !vv->sign;
+		rc = mpi_add(w, u, vv);
+		mpi_free(vv);
+	} else {
+		/* fixme: this is not thread-save (we temp. modify v) */
+		v->sign = !v->sign;
+		rc = mpi_add(w, u, v);
+		v->sign = !v->sign;
+	}
+	return rc;
+}
+
+int mpi_addm(MPI w, MPI u, MPI v, MPI m)
+{
+	if (mpi_add(w, u, v) < 0 || mpi_fdiv_r(w, w, m) < 0)
+		return -ENOMEM;
+	return 0;
+}
+
+int mpi_subm(MPI w, MPI u, MPI v, MPI m)
+{
+	if (mpi_sub(w, u, v) < 0 || mpi_fdiv_r(w, w, m) < 0)
+		return -ENOMEM;
+	return 0;
+}

lib/mpi/mpi-bit.c

+/* mpi-bit.c  -  MPI bit level fucntions
+ * Copyright (C) 1998, 1999 Free Software Foundation, Inc.
+ *
+ * This file is part of GnuPG.
+ *
+ * GnuPG is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * GnuPG is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
+ */
+
+#include "mpi-internal.h"
+#include "longlong.h"
+
+const unsigned char __clz_tab[] = {
+	0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5,
+	    5, 5, 5, 5, 5, 5, 5, 5,
+	6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
+	    6, 6, 6, 6, 6, 6, 6, 6,
+	7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
+	    7, 7, 7, 7, 7, 7, 7, 7,
+	7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
+	    7, 7, 7, 7, 7, 7, 7, 7,
+	8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
+	    8, 8, 8, 8, 8, 8, 8, 8,
+	8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
+	    8, 8, 8, 8, 8, 8, 8, 8,
+	8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
+	    8, 8, 8, 8, 8, 8, 8, 8,
+	8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
+	    8, 8, 8, 8, 8, 8, 8, 8,
+};
+
+#define A_LIMB_1 ((mpi_limb_t) 1)
+
+/****************
+ * Sometimes we have MSL (most significant limbs) which are 0;
+ * this is for some reasons not good, so this function removes them.
+ */
+void mpi_normalize(MPI a)
+{
+	for (; a->nlimbs && !a->d[a->nlimbs - 1]; a->nlimbs--)
+		;
+}
+
+/****************
+ * Return the number of bits in A.
+ */
+unsigned mpi_get_nbits(MPI a)
+{
+	unsigned n;
+
+	mpi_normalize(a);
+
+	if (a->nlimbs) {
+		mpi_limb_t alimb = a->d[a->nlimbs - 1];
+		if (alimb)
+			count_leading_zeros(n, alimb);
+		else
+			n = BITS_PER_MPI_LIMB;
+		n = BITS_PER_MPI_LIMB - n + (a->nlimbs - 1) * BITS_PER_MPI_LIMB;
+	} else
+		n = 0;
+	return n;
+}
+EXPORT_SYMBOL_GPL(mpi_get_nbits);
+
+/****************
+ * Test whether bit N is set.
+ */
+int mpi_test_bit(MPI a, unsigned n)
+{
+	unsigned limbno, bitno;
+	mpi_limb_t limb;
+
+	limbno = n / BITS_PER_MPI_LIMB;
+	bitno = n % BITS_PER_MPI_LIMB;
+
+	if (limbno >= a->nlimbs)
+		return 0;	/* too far left: this is a 0 */
+	limb = a->d[limbno];
+	return (limb & (A_LIMB_1 << bitno)) ? 1 : 0;
+}
+
+/****************
+ * Set bit N of A.
+ */
+int mpi_set_bit(MPI a, unsigned n)
+{
+	unsigned limbno, bitno;
+
+	limbno = n / BITS_PER_MPI_LIMB;
+	bitno = n % BITS_PER_MPI_LIMB;
+
+	if (limbno >= a->nlimbs) {	/* resize */
+		if (a->alloced >= limbno)
+			if (mpi_resize(a, limbno + 1) < 0)
+				return -ENOMEM;
+		a->nlimbs = limbno + 1;
+	}
+	a->d[limbno] |= (A_LIMB_1 << bitno);
+	return 0;
+}
+
+/****************
+ * Set bit N of A. and clear all bits above
+ */
+int mpi_set_highbit(MPI a, unsigned n)
+{
+	unsigned limbno, bitno;
+
+	limbno = n / BITS_PER_MPI_LIMB;
+	bitno = n % BITS_PER_MPI_LIMB;
+
+	if (limbno >= a->nlimbs) {	/* resize */
+		if (a->alloced >= limbno)
+			if (mpi_resize(a, limbno + 1) < 0)
+				return -ENOMEM;
+		a->nlimbs = limbno + 1;
+	}
+	a->d[limbno] |= (A_LIMB_1 << bitno);
+	for (bitno++; bitno < BITS_PER_MPI_LIMB; bitno++)
+		a->d[limbno] &= ~(A_LIMB_1 << bitno);
+	a->nlimbs = limbno + 1;
+	return 0;
+}
+
+/****************
+ * clear bit N of A and all bits above
+ */
+void mpi_clear_highbit(MPI a, unsigned n)
+{
+	unsigned limbno, bitno;
+
+	limbno = n / BITS_PER_MPI_LIMB;
+	bitno = n % BITS_PER_MPI_LIMB;
+
+	if (limbno >= a->nlimbs)
+		return;		/* not allocated, so need to clear bits :-) */
+
+	for (; bitno < BITS_PER_MPI_LIMB; bitno++)
+		a->d[limbno] &= ~(A_LIMB_1 << bitno);
+	a->nlimbs = limbno + 1;
+}
+
+/****************
+ * Clear bit N of A.
+ */
+void mpi_clear_bit(MPI a, unsigned n)
+{
+	unsigned limbno, bitno;
+
+	limbno = n / BITS_PER_MPI_LIMB;
+	bitno = n % BITS_PER_MPI_LIMB;
+
+	if (limbno >= a->nlimbs)
+		return;		/* don't need to clear this bit, it's to far to left */
+	a->d[limbno] &= ~(A_LIMB_1 << bitno);
+}
+
+/****************
+ * Shift A by N bits to the right
+ * FIXME: should use alloc_limb if X and A are same.
+ */
+int mpi_rshift(MPI x, MPI a, unsigned n)
+{
+	mpi_ptr_t xp;
+	mpi_size_t xsize;
+
+	xsize = a->nlimbs;
+	x->sign = a->sign;
+	if (RESIZE_IF_NEEDED(x, (size_t) xsize) < 0)
+		return -ENOMEM;
+	xp = x->d;
+
+	if (xsize) {
+		mpihelp_rshift(xp, a->d, xsize, n);
+		MPN_NORMALIZE(xp, xsize);
+	}
+	x->nlimbs = xsize;
+	return 0;
+}
+
+/****************
+ * Shift A by COUNT limbs to the left
+ * This is used only within the MPI library
+ */
+int mpi_lshift_limbs(MPI a, unsigned int count)
+{
+	mpi_ptr_t ap = a->d;
+	int n = a->nlimbs;
+	int i;
+
+	if (!count || !n)
+		return 0;
+
+	if (RESIZE_IF_NEEDED(a, n + count) < 0)
+		return -ENOMEM;
+
+	for (i = n - 1; i >= 0; i--)
+		ap[i + count] = ap[i];
+	for (i = 0; i < count; i++)
+		ap[i] = 0;
+	a->nlimbs += count;
+	return 0;
+}
+
+/****************
+ * Shift A by COUNT limbs to the right
+ * This is used only within the MPI library
+ */
+void mpi_rshift_limbs(MPI a, unsigned int count)
+{
+	mpi_ptr_t ap = a->d;
+	mpi_size_t n = a->nlimbs;
+	unsigned int i;
+
+	if (count >= n) {
+		a->nlimbs = 0;
+		return;
+	}
+
+	for (i = 0; i < n - count; i++)
+		ap[i] = ap[i + count];
+	ap[i] = 0;
+	a->nlimbs -= count;
+}

lib/mpi/mpi-cmp.c

+/* mpi-cmp.c  -  MPI functions
+ * Copyright (C) 1998, 1999 Free Software Foundation, Inc.
+ *
+ * This file is part of GnuPG.
+ *
+ * GnuPG is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * GnuPG is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
+ */
+
+#include "mpi-internal.h"
+
+int mpi_cmp_ui(MPI u, unsigned long v)
+{
+	mpi_limb_t limb = v;
+
+	mpi_normalize(u);
+	if (!u->nlimbs && !limb)
+		return 0;
+	if (u->sign)
+		return -1;
+	if (u->nlimbs > 1)
+		return 1;
+
+	if (u->d[0] == limb)
+		return 0;
+	else if (u->d[0] > limb)
+		return 1;
+	else
+		return -1;
+}
+
+int mpi_cmp(MPI u, MPI v)
+{
+	mpi_size_t usize, vsize;
+	int cmp;
+
+	mpi_normalize(u);
+	mpi_normalize(v);
+	usize = u->nlimbs;
+	vsize = v->nlimbs;
+	if (!u->sign && v->sign)
+		return 1;
+	if (u->sign && !v->sign)
+		return -1;
+	if (usize != vsize && !u->sign && !v->sign)
+		return usize - vsize;
+	if (usize != vsize && u->sign && v->sign)
+		return vsize + usize;
+	if (!usize)
+		return 0;
+	cmp = mpihelp_cmp(u->d, v->d, usize);
+	if (!cmp)
+		return 0;
+	if ((cmp < 0 ? 1 : 0) == (u->sign ? 1 : 0))
+		return 1;
+	return -1;
+}

lib/mpi/mpi-div.c

+/* mpi-div.c  -  MPI functions
+ *	Copyright (C) 1994, 1996 Free Software Foundation, Inc.
+ *	Copyright (C) 1998, 1999, 2000, 2001 Free Software Foundation, Inc.
+ *
+ * This file is part of GnuPG.
+ *
+ * GnuPG is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * GnuPG is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
+ *
+ * Note: This code is heavily based on the GNU MP Library.
+ *	 Actually it's the same code with only minor changes in the
+ *	 way the data is stored; this is to support the abstraction
+ *	 of an optional secure memory allocation which may be used
+ *	 to avoid revealing of sensitive data due to paging etc.
+ *	 The GNU MP Library itself is published under the LGPL;
+ *	 however I decided to publish this code under the plain GPL.
+ */
+
+#include <linux/string.h>
+#include "mpi-internal.h"
+#include "longlong.h"
+
+int mpi_fdiv_r(MPI rem, MPI dividend, MPI divisor)
+{
+	int rc = -ENOMEM;
+	int divisor_sign = divisor->sign;
+	MPI temp_divisor = NULL;
+
+	/* We need the original value of the divisor after the remainder has been
+	 * preliminary calculated.      We have to copy it to temporary space if it's
+	 * the same variable as REM.  */
+	if (rem == divisor) {
+		if (mpi_copy(&temp_divisor, divisor) < 0)
+			goto nomem;
+		divisor = temp_divisor;
+	}
+
+	if (mpi_tdiv_qr(NULL, rem, dividend, divisor) < 0)
+		goto nomem;
+	if (((divisor_sign ? 1 : 0) ^ (dividend->sign ? 1 : 0)) && rem->nlimbs)
+		if (mpi_add(rem, rem, divisor) < 0)
+			goto nomem;
+
+	rc = 0;
+
+nomem:
+	if (temp_divisor)
+		mpi_free(temp_divisor);
+	return rc;
+}
+
+/****************
+ * Division rounding the quotient towards -infinity.
+ * The remainder gets the same sign as the denominator.
+ * rem is optional
+ */
+
+ulong mpi_fdiv_r_ui(MPI rem, MPI dividend, ulong divisor)
+{
+	mpi_limb_t rlimb;
+
+	rlimb = mpihelp_mod_1(dividend->d, dividend->nlimbs, divisor);
+	if (rlimb && dividend->sign)
+		rlimb = divisor - rlimb;
+
+	if (rem) {
+		rem->d[0] = rlimb;
+		rem->nlimbs = rlimb ? 1 : 0;
+	}
+	return rlimb;
+}
+
+int mpi_fdiv_q(MPI quot, MPI dividend, MPI divisor)
+{
+	MPI tmp = mpi_alloc(mpi_get_nlimbs(quot));
+	if (!tmp)
+		return -ENOMEM;
+	mpi_fdiv_qr(quot, tmp, dividend, divisor);
+	mpi_free(tmp);
+	return 0;
+}
+
+int mpi_fdiv_qr(MPI quot, MPI rem, MPI dividend, MPI divisor)
+{
+	int divisor_sign = divisor->sign;
+	MPI temp_divisor = NULL;
+
+	if (quot == divisor || rem == divisor) {
+		if (mpi_copy(&temp_divisor, divisor) < 0)
+			return -ENOMEM;
+		divisor = temp_divisor;
+	}
+
+	if (mpi_tdiv_qr(quot, rem, dividend, divisor) < 0)
+		goto nomem;
+
+	if ((divisor_sign ^ dividend->sign) && rem->nlimbs) {
+		if (mpi_sub_ui(quot, quot, 1) < 0)
+			goto nomem;
+		if (mpi_add(rem, rem, divisor) < 0)
+			goto nomem;
+	}
+
+	if (temp_divisor)
+		mpi_free(temp_divisor);
+
+	return 0;
+
+nomem:
+	mpi_free(temp_divisor);
+	return -ENOMEM;
+}
+
+/* If den == quot, den needs temporary storage.
+ * If den == rem, den needs temporary storage.
+ * If num == quot, num needs temporary storage.
+ * If den has temporary storage, it can be normalized while being copied,
+ *   i.e no extra storage should be allocated.
+ */
+
+int mpi_tdiv_r(MPI rem, MPI num, MPI den)
+{
+	return mpi_tdiv_qr(NULL, rem, num, den);
+}
+
+int mpi_tdiv_qr(MPI quot, MPI rem, MPI num, MPI den)
+{
+	int rc = -ENOMEM;
+	mpi_ptr_t np, dp;
+	mpi_ptr_t qp, rp;
+	mpi_size_t nsize = num->nlimbs;
+	mpi_size_t dsize = den->nlimbs;
+	mpi_size_t qsize, rsize;
+	mpi_size_t sign_remainder = num->sign;
+	mpi_size_t sign_quotient = num->sign ^ den->sign;
+	unsigned normalization_steps;
+	mpi_limb_t q_limb;
+	mpi_ptr_t marker[5];
+	int markidx = 0;
+
+	memset(marker, 0, sizeof(marker));
+
+	/* Ensure space is enough for quotient and remainder.
+	 * We need space for an extra limb in the remainder, because it's
+	 * up-shifted (normalized) below.  */
+	rsize = nsize + 1;
+	if (mpi_resize(rem, rsize) < 0)
+		goto nomem;
+
+	qsize = rsize - dsize;	/* qsize cannot be bigger than this.  */
+	if (qsize <= 0) {
+		if (num != rem) {
+			rem->nlimbs = num->nlimbs;
+			rem->sign = num->sign;
+			MPN_COPY(rem->d, num->d, nsize);
+		}
+		if (quot) {
+			/* This needs to follow the assignment to rem, in case the
+			 * numerator and quotient are the same.  */
+			quot->nlimbs = 0;
+			quot->sign = 0;
+		}
+		return 0;
+	}
+
+	if (quot)
+		if (mpi_resize(quot, qsize) < 0)
+			goto nomem;
+
+	/* Read pointers here, when reallocation is finished.  */
+	np = num->d;
+	dp = den->d;
+	rp = rem->d;
+
+	/* Optimize division by a single-limb divisor.  */
+	if (dsize == 1) {
+		mpi_limb_t rlimb;
+		if (quot) {
+			qp = quot->d;
+			rlimb = mpihelp_divmod_1(qp, np, nsize, dp[0]);
+			qsize -= qp[qsize - 1] == 0;
+			quot->nlimbs = qsize;
+			quot->sign = sign_quotient;
+		} else
+			rlimb = mpihelp_mod_1(np, nsize, dp[0]);
+		rp[0] = rlimb;
+		rsize = rlimb != 0 ? 1 : 0;
+		rem->nlimbs = rsize;
+		rem->sign = sign_remainder;
+		return 0;
+	}
+
+	if (quot) {
+		qp = quot->d;
+		/* Make sure QP and NP point to different objects.  Otherwise the
+		 * numerator would be gradually overwritten by the quotient limbs.  */
+		if (qp == np) {	/* Copy NP object to temporary space.  */
+			np = marker[markidx++] = mpi_alloc_limb_space(nsize);
+			MPN_COPY(np, qp, nsize);
+		}
+	} else			/* Put quotient at top of remainder. */
+		qp = rp + dsize;
+
+	count_leading_zeros(normalization_steps, dp[dsize - 1]);
+
+	/* Normalize the denominator, i.e. make its most significant bit set by
+	 * shifting it NORMALIZATION_STEPS bits to the left.  Also shift the
+	 * numerator the same number of steps (to keep the quotient the same!).
+	 */
+	if (normalization_steps) {
+		mpi_ptr_t tp;
+		mpi_limb_t nlimb;
+
+		/* Shift up the denominator setting the most significant bit of
+		 * the most significant word.  Use temporary storage not to clobber
+		 * the original contents of the denominator.  */
+		tp = marker[markidx++] = mpi_alloc_limb_space(dsize);
+		if (!tp)
+			goto nomem;
+		mpihelp_lshift(tp, dp, dsize, normalization_steps);
+		dp = tp;
+
+		/* Shift up the numerator, possibly introducing a new most
+		 * significant word.  Move the shifted numerator in the remainder
+		 * meanwhile.  */
+		nlimb = mpihelp_lshift(rp, np, nsize, normalization_steps);
+		if (nlimb) {
+			rp[nsize] = nlimb;
+			rsize = nsize + 1;
+		} else
+			rsize = nsize;
+	} else {
+		/* The denominator is already normalized, as required.  Copy it to
+		 * temporary space if it overlaps with the quotient or remainder.  */
+		if (dp == rp || (quot && (dp == qp))) {
+			mpi_ptr_t tp;
+
+			tp = marker[markidx++] = mpi_alloc_limb_space(dsize);
+			if (!tp)
+				goto nomem;
+			MPN_COPY(tp, dp, dsize);
+			dp = tp;
+		}
+
+		/* Move the numerator to the remainder.  */
+		if (rp != np)
+			MPN_COPY(rp, np, nsize);
+
+		rsize = nsize;
+	}
+
+	q_limb = mpihelp_divrem(qp, 0, rp, rsize, dp, dsize);
+
+	if (quot) {
+		qsize = rsize - dsize;
+		if (q_limb) {
+			qp[qsize] = q_limb;
+			qsize += 1;
+		}
+
+		quot->nlimbs = qsize;
+		quot->sign = sign_quotient;
+	}
+
+	rsize = dsize;
+	MPN_NORMALIZE(rp, rsize);
+
+	if (normalization_steps && rsize) {
+		mpihelp_rshift(rp, rp, rsize, normalization_steps);
+		rsize -= rp[rsize - 1] == 0 ? 1 : 0;
+	}
+
+	rem->nlimbs = rsize;
+	rem->sign = sign_remainder;
+
+	rc = 0;
+nomem:
+	while (markidx)
+		mpi_free_limb_space(marker[--markidx]);
+	return rc;
+}
+
+int mpi_tdiv_q_2exp(MPI w, MPI u, unsigned count)
+{
+	mpi_size_t usize, wsize;
+	mpi_size_t limb_cnt;
+
+	usize = u->nlimbs;
+	limb_cnt = count / BITS_PER_MPI_LIMB;
+	wsize = usize - limb_cnt;
+	if (limb_cnt >= usize)
+		w->nlimbs = 0;
+	else {
+		mpi_ptr_t wp;
+		mpi_ptr_t up;
+
+		if (RESIZE_IF_NEEDED(w, wsize) < 0)
+			return -ENOMEM;
+		wp = w->d;
+		up = u->d;
+
+		count %= BITS_PER_MPI_LIMB;
+		if (count) {
+			mpihelp_rshift(wp, up + limb_cnt, wsize, count);
+			wsize -= !wp[wsize - 1];
+		} else {
+			MPN_COPY_INCR(wp, up + limb_cnt, wsize);
+		}
+
+		w->nlimbs = wsize;
+	}
+	return 0;
+}
+
+/****************
+ * Check whether dividend is divisible by divisor
+ * (note: divisor must fit into a limb)
+ */
+int mpi_divisible_ui(MPI dividend, ulong divisor)
+{
+	return !mpihelp_mod_1(dividend->d, dividend->nlimbs, divisor);
+}

lib/mpi/mpi-gcd.c

+/* mpi-gcd.c  -  MPI functions
+ * Copyright (C) 1998, 1999, 2000, 2001 Free Software Foundation, Inc.
+ *
+ * This file is part of GnuPG.
+ *
+ * GnuPG is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * GnuPG is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
+ */
+
+#include "mpi-internal.h"
+
+/****************
+ * Find the greatest common divisor G of A and B.
+ * Return: true if this 1, false in all other cases
+ */
+int mpi_gcd(MPI g, const MPI xa, const MPI xb)
+{
+	MPI a = NULL, b = NULL;
+
+	if (mpi_copy(&a, xa) < 0)
+		goto nomem;
+
+	if (mpi_copy(&b, xb) < 0)
+		goto nomem;
+
+	/* TAOCP Vol II, 4.5.2, Algorithm A */
+	a->sign = 0;
+	b->sign = 0;
+	while (mpi_cmp_ui(b, 0)) {
+		if (mpi_fdiv_r(g, a, b) < 0)	/* g used as temorary variable */
+			goto nomem;
+		if (mpi_set(a, b) < 0)
+			goto nomem;
+		if (mpi_set(b, g) < 0)
+			goto nomem;
+	}
+	if (mpi_set(g, a) < 0)
+		goto nomem;
+
+	mpi_free(a);
+	mpi_free(b);
+	return !mpi_cmp_ui(g, 1);
+
+nomem:
+	mpi_free(a);
+	mpi_free(b);
+	return -ENOMEM;
+}

lib/mpi/mpi-inline.c

+/* mpi-inline.c
+ * Copyright (C) 1999, 2000, 2001 Free Software Foundation, Inc.
+ *
+ * This file is part of GnuPG.
+ *
+ * GnuPG is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * GnuPG is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
+ */
+
+/* put the inline functions as real functions into the lib */
+#define G10_MPI_INLINE_DECL
+
+#include "mpi-internal.h"
+
+/* always include the header becuase it is only
+ * included by mpi-internal if __GCC__ is defined but we
+ * need it here in all cases and the above definition of
+ * of the macro allows us to do so
+ */
+#include "mpi-inline.h"

lib/mpi/mpi-inline.h

+/* mpi-inline.h  -  Internal to the Multi Precision Integers
+ *	Copyright (C) 1994, 1996, 1998, 1999 Free Software Foundation, Inc.
+ *
+ * This file is part of GnuPG.
+ *
+ * GnuPG is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * GnuPG is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
+ *
+ * Note: This code is heavily based on the GNU MP Library.
+ *	 Actually it's the same code with only minor changes in the
+ *	 way the data is stored; this is to support the abstraction
+ *	 of an optional secure memory allocation which may be used
+ *	 to avoid revealing of sensitive data due to paging etc.
+ *	 The GNU MP Library itself is published under the LGPL;
+ *	 however I decided to publish this code under the plain GPL.
+ */
+
+#ifndef G10_MPI_INLINE_H
+#define G10_MPI_INLINE_H
+
+#ifndef G10_MPI_INLINE_DECL
+#define G10_MPI_INLINE_DECL  extern inline
+#endif
+
+G10_MPI_INLINE_DECL mpi_limb_t
+mpihelp_add_1(mpi_ptr_t res_ptr, mpi_ptr_t s1_ptr,
+	      mpi_size_t s1_size, mpi_limb_t s2_limb)
+{
+	mpi_limb_t x;
+
+	x = *s1_ptr++;
+	s2_limb += x;
+	*res_ptr++ = s2_limb;
+	if (s2_limb < x) {	/* sum is less than the left operand: handle carry */
+		while (--s1_size) {
+			x = *s1_ptr++ + 1;	/* add carry */
+			*res_ptr++ = x;	/* and store */
+			if (x)	/* not 0 (no overflow): we can stop */
+				goto leave;
+		}
+		return 1;	/* return carry (size of s1 to small) */
+	}
+
+leave:
+	if (res_ptr != s1_ptr) {	/* not the same variable */
+		mpi_size_t i;	/* copy the rest */
+		for (i = 0; i < s1_size - 1; i++)
+			res_ptr[i] = s1_ptr[i];
+	}
+	return 0;		/* no carry */
+}
+
+G10_MPI_INLINE_DECL mpi_limb_t
+mpihelp_add(mpi_ptr_t res_ptr, mpi_ptr_t s1_ptr, mpi_size_t s1_size,
+	    mpi_ptr_t s2_ptr, mpi_size_t s2_size)
+{
+	mpi_limb_t cy = 0;
+
+	if (s2_size)
+		cy = mpihelp_add_n(res_ptr, s1_ptr, s2_ptr, s2_size);
+
+	if (s1_size - s2_size)
+		cy = mpihelp_add_1(res_ptr + s2_size, s1_ptr + s2_size,
+				   s1_size - s2_size, cy);
+	return cy;
+}
+
+G10_MPI_INLINE_DECL mpi_limb_t
+mpihelp_sub_1(mpi_ptr_t res_ptr, mpi_ptr_t s1_ptr,
+	      mpi_size_t s1_size, mpi_limb_t s2_limb)
+{
+	mpi_limb_t x;
+
+	x = *s1_ptr++;
+	s2_limb = x - s2_limb;
+	*res_ptr++ = s2_limb;
+	if (s2_limb > x) {
+		while (--s1_size) {
+			x = *s1_ptr++;
+			*res_ptr++ = x - 1;
+			if (x)
+				goto leave;
+		}
+		return 1;
+	}
+
+leave:
+	if (res_ptr != s1_ptr) {
+		mpi_size_t i;
+		for (i = 0; i < s1_size - 1; i++)
+			res_ptr[i] = s1_ptr[i];
+	}
+	return 0;
+}
+
+G10_MPI_INLINE_DECL mpi_limb_t
+mpihelp_sub(mpi_ptr_t res_ptr, mpi_ptr_t s1_ptr, mpi_size_t s1_size,
+	    mpi_ptr_t s2_ptr, mpi_size_t s2_size)
+{
+	mpi_limb_t cy = 0;
+
+	if (s2_size)
+		cy = mpihelp_sub_n(res_ptr, s1_ptr, s2_ptr, s2_size);
+
+	if (s1_size - s2_size)
+		cy = mpihelp_sub_1(res_ptr + s2_size, s1_ptr + s2_size,
+				   s1_size - s2_size, cy);
+	return cy;
+}
+
+#endif /*G10_MPI_INLINE_H */

lib/mpi/mpi-internal.h

+/* mpi-internal.h  -  Internal to the Multi Precision Integers
+ *	Copyright (C) 1994, 1996 Free Software Foundation, Inc.
+ *	Copyright (C) 1998, 2000 Free Software Foundation, Inc.
+ *
+ * This file is part of GnuPG.
+ *
+ * GnuPG is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * GnuPG is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
+ *
+ * Note: This code is heavily based on the GNU MP Library.
+ *	 Actually it's the same code with only minor changes in the
+ *	 way the data is stored; this is to support the abstraction
+ *	 of an optional secure memory allocation which may be used
+ *	 to avoid revealing of sensitive data due to paging etc.
+ *	 The GNU MP Library itself is published under the LGPL;
+ *	 however I decided to publish this code under the plain GPL.
+ */
+
+#ifndef G10_MPI_INTERNAL_H
+#define G10_MPI_INTERNAL_H
+
+#include <linux/module.h>
+#include <linux/kernel.h>
+#include <linux/slab.h>
+#include <linux/string.h>
+#include <linux/mpi.h>
+#include <linux/errno.h>
+
+#define log_debug printk
+#define log_bug printk
+
+#define assert(x) \
+	do { \
+		if (!x) \
+			log_bug("failed assertion\n"); \
+	} while (0);
+
+/* If KARATSUBA_THRESHOLD is not already defined, define it to a
+ * value which is good on most machines.  */
+
+/* tested 4, 16, 32 and 64, where 16 gave the best performance when
+ * checking a 768 and a 1024 bit ElGamal signature.
+ * (wk 22.12.97) */
+#ifndef KARATSUBA_THRESHOLD
+#define KARATSUBA_THRESHOLD 16
+#endif
+
+/* The code can't handle KARATSUBA_THRESHOLD smaller than 2.  */
+#if KARATSUBA_THRESHOLD < 2
+#undef KARATSUBA_THRESHOLD
+#define KARATSUBA_THRESHOLD 2
+#endif
+
+typedef mpi_limb_t *mpi_ptr_t;	/* pointer to a limb */
+typedef int mpi_size_t;		/* (must be a signed type) */
+
+#define ABS(x) (x >= 0 ? x : -x)
+#define MIN(l, o) ((l) < (o) ? (l) : (o))
+#define MAX(h, i) ((h) > (i) ? (h) : (i))
+
+static inline int RESIZE_IF_NEEDED(MPI a, unsigned b)
+{
+	if (a->alloced < b)
+		return mpi_resize(a, b);
+	return 0;
+}
+
+/* Copy N limbs from S to D.  */
+#define MPN_COPY(d, s, n) \
+	do {					\
+		mpi_size_t _i;			\
+		for (_i = 0; _i < (n); _i++)	\
+			(d)[_i] = (s)[_i];	\
+	} while (0)
+
+#define MPN_COPY_INCR(d, s, n) \
+	do {					\
+		mpi_size_t _i;			\
+		for (_i = 0; _i < (n); _i++)	\
+			(d)[_i] = (d)[_i];	\
+	} while (0)
+
+#define MPN_COPY_DECR(d, s, n) \
+	do {					\
+		mpi_size_t _i;			\
+		for (_i = (n)-1; _i >= 0; _i--) \
+			(d)[_i] = (s)[_i];	\
+	} while (0)
+
+/* Zero N limbs at D */
+#define MPN_ZERO(d, n) \
+	do {					\
+		int  _i;			\
+		for (_i = 0; _i < (n); _i++)	\
+			(d)[_i] = 0;		\
+	} while (0)
+
+#define MPN_NORMALIZE(d, n)  \
+	do {					\
+		while ((n) > 0) {		\
+			if ((d)[(n)-1])		\
+				break;		\
+			(n)--;			\
+		}				\
+	} while (0)
+
+#define MPN_NORMALIZE_NOT_ZERO(d, n) \
+	do {				\
+		for (;;) {		\
+			if ((d)[(n)-1])	\
+				break;	\
+			(n)--;		\
+		}			\
+	} while (0)
+
+#define MPN_MUL_N_RECURSE(prodp, up, vp, size, tspace) \
+	do {							\
+		if ((size) < KARATSUBA_THRESHOLD)		\
+			mul_n_basecase(prodp, up, vp, size);	\
+		else						\
+			mul_n(prodp, up, vp, size, tspace);	\
+	} while (0);
+
+/* Divide the two-limb number in (NH,,NL) by D, with DI being the largest
+ * limb not larger than (2**(2*BITS_PER_MP_LIMB))/D - (2**BITS_PER_MP_LIMB).
+ * If this would yield overflow, DI should be the largest possible number
+ * (i.e., only ones).  For correct operation, the most significant bit of D
+ * has to be set.  Put the quotient in Q and the remainder in R.
+ */
+#define UDIV_QRNND_PREINV(q, r, nh, nl, d, di) \
+	do {								\
+		mpi_limb_t _q, _ql, _r;					\
+		mpi_limb_t _xh, _xl;					\
+		umul_ppmm(_q, _ql, (nh), (di));				\
+		_q += (nh);	/* DI is 2**BITS_PER_MPI_LIMB too small */ \
+		umul_ppmm(_xh, _xl, _q, (d));				\
+		sub_ddmmss(_xh, _r, (nh), (nl), _xh, _xl);		\
+		if (_xh) {						\
+			sub_ddmmss(_xh, _r, _xh, _r, 0, (d));		\
+			_q++;						\
+			if (_xh) {					\
+				sub_ddmmss(_xh, _r, _xh, _r, 0, (d));	\
+				_q++;					\
+			}						\
+		}							\
+		if (_r >= (d)) {					\
+			_r -= (d);					\
+			_q++;						\
+		}							\
+		(r) = _r;						\
+		(q) = _q;						\
+	} while (0)
+
+/*-- mpiutil.c --*/
+mpi_ptr_t mpi_alloc_limb_space(unsigned nlimbs);
+void mpi_free_limb_space(mpi_ptr_t a);
+void mpi_assign_limb_space(MPI a, mpi_ptr_t ap, unsigned nlimbs);
+
+/*-- mpi-bit.c --*/
+void mpi_rshift_limbs(MPI a, unsigned int count);
+int mpi_lshift_limbs(MPI a, unsigned int count);
+
+/*-- mpihelp-add.c --*/
+mpi_limb_t mpihelp_add_1(mpi_ptr_t res_ptr, mpi_ptr_t s1_ptr,
+			 mpi_size_t s1_size, mpi_limb_t s2_limb);
+mpi_limb_t mpihelp_add_n(mpi_ptr_t res_ptr, mpi_ptr_t s1_ptr,
+			 mpi_ptr_t s2_ptr, mpi_size_t size);
+mpi_limb_t mpihelp_add(mpi_ptr_t res_ptr, mpi_ptr_t s1_ptr, mpi_size_t s1_size,
+		       mpi_ptr_t s2_ptr, mpi_size_t s2_size);
+
+/*-- mpihelp-sub.c --*/
+mpi_limb_t mpihelp_sub_1(mpi_ptr_t res_ptr, mpi_ptr_t s1_ptr,
+			 mpi_size_t s1_size, mpi_limb_t s2_limb);
+mpi_limb_t mpihelp_sub_n(mpi_ptr_t res_ptr, mpi_ptr_t s1_ptr,
+			 mpi_ptr_t s2_ptr, mpi_size_t size);
+mpi_limb_t mpihelp_sub(mpi_ptr_t res_ptr, mpi_ptr_t s1_ptr, mpi_size_t s1_size,
+		       mpi_ptr_t s2_ptr, mpi_size_t s2_size);
+
+/*-- mpihelp-cmp.c --*/
+int mpihelp_cmp(mpi_ptr_t op1_ptr, mpi_ptr_t op2_ptr, mpi_size_t size);
+
+/*-- mpihelp-mul.c --*/
+
+struct karatsuba_ctx {
+	struct karatsuba_ctx *next;
+	mpi_ptr_t tspace;
+	mpi_size_t tspace_size;
+	mpi_ptr_t tp;
+	mpi_size_t tp_size;
+};
+
+void mpihelp_release_karatsuba_ctx(struct karatsuba_ctx *ctx);
+
+mpi_limb_t mpihelp_addmul_1(mpi_ptr_t res_ptr, mpi_ptr_t s1_ptr,
+			    mpi_size_t s1_size, mpi_limb_t s2_limb);
+mpi_limb_t mpihelp_submul_1(mpi_ptr_t res_ptr, mpi_ptr_t s1_ptr,
+			    mpi_size_t s1_size, mpi_limb_t s2_limb);
+int mpihelp_mul_n(mpi_ptr_t prodp, mpi_ptr_t up, mpi_ptr_t vp, mpi_size_t size);
+int mpihelp_mul(mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t usize,
+		mpi_ptr_t vp, mpi_size_t vsize, mpi_limb_t *_result);
+void mpih_sqr_n_basecase(mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t size);
+void mpih_sqr_n(mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t size,
+		mpi_ptr_t tspace);
+
+int mpihelp_mul_karatsuba_case(mpi_ptr_t prodp,
+			       mpi_ptr_t up, mpi_size_t usize,
+			       mpi_ptr_t vp, mpi_size_t vsize,
+			       struct karatsuba_ctx *ctx);
+
+/*-- mpihelp-mul_1.c (or xxx/cpu/ *.S) --*/
+mpi_limb_t mpihelp_mul_1(mpi_ptr_t res_ptr, mpi_ptr_t s1_ptr,
+			 mpi_size_t s1_size, mpi_limb_t s2_limb);
+
+/*-- mpihelp-div.c --*/
+mpi_limb_t mpihelp_mod_1(mpi_ptr_t dividend_ptr, mpi_size_t dividend_size,
+			 mpi_limb_t divisor_limb);
+mpi_limb_t mpihelp_divrem(mpi_ptr_t qp, mpi_size_t qextra_limbs,
+			  mpi_ptr_t np, mpi_size_t nsize,
+			  mpi_ptr_t dp, mpi_size_t dsize);
+mpi_limb_t mpihelp_divmod_1(mpi_ptr_t quot_ptr,
+			    mpi_ptr_t dividend_ptr, mpi_size_t dividend_size,
+			    mpi_limb_t divisor_limb);
+
+/*-- mpihelp-shift.c --*/
+mpi_limb_t mpihelp_lshift(mpi_ptr_t wp, mpi_ptr_t up, mpi_size_t usize,
+			  unsigned cnt);
+mpi_limb_t mpihelp_rshift(mpi_ptr_t wp, mpi_ptr_t up, mpi_size_t usize,
+			  unsigned cnt);
+
+/* Define stuff for longlong.h.  */
+#define W_TYPE_SIZE BITS_PER_MPI_LIMB
+typedef mpi_limb_t UWtype;
+typedef unsigned int UHWtype;
+#if defined(__GNUC__)
+typedef unsigned int UQItype __attribute__ ((mode(QI)));
+typedef int SItype __attribute__ ((mode(SI)));
+typedef unsigned int USItype __attribute__ ((mode(SI)));
+typedef int DItype __attribute__ ((mode(DI)));
+typedef unsigned int UDItype __attribute__ ((mode(DI)));
+#else
+typedef unsigned char UQItype;
+typedef long SItype;
+typedef unsigned long USItype;
+#endif
+
+#ifdef __GNUC__
+#include "mpi-inline.h"
+#endif
+
+#endif /*G10_MPI_INTERNAL_H */

lib/mpi/mpi-inv.c

+/* mpi-inv.c  -  MPI functions
+ * Copyright (C) 1998, 1999, 2000, 2001 Free Software Foundation, Inc.
+ *
+ * This file is part of GnuPG.
+ *
+ * GnuPG is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * GnuPG is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
+ */
+
+#include "mpi-internal.h"
+
+/****************
+ * Calculate the multiplicative inverse X of A mod N
+ * That is: Find the solution x for
+ *		1 = (a*x) mod n
+ */
+int mpi_invm(MPI x, const MPI a, const MPI n)
+{
+	/* Extended Euclid's algorithm (See TAOPC Vol II, 4.5.2, Alg X)
+	 * modified according to Michael Penk's solution for Exercice 35
+	 * with further enhancement */
+	MPI u = NULL, v = NULL;
+	MPI u1 = NULL, u2 = NULL, u3 = NULL;
+	MPI v1 = NULL, v2 = NULL, v3 = NULL;
+	MPI t1 = NULL, t2 = NULL, t3 = NULL;
+	unsigned k;
+	int sign;
+	int odd = 0;
+	int rc = -ENOMEM;
+
+	if (mpi_copy(&u, a) < 0)
+		goto cleanup;
+	if (mpi_copy(&v, n) < 0)
+		goto cleanup;
+
+	for (k = 0; !mpi_test_bit(u, 0) && !mpi_test_bit(v, 0); k++) {
+		if (mpi_rshift(u, u, 1) < 0)
+			goto cleanup;
+		if (mpi_rshift(v, v, 1) < 0)
+			goto cleanup;
+	}
+	odd = mpi_test_bit(v, 0);
+
+	u1 = mpi_alloc_set_ui(1);
+	if (!u1)
+		goto cleanup;
+	if (!odd) {
+		u2 = mpi_alloc_set_ui(0);
+		if (!u2)
+			goto cleanup;
+	}
+	if (mpi_copy(&u3, u) < 0)
+		goto cleanup;
+	if (mpi_copy(&v1, v) < 0)
+		goto cleanup;
+	if (!odd) {
+		v2 = mpi_alloc(mpi_get_nlimbs(u));
+		if (!v2)
+			goto cleanup;
+		if (mpi_sub(v2, u1, u) < 0)
+			goto cleanup;	/* U is used as const 1 */
+	}
+	if (mpi_copy(&v3, v) < 0)
+		goto cleanup;
+	if (mpi_test_bit(u, 0)) {	/* u is odd */
+		t1 = mpi_alloc_set_ui(0);
+		if (!t1)
+			goto cleanup;
+		if (!odd) {
+			t2 = mpi_alloc_set_ui(1);
+			if (!t2)
+				goto cleanup;
+			t2->sign = 1;
+		}
+		if (mpi_copy(&t3, v) < 0)
+			goto cleanup;
+		t3->sign = !t3->sign;
+		goto Y4;
+	} else {
+		t1 = mpi_alloc_set_ui(1);
+		if (!t1)
+			goto cleanup;
+		if (!odd) {
+			t2 = mpi_alloc_set_ui(0);
+			if (!t2)
+				goto cleanup;
+		}
+		if (mpi_copy(&t3, u) < 0)
+			goto cleanup;
+	}
+	do {
+		do {
+			if (!odd) {
+				if (mpi_test_bit(t1, 0) || mpi_test_bit(t2, 0)) {	/* one is odd */
+					if (mpi_add(t1, t1, v) < 0)
+						goto cleanup;
+					if (mpi_sub(t2, t2, u) < 0)
+						goto cleanup;
+				}
+				if (mpi_rshift(t1, t1, 1) < 0)
+					goto cleanup;
+				if (mpi_rshift(t2, t2, 1) < 0)
+					goto cleanup;
+				if (mpi_rshift(t3, t3, 1) < 0)
+					goto cleanup;
+			} else {
+				if (mpi_test_bit(t1, 0))
+					if (mpi_add(t1, t1, v) < 0)
+						goto cleanup;
+				if (mpi_rshift(t1, t1, 1) < 0)
+					goto cleanup;
+				if (mpi_rshift(t3, t3, 1) < 0)
+					goto cleanup;
+			}
+Y4:
+			;
+		} while (!mpi_test_bit(t3, 0));	/* while t3 is even */
+
+		if (!t3->sign) {
+			if (mpi_set(u1, t1) < 0)
+				goto cleanup;
+			if (!odd)
+				if (mpi_set(u2, t2) < 0)
+					goto cleanup;
+			if (mpi_set(u3, t3) < 0)
+				goto cleanup;
+		} else {
+			if (mpi_sub(v1, v, t1) < 0)
+				goto cleanup;
+			sign = u->sign;
+			u->sign = !u->sign;
+			if (!odd)
+				if (mpi_sub(v2, u, t2) < 0)
+					goto cleanup;
+			u->sign = sign;
+			sign = t3->sign;
+			t3->sign = !t3->sign;
+			if (mpi_set(v3, t3) < 0)
+				goto cleanup;
+			t3->sign = sign;
+		}
+		if (mpi_sub(t1, u1, v1) < 0)
+			goto cleanup;
+		if (!odd)
+			if (mpi_sub(t2, u2, v2) < 0)
+				goto cleanup;
+		if (mpi_sub(t3, u3, v3) < 0)
+			goto cleanup;
+		if (t1->sign) {
+			if (mpi_add(t1, t1, v) < 0)
+				goto cleanup;
+			if (!odd)
+				if (mpi_sub(t2, t2, u) < 0)
+					goto cleanup;
+		}
+	} while (mpi_cmp_ui(t3, 0));	/* while t3 != 0 */
+	/* mpi_lshift( u3, k ); */
+	rc = mpi_set(x, u1);
+
+cleanup:
+	mpi_free(u1);
+	mpi_free(v1);
+	mpi_free(t1);
+	if (!odd) {
+		mpi_free(u2);
+		mpi_free(v2);
+		mpi_free(t2);
+	}
+	mpi_free(u3);
+	mpi_free(v3);
+	mpi_free(t3);
+
+	mpi_free(u);
+	mpi_free(v);
+	return rc;
+}

lib/mpi/mpi-mpow.c

+/* mpi-mpow.c  -  MPI functions
+ * Copyright (C) 1998, 1999, 2000 Free Software Foundation, Inc.
+ *
+ * This file is part of GnuPG.
+ *
+ * GnuPG is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * GnuPG is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
+ */
+
+#include "mpi-internal.h"
+#include "longlong.h"
+
+static int build_index(const MPI *exparray, int k, int i, int t)
+{
+	int j, bitno;
+	int index = 0;
+
+	bitno = t - i;
+	for (j = k - 1; j >= 0; j--) {
+		index <<= 1;
+		if (mpi_test_bit(exparray[j], bitno))
+			index |= 1;
+	}
+	return index;
+}
+
+/****************
+ * RES = (BASE[0] ^ EXP[0]) *  (BASE[1] ^ EXP[1]) * ... * mod M
+ */
+int mpi_mulpowm(MPI res, MPI *basearray, MPI *exparray, MPI m)
+{
+	int rc = -ENOMEM;
+	int k;			/* number of elements */
+	int t;			/* bit size of largest exponent */
+	int i, j, idx;
+	MPI *G = NULL;		/* table with precomputed values of size 2^k */
+	MPI tmp = NULL;
+
+	for (k = 0; basearray[k]; k++)
+		;
+	if (!k) {
+		pr_emerg("mpi_mulpowm: assert(k) failed\n");
+		BUG();
+	}
+	for (t = 0, i = 0; (tmp = exparray[i]); i++) {
+		j = mpi_get_nbits(tmp);
+		if (j > t)
+			t = j;
+	}
+	if (i != k) {
+		pr_emerg("mpi_mulpowm: assert(i==k) failed\n");
+		BUG();
+	}
+	if (!t) {
+		pr_emerg("mpi_mulpowm: assert(t) failed\n");
+		BUG();
+	}
+	if (k >= 10) {
+		pr_emerg("mpi_mulpowm: assert(k<10) failed\n");
+		BUG();
+	}
+
+	G = kzalloc((1 << k) * sizeof *G, GFP_KERNEL);
+	if (!G)
+		goto nomem;
+
+	/* and calculate */
+	tmp = mpi_alloc(mpi_get_nlimbs(m) + 1);
+	if (!tmp)
+		goto nomem;
+	if (mpi_set_ui(res, 1) < 0)
+		goto nomem;
+	for (i = 1; i <= t; i++) {
+		if (mpi_mulm(tmp, res, res, m) < 0)
+			goto nomem;
+		idx = build_index(exparray, k, i, t);
+		if (!(idx >= 0 && idx < (1 << k))) {
+			pr_emerg("mpi_mulpowm: assert(idx >= 0 && idx < (1<<k)) failed\n");
+			BUG();
+		}
+		if (!G[idx]) {
+			if (!idx) {
+				G[0] = mpi_alloc_set_ui(1);
+				if (!G[0])
+					goto nomem;
+			} else {
+				for (j = 0; j < k; j++) {
+					if ((idx & (1 << j))) {
+						if (!G[idx]) {
+							if (mpi_copy
+							    (&G[idx],
+							     basearray[j]) < 0)
+								goto nomem;
+						} else {
+							if (mpi_mulm
+							    (G[idx], G[idx],
+							     basearray[j],
+							     m) < 0)
+								goto nomem;
+						}
+					}
+				}
+				if (!G[idx]) {
+					G[idx] = mpi_alloc(0);
+					if (!G[idx])
+						goto nomem;
+				}
+			}
+		}
+		if (mpi_mulm(res, tmp, G[idx], m) < 0)
+			goto nomem;
+	}
+
+	rc = 0;
+nomem:
+	/* cleanup */
+	mpi_free(tmp);
+	for (i = 0; i < (1 << k); i++)
+		mpi_free(G[i]);
+	kfree(G);
+	return rc;
+}

lib/mpi/mpi-mul.c

+/* mpi-mul.c  -  MPI functions
+ *	Copyright (C) 1994, 1996 Free Software Foundation, Inc.
+ *	Copyright (C) 1998, 2001 Free Software Foundation, Inc.
+ *
+ * This file is part of GnuPG.
+ *
+ * GnuPG is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * GnuPG is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
+ *
+ * Note: This code is heavily based on the GNU MP Library.
+ *	 Actually it's the same code with only minor changes in the
+ *	 way the data is stored; this is to support the abstraction
+ *	 of an optional secure memory allocation which may be used
+ *	 to avoid revealing of sensitive data due to paging etc.
+ *	 The GNU MP Library itself is published under the LGPL;
+ *	 however I decided to publish this code under the plain GPL.
+ */
+
+#include "mpi-internal.h"
+
+int mpi_mul_ui(MPI prod, MPI mult, unsigned long small_mult)
+{
+	mpi_size_t size, prod_size;
+	mpi_ptr_t prod_ptr;
+	mpi_limb_t cy;
+	int sign;
+
+	size = mult->nlimbs;
+	sign = mult->sign;
+
+	if (!size || !small_mult) {
+		prod->nlimbs = 0;
+		prod->sign = 0;
+		return 0;
+	}
+
+	prod_size = size + 1;
+	if (prod->alloced < prod_size)
+		if (mpi_resize(prod, prod_size) < 0)
+			return -ENOMEM;
+	prod_ptr = prod->d;
+
+	cy = mpihelp_mul_1(prod_ptr, mult->d, size, (mpi_limb_t) small_mult);
+	if (cy)
+		prod_ptr[size++] = cy;
+	prod->nlimbs = size;
+	prod->sign = sign;
+	return 0;
+}
+
+int mpi_mul_2exp(MPI w, MPI u, unsigned long cnt)
+{
+	mpi_size_t usize, wsize, limb_cnt;
+	mpi_ptr_t wp;
+	mpi_limb_t wlimb;
+	int usign, wsign;
+
+	usize = u->nlimbs;
+	usign = u->sign;
+
+	if (!usize) {
+		w->nlimbs = 0;
+		w->sign = 0;
+		return 0;
+	}
+
+	limb_cnt = cnt / BITS_PER_MPI_LIMB;
+	wsize = usize + limb_cnt + 1;
+	if (w->alloced < wsize)
+		if (mpi_resize(w, wsize) < 0)
+			return -ENOMEM;
+	wp = w->d;
+	wsize = usize + limb_cnt;
+	wsign = usign;
+
+	cnt %= BITS_PER_MPI_LIMB;
+	if (cnt) {
+		wlimb = mpihelp_lshift(wp + limb_cnt, u->d, usize, cnt);
+		if (wlimb) {
+			wp[wsize] = wlimb;
+			wsize++;
+		}
+	} else {
+		MPN_COPY_DECR(wp + limb_cnt, u->d, usize);
+	}
+
+	/* Zero all whole limbs at low end.  Do it here and not before calling
+	 * mpn_lshift, not to lose for U == W.  */
+	MPN_ZERO(wp, limb_cnt);
+
+	w->nlimbs = wsize;
+	w->sign = wsign;
+	return 0;
+}
+
+int mpi_mul(MPI w, MPI u, MPI v)
+{
+	int rc = -ENOMEM;
+	mpi_size_t usize, vsize, wsize;
+	mpi_ptr_t up, vp, wp;
+	mpi_limb_t cy;
+	int usign, vsign, sign_product;
+	int assign_wp = 0;
+	mpi_ptr_t tmp_limb = NULL;
+
+	if (u->nlimbs < v->nlimbs) {	/* Swap U and V. */
+		usize = v->nlimbs;
+		usign = v->sign;
+		up = v->d;
+		vsize = u->nlimbs;
+		vsign = u->sign;
+		vp = u->d;
+	} else {
+		usize = u->nlimbs;
+		usign = u->sign;
+		up = u->d;
+		vsize = v->nlimbs;
+		vsign = v->sign;
+		vp = v->d;
+	}
+	sign_product = usign ^ vsign;
+	wp = w->d;
+
+	/* Ensure W has space enough to store the result.  */
+	wsize = usize + vsize;
+	if (w->alloced < (size_t) wsize) {
+		if (wp == up || wp == vp) {
+			wp = mpi_alloc_limb_space(wsize);
+			if (!wp)
+				goto nomem;
+			assign_wp = 1;
+		} else {
+			if (mpi_resize(w, wsize) < 0)
+				goto nomem;
+			wp = w->d;
+		}
+	} else {		/* Make U and V not overlap with W.      */
+		if (wp == up) {
+			/* W and U are identical.  Allocate temporary space for U.      */
+			up = tmp_limb = mpi_alloc_limb_space(usize);
+			if (!up)
+				goto nomem;
+			/* Is V identical too?  Keep it identical with U.  */
+			if (wp == vp)
+				vp = up;
+			/* Copy to the temporary space.  */
+			MPN_COPY(up, wp, usize);
+		} else if (wp == vp) {
+			/* W and V are identical.  Allocate temporary space for V.      */
+			vp = tmp_limb = mpi_alloc_limb_space(vsize);
+			if (!vp)
+				goto nomem;
+			/* Copy to the temporary space.  */
+			MPN_COPY(vp, wp, vsize);
+		}
+	}
+
+	if (!vsize)
+		wsize = 0;
+	else {
+		if (mpihelp_mul(wp, up, usize, vp, vsize, &cy) < 0)
+			goto nomem;
+		wsize -= cy ? 0 : 1;
+	}
+
+	if (assign_wp)
+		mpi_assign_limb_space(w, wp, wsize);
+
+	w->nlimbs = wsize;
+	w->sign = sign_product;
+	rc = 0;
+nomem:
+	if (tmp_limb)
+		mpi_free_limb_space(tmp_limb);
+	return rc;
+}
+
+int mpi_mulm(MPI w, MPI u, MPI v, MPI m)
+{
+	if (mpi_mul(w, u, v) < 0)
+		return -ENOMEM;
+	return mpi_fdiv_r(w, w, m);
+}

lib/mpi/mpi-pow.c

+/* mpi-pow.c  -  MPI functions
+ *	Copyright (C) 1994, 1996, 1998, 2000 Free Software Foundation, Inc.
+ *
+ * This file is part of GnuPG.
+ *
+ * GnuPG is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * GnuPG is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
+ *
+ * Note: This code is heavily based on the GNU MP Library.
+ *	 Actually it's the same code with only minor changes in the
+ *	 way the data is stored; this is to support the abstraction
+ *	 of an optional secure memory allocation which may be used
+ *	 to avoid revealing of sensitive data due to paging etc.
+ *	 The GNU MP Library itself is published under the LGPL;
+ *	 however I decided to publish this code under the plain GPL.
+ */
+
+#include <linux/string.h>
+#include "mpi-internal.h"
+#include "longlong.h"
+
+/****************
+ * RES = BASE ^ EXP mod MOD
+ */
+int mpi_powm(MPI res, MPI base, MPI exp, MPI mod)
+{
+	mpi_ptr_t mp_marker = NULL, bp_marker = NULL, ep_marker = NULL;
+	mpi_ptr_t xp_marker = NULL;
+	mpi_ptr_t tspace = NULL;
+	mpi_ptr_t rp, ep, mp, bp;
+	mpi_size_t esize, msize, bsize, rsize;
+	int esign, msign, bsign, rsign;
+	mpi_size_t size;
+	int mod_shift_cnt;
+	int negative_result;
+	int assign_rp = 0;
+	mpi_size_t tsize = 0;	/* to avoid compiler warning */
+	/* fixme: we should check that the warning is void */
+	int rc = -ENOMEM;
+
+	esize = exp->nlimbs;
+	msize = mod->nlimbs;
+	size = 2 * msize;
+	esign = exp->sign;
+	msign = mod->sign;
+
+	rp = res->d;
+	ep = exp->d;
+
+	if (!msize)
+		msize = 1 / msize;	/* provoke a signal */
+
+	if (!esize) {
+		/* Exponent is zero, result is 1 mod MOD, i.e., 1 or 0
+		 * depending on if MOD equals 1.  */
+		rp[0] = 1;
+		res->nlimbs = (msize == 1 && mod->d[0] == 1) ? 0 : 1;
+		res->sign = 0;
+		goto leave;
+	}
+
+	/* Normalize MOD (i.e. make its most significant bit set) as required by
+	 * mpn_divrem.  This will make the intermediate values in the calculation
+	 * slightly larger, but the correct result is obtained after a final
+	 * reduction using the original MOD value.  */
+	mp = mp_marker = mpi_alloc_limb_space(msize);
+	if (!mp)
+		goto enomem;
+	count_leading_zeros(mod_shift_cnt, mod->d[msize - 1]);
+	if (mod_shift_cnt)
+		mpihelp_lshift(mp, mod->d, msize, mod_shift_cnt);
+	else
+		MPN_COPY(mp, mod->d, msize);
+
+	bsize = base->nlimbs;
+	bsign = base->sign;
+	if (bsize > msize) {	/* The base is larger than the module. Reduce it. */
+		/* Allocate (BSIZE + 1) with space for remainder and quotient.
+		 * (The quotient is (bsize - msize + 1) limbs.)  */
+		bp = bp_marker = mpi_alloc_limb_space(bsize + 1);
+		if (!bp)
+			goto enomem;
+		MPN_COPY(bp, base->d, bsize);
+		/* We don't care about the quotient, store it above the remainder,
+		 * at BP + MSIZE.  */
+		mpihelp_divrem(bp + msize, 0, bp, bsize, mp, msize);
+		bsize = msize;
+		/* Canonicalize the base, since we are going to multiply with it
+		 * quite a few times.  */
+		MPN_NORMALIZE(bp, bsize);
+	} else
+		bp = base->d;
+
+	if (!bsize) {
+		res->nlimbs = 0;
+		res->sign = 0;
+		goto leave;
+	}
+
+	if (res->alloced < size) {
+		/* We have to allocate more space for RES.  If any of the input
+		 * parameters are identical to RES, defer deallocation of the old
+		 * space.  */
+		if (rp == ep || rp == mp || rp == bp) {
+			rp = mpi_alloc_limb_space(size);
+			if (!rp)
+				goto enomem;
+			assign_rp = 1;
+		} else {
+			if (mpi_resize(res, size) < 0)
+				goto enomem;
+			rp = res->d;
+		}
+	} else {		/* Make BASE, EXP and MOD not overlap with RES.  */
+		if (rp == bp) {
+			/* RES and BASE are identical.  Allocate temp. space for BASE.  */
+			BUG_ON(bp_marker);
+			bp = bp_marker = mpi_alloc_limb_space(bsize);
+			if (!bp)
+				goto enomem;
+			MPN_COPY(bp, rp, bsize);
+		}
+		if (rp == ep) {
+			/* RES and EXP are identical.  Allocate temp. space for EXP.  */
+			ep = ep_marker = mpi_alloc_limb_space(esize);
+			if (!ep)
+				goto enomem;
+			MPN_COPY(ep, rp, esize);
+		}
+		if (rp == mp) {
+			/* RES and MOD are identical.  Allocate temporary space for MOD. */
+			BUG_ON(mp_marker);
+			mp = mp_marker = mpi_alloc_limb_space(msize);
+			if (!mp)
+				goto enomem;
+			MPN_COPY(mp, rp, msize);
+		}
+	}
+
+	MPN_COPY(rp, bp, bsize);
+	rsize = bsize;
+	rsign = bsign;
+
+	{
+		mpi_size_t i;
+		mpi_ptr_t xp;
+		int c;
+		mpi_limb_t e;
+		mpi_limb_t carry_limb;
+		struct karatsuba_ctx karactx;
+
+		xp = xp_marker = mpi_alloc_limb_space(2 * (msize + 1));
+		if (!xp)
+			goto enomem;
+
+		memset(&karactx, 0, sizeof karactx);
+		negative_result = (ep[0] & 1) && base->sign;
+
+		i = esize - 1;
+		e = ep[i];
+		count_leading_zeros(c, e);
+		e = (e << c) << 1;	/* shift the exp bits to the left, lose msb */
+		c = BITS_PER_MPI_LIMB - 1 - c;
+
+		/* Main loop.
+		 *
+		 * Make the result be pointed to alternately by XP and RP.  This
+		 * helps us avoid block copying, which would otherwise be necessary
+		 * with the overlap restrictions of mpihelp_divmod. With 50% probability
+		 * the result after this loop will be in the area originally pointed
+		 * by RP (==RES->d), and with 50% probability in the area originally
+		 * pointed to by XP.
+		 */
+
+		for (;;) {
+			while (c) {
+				mpi_ptr_t tp;
+				mpi_size_t xsize;
+
+				/*if (mpihelp_mul_n(xp, rp, rp, rsize) < 0) goto enomem */
+				if (rsize < KARATSUBA_THRESHOLD)
+					mpih_sqr_n_basecase(xp, rp, rsize);
+				else {
+					if (!tspace) {
+						tsize = 2 * rsize;
+						tspace =
+						    mpi_alloc_limb_space(tsize);
+						if (!tspace)
+							goto enomem;
+					} else if (tsize < (2 * rsize)) {
+						mpi_free_limb_space(tspace);
+						tsize = 2 * rsize;
+						tspace =
+						    mpi_alloc_limb_space(tsize);
+						if (!tspace)
+							goto enomem;
+					}
+					mpih_sqr_n(xp, rp, rsize, tspace);
+				}
+
+				xsize = 2 * rsize;
+				if (xsize > msize) {
+					mpihelp_divrem(xp + msize, 0, xp, xsize,
+						       mp, msize);
+					xsize = msize;
+				}
+
+				tp = rp;
+				rp = xp;
+				xp = tp;
+				rsize = xsize;
+
+				if ((mpi_limb_signed_t) e < 0) {
+					/*mpihelp_mul( xp, rp, rsize, bp, bsize ); */
+					if (bsize < KARATSUBA_THRESHOLD) {
+						mpi_limb_t tmp;
+						if (mpihelp_mul
+						    (xp, rp, rsize, bp, bsize,
+						     &tmp) < 0)
+							goto enomem;
+					} else {
+						if (mpihelp_mul_karatsuba_case
+						    (xp, rp, rsize, bp, bsize,
+						     &karactx) < 0)
+							goto enomem;
+					}
+
+					xsize = rsize + bsize;
+					if (xsize > msize) {
+						mpihelp_divrem(xp + msize, 0,
+							       xp, xsize, mp,
+							       msize);
+						xsize = msize;
+					}
+
+					tp = rp;
+					rp = xp;
+					xp = tp;
+					rsize = xsize;
+				}
+				e <<= 1;
+				c--;
+			}
+
+			i--;
+			if (i < 0)
+				break;
+			e = ep[i];
+			c = BITS_PER_MPI_LIMB;
+		}
+
+		/* We shifted MOD, the modulo reduction argument, left MOD_SHIFT_CNT
+		 * steps.  Adjust the result by reducing it with the original MOD.
+		 *
+		 * Also make sure the result is put in RES->d (where it already
+		 * might be, see above).
+		 */
+		if (mod_shift_cnt) {
+			carry_limb =
+			    mpihelp_lshift(res->d, rp, rsize, mod_shift_cnt);
+			rp = res->d;
+			if (carry_limb) {
+				rp[rsize] = carry_limb;
+				rsize++;
+			}
+		} else {
+			MPN_COPY(res->d, rp, rsize);
+			rp = res->d;
+		}
+
+		if (rsize >= msize) {
+			mpihelp_divrem(rp + msize, 0, rp, rsize, mp, msize);
+			rsize = msize;
+		}
+
+		/* Remove any leading zero words from the result.  */
+		if (mod_shift_cnt)
+			mpihelp_rshift(rp, rp, rsize, mod_shift_cnt);
+		MPN_NORMALIZE(rp, rsize);
+
+		mpihelp_release_karatsuba_ctx(&karactx);
+	}
+
+	if (negative_result && rsize) {
+		if (mod_shift_cnt)
+			mpihelp_rshift(mp, mp, msize, mod_shift_cnt);
+		mpihelp_sub(rp, mp, msize, rp, rsize);
+		rsize = msize;
+		rsign = msign;
+		MPN_NORMALIZE(rp, rsize);
+	}
+	res->nlimbs = rsize;
+	res->sign = rsign;
+
+leave:
+	rc = 0;
+enomem:
+	if (assign_rp)
+		mpi_assign_limb_space(res, rp, size);
+	if (mp_marker)
+		mpi_free_limb_space(mp_marker);
+	if (bp_marker)
+		mpi_free_limb_space(bp_marker);
+	if (ep_marker)
+		mpi_free_limb_space(ep_marker);
+	if (xp_marker)
+		mpi_free_limb_space(xp_marker);
+	if (tspace)
+		mpi_free_limb_space(tspace);
+	return rc;
+}
+EXPORT_SYMBOL_GPL(mpi_powm);

lib/mpi/mpi-scan.c

+/* mpi-scan.c  -  MPI functions
+ * Copyright (C) 1998, 1999, 2000, 2001 Free Software Foundation, Inc.
+ *
+ * This file is part of GnuPG.
+ *
+ * GnuPG is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * GnuPG is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
+ */
+
+#include "mpi-internal.h"
+#include "longlong.h"
+
+/****************
+ * Scan through an mpi and return byte for byte. a -1 is returned to indicate
+ * the end of the mpi. Scanning is done from the lsb to the msb, returned
+ * values are in the range of 0 .. 255.
+ *
+ * FIXME: This code is VERY ugly!
+ */
+int mpi_getbyte(const MPI a, unsigned idx)
+{
+	int i, j;
+	unsigned n;
+	mpi_ptr_t ap;
+	mpi_limb_t limb;
+
+	ap = a->d;
+	for (n = 0, i = 0; i < a->nlimbs; i++) {
+		limb = ap[i];
+		for (j = 0; j < BYTES_PER_MPI_LIMB; j++, n++)
+			if (n == idx)
+				return (limb >> j * 8) & 0xff;
+	}
+	return -1;
+}
+
+/****************
+ * Put a value at position IDX into A. idx counts from lsb to msb
+ */
+void mpi_putbyte(MPI a, unsigned idx, int xc)
+{
+	int i, j;
+	unsigned n;
+	mpi_ptr_t ap;
+	mpi_limb_t limb, c;
+
+	c = xc & 0xff;
+	ap = a->d;
+	for (n = 0, i = 0; i < a->alloced; i++) {
+		limb = ap[i];
+		for (j = 0; j < BYTES_PER_MPI_LIMB; j++, n++)
+			if (n == idx) {
+#if BYTES_PER_MPI_LIMB == 4
+				if (j == 0)
+					limb = (limb & 0xffffff00) | c;
+				else if (j == 1)
+					limb = (limb & 0xffff00ff) | (c << 8);
+				else if (j == 2)
+					limb = (limb & 0xff00ffff) | (c << 16);
+				else
+					limb = (limb & 0x00ffffff) | (c << 24);
+#elif BYTES_PER_MPI_LIMB == 8
+				if (j == 0)
+					limb = (limb & 0xffffffffffffff00) | c;
+				else if (j == 1)
+					limb =
+					    (limb & 0xffffffffffff00ff) | (c <<
+									   8);
+				else if (j == 2)
+					limb =
+					    (limb & 0xffffffffff00ffff) | (c <<
+									   16);
+				else if (j == 3)
+					limb =
+					    (limb & 0xffffffff00ffffff) | (c <<
+									   24);
+				else if (j == 4)
+					limb =
+					    (limb & 0xffffff00ffffffff) | (c <<
+									   32);
+				else if (j == 5)
+					limb =
+					    (limb & 0xffff00ffffffffff) | (c <<
+									   40);
+				else if (j == 6)
+					limb =
+					    (limb & 0xff00ffffffffffff) | (c <<
+									   48);
+				else
+					limb =
+					    (limb & 0x00ffffffffffffff) | (c <<
+									   56);
+#else
+#error please enhance this function, its ugly - i know.
+#endif
+				if (a->nlimbs <= i)
+					a->nlimbs = i + 1;
+				ap[i] = limb;
+				return;
+			}
+	}
+	log_bug("index out of range\n");
+}
+
+/****************
+ * Count the number of zerobits at the low end of A
+ */
+unsigned mpi_trailing_zeros(const MPI a)
+{
+	unsigned n, count = 0;
+
+	for (n = 0; n < a->nlimbs; n++) {
+		if (a->d[n]) {
+			unsigned nn;
+			mpi_limb_t alimb = a->d[n];
+
+			count_trailing_zeros(nn, alimb);
+			count += nn;
+			break;
+		}
+		count += BITS_PER_MPI_LIMB;
+	}
+	return count;
+
+}

lib/mpi/mpicoder.c

+/* mpicoder.c  -  Coder for the external representation of MPIs
+ * Copyright (C) 1998, 1999 Free Software Foundation, Inc.
+ *
+ * This file is part of GnuPG.
+ *
+ * GnuPG is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * GnuPG is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
+ */
+
+#include "mpi-internal.h"
+
+#define DIM(v) (sizeof(v)/sizeof((v)[0]))
+#define MAX_EXTERN_MPI_BITS 16384
+
+static uint8_t asn[15] =	/* Object ID is 1.3.14.3.2.26 */
+{ 0x30, 0x21, 0x30, 0x09, 0x06, 0x05, 0x2b, 0x0e, 0x03,
+	0x02, 0x1a, 0x05, 0x00, 0x04, 0x14
+};
+
+MPI do_encode_md(const void *sha_buffer, unsigned nbits)
+{
+	int nframe = (nbits + 7) / 8;
+	uint8_t *frame, *fr_pt;
+	int i = 0, n;
+	size_t asnlen = DIM(asn);
+	MPI a = MPI_NULL;
+
+	if (SHA1_DIGEST_LENGTH + asnlen + 4 > nframe)
+		pr_info("MPI: can't encode a %d bit MD into a %d bits frame\n",
+		       (int)(SHA1_DIGEST_LENGTH * 8), (int)nbits);
+
+	/* We encode the MD in this way:
+	 *
+	 *       0  A PAD(n bytes)   0  ASN(asnlen bytes)  MD(len bytes)
+	 *
+	 * PAD consists of FF bytes.
+	 */
+	frame = kmalloc(nframe, GFP_KERNEL);
+	if (!frame)
+		return MPI_NULL;
+	n = 0;
+	frame[n++] = 0;
+	frame[n++] = 1;		/* block type */
+	i = nframe - SHA1_DIGEST_LENGTH - asnlen - 3;
+
+	if (i <= 1) {
+		pr_info("MPI: message digest encoding failed\n");
+		kfree(frame);
+		return a;
+	}
+
+	memset(frame + n, 0xff, i);
+	n += i;
+	frame[n++] = 0;
+	memcpy(frame + n, &asn, asnlen);
+	n += asnlen;
+	memcpy(frame + n, sha_buffer, SHA1_DIGEST_LENGTH);
+	n += SHA1_DIGEST_LENGTH;
+
+	i = nframe;
+	fr_pt = frame;
+
+	if (n != nframe) {
+		printk
+		    ("MPI: message digest encoding failed, frame length is wrong\n");
+		kfree(frame);
+		return a;
+	}
+
+	a = mpi_alloc((nframe + BYTES_PER_MPI_LIMB - 1) / BYTES_PER_MPI_LIMB);
+	mpi_set_buffer(a, frame, nframe, 0);
+	kfree(frame);
+
+	return a;
+}
+
+MPI mpi_read_from_buffer(const void *xbuffer, unsigned *ret_nread)
+{
+	const uint8_t *buffer = xbuffer;
+	int i, j;
+	unsigned nbits, nbytes, nlimbs, nread = 0;
+	mpi_limb_t a;
+	MPI val = MPI_NULL;
+
+	if (*ret_nread < 2)
+		goto leave;
+	nbits = buffer[0] << 8 | buffer[1];
+
+	if (nbits > MAX_EXTERN_MPI_BITS) {
+		pr_info("MPI: mpi too large (%u bits)\n", nbits);
+		goto leave;
+	}
+	buffer += 2;
+	nread = 2;
+
+	nbytes = (nbits + 7) / 8;
+	nlimbs = (nbytes + BYTES_PER_MPI_LIMB - 1) / BYTES_PER_MPI_LIMB;
+	val = mpi_alloc(nlimbs);
+	if (!val)
+		return MPI_NULL;
+	i = BYTES_PER_MPI_LIMB - nbytes % BYTES_PER_MPI_LIMB;
+	i %= BYTES_PER_MPI_LIMB;
+	val->nbits = nbits;
+	j = val->nlimbs = nlimbs;
+	val->sign = 0;
+	for (; j > 0; j--) {
+		a = 0;
+		for (; i < BYTES_PER_MPI_LIMB; i++) {
+			if (++nread > *ret_nread) {
+				printk
+				    ("MPI: mpi larger than buffer nread=%d ret_nread=%d\n",
+				     nread, *ret_nread);
+				goto leave;
+			}
+			a <<= 8;
+			a |= *buffer++;
+		}
+		i = 0;
+		val->d[j - 1] = a;
+	}
+
+leave:
+	*ret_nread = nread;
+	return val;
+}
+EXPORT_SYMBOL_GPL(mpi_read_from_buffer);
+
+/****************
+ * Make an mpi from a character string.
+ */
+int mpi_fromstr(MPI val, const char *str)
+{
+	int hexmode = 0, sign = 0, prepend_zero = 0, i, j, c, c1, c2;
+	unsigned nbits, nbytes, nlimbs;
+	mpi_limb_t a;
+
+	if (*str == '-') {
+		sign = 1;
+		str++;
+	}
+	if (*str == '0' && str[1] == 'x')
+		hexmode = 1;
+	else
+		return -EINVAL;	/* other bases are not yet supported */
+	str += 2;
+
+	nbits = strlen(str) * 4;
+	if (nbits % 8)
+		prepend_zero = 1;
+	nbytes = (nbits + 7) / 8;
+	nlimbs = (nbytes + BYTES_PER_MPI_LIMB - 1) / BYTES_PER_MPI_LIMB;
+	if (val->alloced < nlimbs)
+		if (!mpi_resize(val, nlimbs))
+			return -ENOMEM;
+	i = BYTES_PER_MPI_LIMB - nbytes % BYTES_PER_MPI_LIMB;
+	i %= BYTES_PER_MPI_LIMB;
+	j = val->nlimbs = nlimbs;
+	val->sign = sign;
+	for (; j > 0; j--) {
+		a = 0;
+		for (; i < BYTES_PER_MPI_LIMB; i++) {
+			if (prepend_zero) {
+				c1 = '0';
+				prepend_zero = 0;
+			} else
+				c1 = *str++;
+			assert(c1);
+			c2 = *str++;
+			assert(c2);
+			if (c1 >= '0' && c1 <= '9')
+				c = c1 - '0';
+			else if (c1 >= 'a' && c1 <= 'f')
+				c = c1 - 'a' + 10;
+			else if (c1 >= 'A' && c1 <= 'F')
+				c = c1 - 'A' + 10;
+			else {
+				mpi_clear(val);
+				return 1;
+			}
+			c <<= 4;
+			if (c2 >= '0' && c2 <= '9')
+				c |= c2 - '0';
+			else if (c2 >= 'a' && c2 <= 'f')
+				c |= c2 - 'a' + 10;
+			else if (c2 >= 'A' && c2 <= 'F')
+				c |= c2 - 'A' + 10;
+			else {
+				mpi_clear(val);
+				return 1;
+			}
+			a <<= 8;
+			a |= c;
+		}
+		i = 0;
+
+		val->d[j - 1] = a;
+	}
+
+	return 0;
+}
+EXPORT_SYMBOL_GPL(mpi_fromstr);
+
+/****************
+ * Special function to get the low 8 bytes from an mpi.
+ * This can be used as a keyid; KEYID is an 2 element array.
+ * Return the low 4 bytes.
+ */
+u32 mpi_get_keyid(const MPI a, u32 *keyid)
+{
+#if BYTES_PER_MPI_LIMB == 4
+	if (keyid) {
+		keyid[0] = a->nlimbs >= 2 ? a->d[1] : 0;
+		keyid[1] = a->nlimbs >= 1 ? a->d[0] : 0;
+	}
+	return a->nlimbs >= 1 ? a->d[0] : 0;
+#elif BYTES_PER_MPI_LIMB == 8
+	if (keyid) {
+		keyid[0] = a->nlimbs ? (u32) (a->d[0] >> 32) : 0;
+		keyid[1] = a->nlimbs ? (u32) (a->d[0] & 0xffffffff) : 0;
+	}
+	return a->nlimbs ? (u32) (a->d[0] & 0xffffffff) : 0;
+#else
+#error Make this function work with other LIMB sizes
+#endif
+}
+
+/****************
+ * Return an allocated buffer with the MPI (msb first).
+ * NBYTES receives the length of this buffer. Caller must free the
+ * return string (This function does return a 0 byte buffer with NBYTES
+ * set to zero if the value of A is zero. If sign is not NULL, it will
+ * be set to the sign of the A.
+ */
+void *mpi_get_buffer(MPI a, unsigned *nbytes, int *sign)
+{
+	uint8_t *p, *buffer;
+	mpi_limb_t alimb;
+	int i;
+	unsigned int n;
+
+	if (sign)
+		*sign = a->sign;
+	*nbytes = n = a->nlimbs * BYTES_PER_MPI_LIMB;
+	if (!n)
+		n++;		/* avoid zero length allocation */
+	p = buffer = kmalloc(n, GFP_KERNEL);
+
+	for (i = a->nlimbs - 1; i >= 0; i--) {
+		alimb = a->d[i];
+#if BYTES_PER_MPI_LIMB == 4
+		*p++ = alimb >> 24;
+		*p++ = alimb >> 16;
+		*p++ = alimb >> 8;
+		*p++ = alimb;
+#elif BYTES_PER_MPI_LIMB == 8
+		*p++ = alimb >> 56;
+		*p++ = alimb >> 48;
+		*p++ = alimb >> 40;
+		*p++ = alimb >> 32;
+		*p++ = alimb >> 24;
+		*p++ = alimb >> 16;
+		*p++ = alimb >> 8;
+		*p++ = alimb;
+#else
+#error please implement for this limb size.
+#endif
+	}
+
+	/* this is sub-optimal but we need to do the shift operation
+	 * because the caller has to free the returned buffer */
+	for (p = buffer; !*p && *nbytes; p++, --*nbytes)
+		;
+	if (p != buffer)
+		memmove(buffer, p, *nbytes);
+
+	return buffer;
+}
+EXPORT_SYMBOL_GPL(mpi_get_buffer);
+
+/****************
+ * Use BUFFER to update MPI.
+ */
+int mpi_set_buffer(MPI a, const void *xbuffer, unsigned nbytes, int sign)
+{
+	const uint8_t *buffer = xbuffer, *p;
+	mpi_limb_t alimb;
+	int nlimbs;
+	int i;
+
+	nlimbs = (nbytes + BYTES_PER_MPI_LIMB - 1) / BYTES_PER_MPI_LIMB;
+	if (RESIZE_IF_NEEDED(a, nlimbs) < 0)
+		return -ENOMEM;
+	a->sign = sign;
+
+	for (i = 0, p = buffer + nbytes - 1; p >= buffer + BYTES_PER_MPI_LIMB;) {
+#if BYTES_PER_MPI_LIMB == 4
+		alimb = (mpi_limb_t) *p--;
+		alimb |= (mpi_limb_t) *p-- << 8;
+		alimb |= (mpi_limb_t) *p-- << 16;
+		alimb |= (mpi_limb_t) *p-- << 24;
+#elif BYTES_PER_MPI_LIMB == 8
+		alimb = (mpi_limb_t) *p--;
+		alimb |= (mpi_limb_t) *p-- << 8;
+		alimb |= (mpi_limb_t) *p-- << 16;
+		alimb |= (mpi_limb_t) *p-- << 24;
+		alimb |= (mpi_limb_t) *p-- << 32;
+		alimb |= (mpi_limb_t) *p-- << 40;
+		alimb |= (mpi_limb_t) *p-- << 48;
+		alimb |= (mpi_limb_t) *p-- << 56;
+#else
+#error please implement for this limb size.
+#endif
+		a->d[i++] = alimb;
+	}
+	if (p >= buffer) {
+#if BYTES_PER_MPI_LIMB == 4
+		alimb = *p--;
+		if (p >= buffer)
+			alimb |= (mpi_limb_t) *p-- << 8;
+		if (p >= buffer)
+			alimb |= (mpi_limb_t) *p-- << 16;
+		if (p >= buffer)
+			alimb |= (mpi_limb_t) *p-- << 24;
+#elif BYTES_PER_MPI_LIMB == 8
+		alimb = (mpi_limb_t) *p--;
+		if (p >= buffer)
+			alimb |= (mpi_limb_t) *p-- << 8;
+		if (p >= buffer)
+			alimb |= (mpi_limb_t) *p-- << 16;
+		if (p >= buffer)
+			alimb |= (mpi_limb_t) *p-- << 24;
+		if (p >= buffer)
+			alimb |= (mpi_limb_t) *p-- << 32;
+		if (p >= buffer)
+			alimb |= (mpi_limb_t) *p-- << 40;
+		if (p >= buffer)
+			alimb |= (mpi_limb_t) *p-- << 48;
+		if (p >= buffer)
+			alimb |= (mpi_limb_t) *p-- << 56;
+#else
+#error please implement for this limb size.
+#endif
+		a->d[i++] = alimb;
+	}
+	a->nlimbs = i;
+
+	if (i != nlimbs) {
+		pr_emerg("MPI: mpi_set_buffer: Assertion failed (%d != %d)", i,
+		       nlimbs);
+		BUG();
+	}
+	return 0;
+}
+EXPORT_SYMBOL_GPL(mpi_set_buffer);

lib/mpi/mpih-cmp.c

+/* mpihelp-sub.c  -  MPI helper functions
+ *	Copyright (C) 1994, 1996 Free Software Foundation, Inc.
+ *	Copyright (C) 1998, 1999, 2000, 2001 Free Software Foundation, Inc.
+ *
+ * This file is part of GnuPG.
+ *
+ * GnuPG is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * GnuPG is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
+ *
+ * Note: This code is heavily based on the GNU MP Library.
+ *	 Actually it's the same code with only minor changes in the
+ *	 way the data is stored; this is to support the abstraction
+ *	 of an optional secure memory allocation which may be used
+ *	 to avoid revealing of sensitive data due to paging etc.
+ *	 The GNU MP Library itself is published under the LGPL;
+ *	 however I decided to publish this code under the plain GPL.
+ */
+
+#include "mpi-internal.h"
+
+/****************
+ * Compare OP1_PTR/OP1_SIZE with OP2_PTR/OP2_SIZE.
+ * There are no restrictions on the relative sizes of
+ * the two arguments.
+ * Return 1 if OP1 > OP2, 0 if they are equal, and -1 if OP1 < OP2.
+ */
+int mpihelp_cmp(mpi_ptr_t op1_ptr, mpi_ptr_t op2_ptr, mpi_size_t size)
+{
+	mpi_size_t i;
+	mpi_limb_t op1_word, op2_word;
+
+	for (i = size - 1; i >= 0; i--) {
+		op1_word = op1_ptr[i];
+		op2_word = op2_ptr[i];
+		if (op1_word != op2_word)
+			goto diff;
+	}
+	return 0;
+
+diff:
+	/* This can *not* be simplified to
+	 *   op2_word - op2_word
+	 * since that expression might give signed overflow.  */
+	return (op1_word > op2_word) ? 1 : -1;
+}

lib/mpi/mpih-div.c

+/* mpihelp-div.c  -  MPI helper functions
+ *	Copyright (C) 1994, 1996 Free Software Foundation, Inc.
+ *	Copyright (C) 1998, 1999 Free Software Foundation, Inc.
+ *
+ * This file is part of GnuPG.
+ *
+ * GnuPG is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * GnuPG is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
+ *
+ * Note: This code is heavily based on the GNU MP Library.
+ *	 Actually it's the same code with only minor changes in the
+ *	 way the data is stored; this is to support the abstraction
+ *	 of an optional secure memory allocation which may be used
+ *	 to avoid revealing of sensitive data due to paging etc.
+ *	 The GNU MP Library itself is published under the LGPL;
+ *	 however I decided to publish this code under the plain GPL.
+ */
+
+#include "mpi-internal.h"
+#include "longlong.h"
+
+#ifndef UMUL_TIME
+#define UMUL_TIME 1
+#endif
+#ifndef UDIV_TIME
+#define UDIV_TIME UMUL_TIME
+#endif
+
+/* FIXME: We should be using invert_limb (or invert_normalized_limb)
+ * here (not udiv_qrnnd).
+ */
+
+mpi_limb_t
+mpihelp_mod_1(mpi_ptr_t dividend_ptr, mpi_size_t dividend_size,
+	      mpi_limb_t divisor_limb)
+{
+	mpi_size_t i;
+	mpi_limb_t n1, n0, r;
+	int dummy;
+
+	/* Botch: Should this be handled at all?  Rely on callers?  */
+	if (!dividend_size)
+		return 0;
+
+	/* If multiplication is much faster than division, and the
+	 * dividend is large, pre-invert the divisor, and use
+	 * only multiplications in the inner loop.
+	 *
+	 * This test should be read:
+	 *   Does it ever help to use udiv_qrnnd_preinv?
+	 *     && Does what we save compensate for the inversion overhead?
+	 */
+	if (UDIV_TIME > (2 * UMUL_TIME + 6)
+	    && (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME) {
+		int normalization_steps;
+
+		count_leading_zeros(normalization_steps, divisor_limb);
+		if (normalization_steps) {
+			mpi_limb_t divisor_limb_inverted;
+
+			divisor_limb <<= normalization_steps;
+
+			/* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The
+			 * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
+			 * most significant bit (with weight 2**N) implicit.
+			 *
+			 * Special case for DIVISOR_LIMB == 100...000.
+			 */
+			if (!(divisor_limb << 1))
+				divisor_limb_inverted = ~(mpi_limb_t) 0;
+			else
+				udiv_qrnnd(divisor_limb_inverted, dummy,
+					   -divisor_limb, 0, divisor_limb);
+
+			n1 = dividend_ptr[dividend_size - 1];
+			r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);
+
+			/* Possible optimization:
+			 * if (r == 0
+			 * && divisor_limb > ((n1 << normalization_steps)
+			 *                 | (dividend_ptr[dividend_size - 2] >> ...)))
+			 * ...one division less...
+			 */
+			for (i = dividend_size - 2; i >= 0; i--) {
+				n0 = dividend_ptr[i];
+				UDIV_QRNND_PREINV(dummy, r, r,
+						  ((n1 << normalization_steps)
+						   | (n0 >>
+						      (BITS_PER_MPI_LIMB -
+						       normalization_steps))),
+						  divisor_limb,
+						  divisor_limb_inverted);
+				n1 = n0;
+			}
+			UDIV_QRNND_PREINV(dummy, r, r,
+					  n1 << normalization_steps,
+					  divisor_limb, divisor_limb_inverted);
+			return r >> normalization_steps;
+		} else {
+			mpi_limb_t divisor_limb_inverted;
+
+			/* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The
+			 * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
+			 * most significant bit (with weight 2**N) implicit.
+			 *
+			 * Special case for DIVISOR_LIMB == 100...000.
+			 */
+			if (!(divisor_limb << 1))
+				divisor_limb_inverted = ~(mpi_limb_t) 0;
+			else
+				udiv_qrnnd(divisor_limb_inverted, dummy,
+					   -divisor_limb, 0, divisor_limb);
+
+			i = dividend_size - 1;
+			r = dividend_ptr[i];
+
+			if (r >= divisor_limb)
+				r = 0;
+			else
+				i--;
+
+			for (; i >= 0; i--) {
+				n0 = dividend_ptr[i];
+				UDIV_QRNND_PREINV(dummy, r, r,
+						  n0, divisor_limb,
+						  divisor_limb_inverted);
+			}
+			return r;
+		}
+	} else {
+		if (UDIV_NEEDS_NORMALIZATION) {
+			int normalization_steps;
+
+			count_leading_zeros(normalization_steps, divisor_limb);
+			if (normalization_steps) {
+				divisor_limb <<= normalization_steps;
+
+				n1 = dividend_ptr[dividend_size - 1];
+				r = n1 >> (BITS_PER_MPI_LIMB -
+					   normalization_steps);
+
+				/* Possible optimization:
+				 * if (r == 0
+				 * && divisor_limb > ((n1 << normalization_steps)
+				 *                 | (dividend_ptr[dividend_size - 2] >> ...)))
+				 * ...one division less...
+				 */
+				for (i = dividend_size - 2; i >= 0; i--) {
+					n0 = dividend_ptr[i];
+					udiv_qrnnd(dummy, r, r,
+						   ((n1 << normalization_steps)
+						    | (n0 >>
+						       (BITS_PER_MPI_LIMB -
+							normalization_steps))),
+						   divisor_limb);
+					n1 = n0;
+				}
+				udiv_qrnnd(dummy, r, r,
+					   n1 << normalization_steps,
+					   divisor_limb);
+				return r >> normalization_steps;
+			}
+		}
+		/* No normalization needed, either because udiv_qrnnd doesn't require
+		 * it, or because DIVISOR_LIMB is already normalized.  */
+		i = dividend_size - 1;
+		r = dividend_ptr[i];
+
+		if (r >= divisor_limb)
+			r = 0;
+		else
+			i--;
+
+		for (; i >= 0; i--) {
+			n0 = dividend_ptr[i];
+			udiv_qrnnd(dummy, r, r, n0, divisor_limb);
+		}
+		return r;
+	}
+}
+
+/* Divide num (NP/NSIZE) by den (DP/DSIZE) and write
+ * the NSIZE-DSIZE least significant quotient limbs at QP
+ * and the DSIZE long remainder at NP.	If QEXTRA_LIMBS is
+ * non-zero, generate that many fraction bits and append them after the
+ * other quotient limbs.
+ * Return the most significant limb of the quotient, this is always 0 or 1.
+ *
+ * Preconditions:
+ * 0. NSIZE >= DSIZE.
+ * 1. The most significant bit of the divisor must be set.
+ * 2. QP must either not overlap with the input operands at all, or
+ *    QP + DSIZE >= NP must hold true.	(This means that it's
+ *    possible to put the quotient in the high part of NUM, right after the
+ *    remainder in NUM.
+ * 3. NSIZE >= DSIZE, even if QEXTRA_LIMBS is non-zero.
+ */
+
+mpi_limb_t
+mpihelp_divrem(mpi_ptr_t qp, mpi_size_t qextra_limbs,
+	       mpi_ptr_t np, mpi_size_t nsize, mpi_ptr_t dp, mpi_size_t dsize)
+{
+	mpi_limb_t most_significant_q_limb = 0;
+
+	switch (dsize) {
+	case 0:
+		/* We are asked to divide by zero, so go ahead and do it!  (To make
+		   the compiler not remove this statement, return the value.)  */
+		return 1 / dsize;
+
+	case 1:
+		{
+			mpi_size_t i;
+			mpi_limb_t n1;
+			mpi_limb_t d;
+
+			d = dp[0];
+			n1 = np[nsize - 1];
+
+			if (n1 >= d) {
+				n1 -= d;
+				most_significant_q_limb = 1;
+			}
+
+			qp += qextra_limbs;
+			for (i = nsize - 2; i >= 0; i--)
+				udiv_qrnnd(qp[i], n1, n1, np[i], d);
+			qp -= qextra_limbs;
+
+			for (i = qextra_limbs - 1; i >= 0; i--)
+				udiv_qrnnd(qp[i], n1, n1, 0, d);
+
+			np[0] = n1;
+		}
+		break;
+
+	case 2:
+		{
+			mpi_size_t i;
+			mpi_limb_t n1, n0, n2;
+			mpi_limb_t d1, d0;
+
+			np += nsize - 2;
+			d1 = dp[1];
+			d0 = dp[0];
+			n1 = np[1];
+			n0 = np[0];
+
+			if (n1 >= d1 && (n1 > d1 || n0 >= d0)) {
+				sub_ddmmss(n1, n0, n1, n0, d1, d0);
+				most_significant_q_limb = 1;
+			}
+
+			for (i = qextra_limbs + nsize - 2 - 1; i >= 0; i--) {
+				mpi_limb_t q;
+				mpi_limb_t r;
+
+				if (i >= qextra_limbs)
+					np--;
+				else
+					np[0] = 0;
+
+				if (n1 == d1) {
+					/* Q should be either 111..111 or 111..110.  Need special
+					 * treatment of this rare case as normal division would
+					 * give overflow.  */
+					q = ~(mpi_limb_t) 0;
+
+					r = n0 + d1;
+					if (r < d1) {	/* Carry in the addition? */
+						add_ssaaaa(n1, n0, r - d0,
+							   np[0], 0, d0);
+						qp[i] = q;
+						continue;
+					}
+					n1 = d0 - (d0 != 0 ? 1 : 0);
+					n0 = -d0;
+				} else {
+					udiv_qrnnd(q, r, n1, n0, d1);
+					umul_ppmm(n1, n0, d0, q);
+				}
+
+				n2 = np[0];
+q_test:
+				if (n1 > r || (n1 == r && n0 > n2)) {
+					/* The estimated Q was too large.  */
+					q--;
+					sub_ddmmss(n1, n0, n1, n0, 0, d0);
+					r += d1;
+					if (r >= d1)	/* If not carry, test Q again.  */
+						goto q_test;
+				}
+
+				qp[i] = q;
+				sub_ddmmss(n1, n0, r, n2, n1, n0);
+			}
+			np[1] = n1;
+			np[0] = n0;
+		}
+		break;
+
+	default:
+		{
+			mpi_size_t i;
+			mpi_limb_t dX, d1, n0;
+
+			np += nsize - dsize;
+			dX = dp[dsize - 1];
+			d1 = dp[dsize - 2];
+			n0 = np[dsize - 1];
+
+			if (n0 >= dX) {
+				if (n0 > dX
+				    || mpihelp_cmp(np, dp, dsize - 1) >= 0) {
+					mpihelp_sub_n(np, np, dp, dsize);
+					n0 = np[dsize - 1];
+					most_significant_q_limb = 1;
+				}
+			}
+
+			for (i = qextra_limbs + nsize - dsize - 1; i >= 0; i--) {
+				mpi_limb_t q;
+				mpi_limb_t n1, n2;
+				mpi_limb_t cy_limb;
+
+				if (i >= qextra_limbs) {
+					np--;
+					n2 = np[dsize];
+				} else {
+					n2 = np[dsize - 1];
+					MPN_COPY_DECR(np + 1, np, dsize - 1);
+					np[0] = 0;
+				}
+
+				if (n0 == dX) {
+					/* This might over-estimate q, but it's probably not worth
+					 * the extra code here to find out.  */
+					q = ~(mpi_limb_t) 0;
+				} else {
+					mpi_limb_t r;
+
+					udiv_qrnnd(q, r, n0, np[dsize - 1], dX);
+					umul_ppmm(n1, n0, d1, q);
+
+					while (n1 > r
+					       || (n1 == r
+						   && n0 > np[dsize - 2])) {
+						q--;
+						r += dX;
+						if (r < dX)	/* I.e. "carry in previous addition?" */
+							break;
+						n1 -= n0 < d1;
+						n0 -= d1;
+					}
+				}
+
+				/* Possible optimization: We already have (q * n0) and (1 * n1)
+				 * after the calculation of q.  Taking advantage of that, we
+				 * could make this loop make two iterations less.  */
+				cy_limb = mpihelp_submul_1(np, dp, dsize, q);
+
+				if (n2 != cy_limb) {
+					mpihelp_add_n(np, np, dp, dsize);
+					q--;
+				}
+
+				qp[i] = q;
+				n0 = np[dsize - 1];
+			}
+		}
+	}
+
+	return most_significant_q_limb;
+}
+
+/****************
+ * Divide (DIVIDEND_PTR,,DIVIDEND_SIZE) by DIVISOR_LIMB.
+ * Write DIVIDEND_SIZE limbs of quotient at QUOT_PTR.
+ * Return the single-limb remainder.
+ * There are no constraints on the value of the divisor.
+ *
+ * QUOT_PTR and DIVIDEND_PTR might point to the same limb.
+ */
+
+mpi_limb_t
+mpihelp_divmod_1(mpi_ptr_t quot_ptr,
+		 mpi_ptr_t dividend_ptr, mpi_size_t dividend_size,
+		 mpi_limb_t divisor_limb)
+{
+	mpi_size_t i;
+	mpi_limb_t n1, n0, r;
+	int dummy;
+
+	if (!dividend_size)
+		return 0;
+
+	/* If multiplication is much faster than division, and the
+	 * dividend is large, pre-invert the divisor, and use
+	 * only multiplications in the inner loop.
+	 *
+	 * This test should be read:
+	 * Does it ever help to use udiv_qrnnd_preinv?
+	 * && Does what we save compensate for the inversion overhead?
+	 */
+	if (UDIV_TIME > (2 * UMUL_TIME + 6)
+	    && (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME) {
+		int normalization_steps;
+
+		count_leading_zeros(normalization_steps, divisor_limb);
+		if (normalization_steps) {
+			mpi_limb_t divisor_limb_inverted;
+
+			divisor_limb <<= normalization_steps;
+
+			/* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The
+			 * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
+			 * most significant bit (with weight 2**N) implicit.
+			 */
+			/* Special case for DIVISOR_LIMB == 100...000.  */
+			if (!(divisor_limb << 1))
+				divisor_limb_inverted = ~(mpi_limb_t) 0;
+			else
+				udiv_qrnnd(divisor_limb_inverted, dummy,
+					   -divisor_limb, 0, divisor_limb);
+
+			n1 = dividend_ptr[dividend_size - 1];
+			r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);
+
+			/* Possible optimization:
+			 * if (r == 0
+			 * && divisor_limb > ((n1 << normalization_steps)
+			 *                 | (dividend_ptr[dividend_size - 2] >> ...)))
+			 * ...one division less...
+			 */
+			for (i = dividend_size - 2; i >= 0; i--) {
+				n0 = dividend_ptr[i];
+				UDIV_QRNND_PREINV(quot_ptr[i + 1], r, r,
+						  ((n1 << normalization_steps)
+						   | (n0 >>
+						      (BITS_PER_MPI_LIMB -
+						       normalization_steps))),
+						  divisor_limb,
+						  divisor_limb_inverted);
+				n1 = n0;
+			}
+			UDIV_QRNND_PREINV(quot_ptr[0], r, r,
+					  n1 << normalization_steps,
+					  divisor_limb, divisor_limb_inverted);
+			return r >> normalization_steps;
+		} else {
+			mpi_limb_t divisor_limb_inverted;
+
+			/* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The
+			 * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
+			 * most significant bit (with weight 2**N) implicit.
+			 */
+			/* Special case for DIVISOR_LIMB == 100...000.  */
+			if (!(divisor_limb << 1))
+				divisor_limb_inverted = ~(mpi_limb_t) 0;
+			else
+				udiv_qrnnd(divisor_limb_inverted, dummy,
+					   -divisor_limb, 0, divisor_limb);
+
+			i = dividend_size - 1;
+			r = dividend_ptr[i];
+
+			if (r >= divisor_limb)
+				r = 0;
+			else
+				quot_ptr[i--] = 0;
+
+			for (; i >= 0; i--) {
+				n0 = dividend_ptr[i];
+				UDIV_QRNND_PREINV(quot_ptr[i], r, r,
+						  n0, divisor_limb,
+						  divisor_limb_inverted);
+			}
+			return r;
+		}
+	} else {
+		if (UDIV_NEEDS_NORMALIZATION) {
+			int normalization_steps;
+
+			count_leading_zeros(normalization_steps, divisor_limb);
+			if (normalization_steps) {
+				divisor_limb <<= normalization_steps;
+
+				n1 = dividend_ptr[dividend_size - 1];
+				r = n1 >> (BITS_PER_MPI_LIMB -
+					   normalization_steps);
+
+				/* Possible optimization:
+				 * if (r == 0
+				 * && divisor_limb > ((n1 << normalization_steps)
+				 *                 | (dividend_ptr[dividend_size - 2] >> ...)))
+				 * ...one division less...
+				 */
+				for (i = dividend_size - 2; i >= 0; i--) {
+					n0 = dividend_ptr[i];
+					udiv_qrnnd(quot_ptr[i + 1], r, r,
+						   ((n1 << normalization_steps)
+						    | (n0 >>
+						       (BITS_PER_MPI_LIMB -
+							normalization_steps))),
+						   divisor_limb);
+					n1 = n0;
+				}
+				udiv_qrnnd(quot_ptr[0], r, r,
+					   n1 << normalization_steps,
+					   divisor_limb);
+				return r >> normalization_steps;
+			}
+		}
+		/* No normalization needed, either because udiv_qrnnd doesn't require
+		 * it, or because DIVISOR_LIMB is already normalized.  */
+		i = dividend_size - 1;
+		r = dividend_ptr[i];
+
+		if (r >= divisor_limb)
+			r = 0;
+		else
+			quot_ptr[i--] = 0;
+
+		for (; i >= 0; i--) {
+			n0 = dividend_ptr[i];
+			udiv_qrnnd(quot_ptr[i], r, r, n0, divisor_limb);
+		}
+		return r;
+	}
+}

lib/mpi/mpih-mul.c

+/* mpihelp-mul.c  -  MPI helper functions
+ * Copyright (C) 1994, 1996, 1998, 1999,
+ *               2000 Free Software Foundation, Inc.
+ *
+ * This file is part of GnuPG.
+ *
+ * GnuPG is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * GnuPG is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
+ *
+ * Note: This code is heavily based on the GNU MP Library.
+ *	 Actually it's the same code with only minor changes in the
+ *	 way the data is stored; this is to support the abstraction
+ *	 of an optional secure memory allocation which may be used
+ *	 to avoid revealing of sensitive data due to paging etc.
+ *	 The GNU MP Library itself is published under the LGPL;
+ *	 however I decided to publish this code under the plain GPL.
+ */
+
+#include <linux/string.h>
+#include "mpi-internal.h"
+#include "longlong.h"
+
+#define MPN_MUL_N_RECURSE(prodp, up, vp, size, tspace)		\
+	do {							\
+		if ((size) < KARATSUBA_THRESHOLD)		\
+			mul_n_basecase(prodp, up, vp, size);	\
+		else						\
+			mul_n(prodp, up, vp, size, tspace);	\
+	} while (0);
+
+#define MPN_SQR_N_RECURSE(prodp, up, size, tspace)		\
+	do {							\
+		if ((size) < KARATSUBA_THRESHOLD)		\
+			mpih_sqr_n_basecase(prodp, up, size);	\
+		else						\
+			mpih_sqr_n(prodp, up, size, tspace);	\
+	} while (0);
+
+/* Multiply the natural numbers u (pointed to by UP) and v (pointed to by VP),
+ * both with SIZE limbs, and store the result at PRODP.  2 * SIZE limbs are
+ * always stored.  Return the most significant limb.
+ *
+ * Argument constraints:
+ * 1. PRODP != UP and PRODP != VP, i.e. the destination
+ *    must be distinct from the multiplier and the multiplicand.
+ *
+ *
+ * Handle simple cases with traditional multiplication.
+ *
+ * This is the most critical code of multiplication.  All multiplies rely
+ * on this, both small and huge.  Small ones arrive here immediately.  Huge
+ * ones arrive here as this is the base case for Karatsuba's recursive
+ * algorithm below.
+ */
+
+static mpi_limb_t
+mul_n_basecase(mpi_ptr_t prodp, mpi_ptr_t up, mpi_ptr_t vp, mpi_size_t size)
+{
+	mpi_size_t i;
+	mpi_limb_t cy;
+	mpi_limb_t v_limb;
+
+	/* Multiply by the first limb in V separately, as the result can be
+	 * stored (not added) to PROD.  We also avoid a loop for zeroing.  */
+	v_limb = vp[0];
+	if (v_limb <= 1) {
+		if (v_limb == 1)
+			MPN_COPY(prodp, up, size);
+		else
+			MPN_ZERO(prodp, size);
+		cy = 0;
+	} else
+		cy = mpihelp_mul_1(prodp, up, size, v_limb);
+
+	prodp[size] = cy;
+	prodp++;
+
+	/* For each iteration in the outer loop, multiply one limb from
+	 * U with one limb from V, and add it to PROD.  */
+	for (i = 1; i < size; i++) {
+		v_limb = vp[i];
+		if (v_limb <= 1) {
+			cy = 0;
+			if (v_limb == 1)
+				cy = mpihelp_add_n(prodp, prodp, up, size);
+		} else
+			cy = mpihelp_addmul_1(prodp, up, size, v_limb);
+
+		prodp[size] = cy;
+		prodp++;
+	}
+
+	return cy;
+}
+
+static void
+mul_n(mpi_ptr_t prodp, mpi_ptr_t up, mpi_ptr_t vp,
+		mpi_size_t size, mpi_ptr_t tspace)
+{
+	if (size & 1) {
+		/* The size is odd, and the code below doesn't handle that.
+		 * Multiply the least significant (size - 1) limbs with a recursive
+		 * call, and handle the most significant limb of S1 and S2
+		 * separately.
+		 * A slightly faster way to do this would be to make the Karatsuba
+		 * code below behave as if the size were even, and let it check for
+		 * odd size in the end.  I.e., in essence move this code to the end.
+		 * Doing so would save us a recursive call, and potentially make the
+		 * stack grow a lot less.
+		 */
+		mpi_size_t esize = size - 1;	/* even size */
+		mpi_limb_t cy_limb;
+
+		MPN_MUL_N_RECURSE(prodp, up, vp, esize, tspace);
+		cy_limb = mpihelp_addmul_1(prodp + esize, up, esize, vp[esize]);
+		prodp[esize + esize] = cy_limb;
+		cy_limb = mpihelp_addmul_1(prodp + esize, vp, size, up[esize]);
+		prodp[esize + size] = cy_limb;
+	} else {
+		/* Anatolij Alekseevich Karatsuba's divide-and-conquer algorithm.
+		 *
+		 * Split U in two pieces, U1 and U0, such that
+		 * U = U0 + U1*(B**n),
+		 * and V in V1 and V0, such that
+		 * V = V0 + V1*(B**n).
+		 *
+		 * UV is then computed recursively using the identity
+		 *
+		 *        2n   n          n                     n
+		 * UV = (B  + B )U V  +  B (U -U )(V -V )  +  (B + 1)U V
+		 *                1 1        1  0   0  1              0 0
+		 *
+		 * Where B = 2**BITS_PER_MP_LIMB.
+		 */
+		mpi_size_t hsize = size >> 1;
+		mpi_limb_t cy;
+		int negflg;
+
+		/* Product H.      ________________  ________________
+		 *                |_____U1 x V1____||____U0 x V0_____|
+		 * Put result in upper part of PROD and pass low part of TSPACE
+		 * as new TSPACE.
+		 */
+		MPN_MUL_N_RECURSE(prodp + size, up + hsize, vp + hsize, hsize,
+				  tspace);
+
+		/* Product M.      ________________
+		 *                |_(U1-U0)(V0-V1)_|
+		 */
+		if (mpihelp_cmp(up + hsize, up, hsize) >= 0) {
+			mpihelp_sub_n(prodp, up + hsize, up, hsize);
+			negflg = 0;
+		} else {
+			mpihelp_sub_n(prodp, up, up + hsize, hsize);
+			negflg = 1;
+		}
+		if (mpihelp_cmp(vp + hsize, vp, hsize) >= 0) {
+			mpihelp_sub_n(prodp + hsize, vp + hsize, vp, hsize);
+			negflg ^= 1;
+		} else {
+			mpihelp_sub_n(prodp + hsize, vp, vp + hsize, hsize);
+			/* No change of NEGFLG.  */
+		}
+		/* Read temporary operands from low part of PROD.
+		 * Put result in low part of TSPACE using upper part of TSPACE
+		 * as new TSPACE.
+		 */
+		MPN_MUL_N_RECURSE(tspace, prodp, prodp + hsize, hsize,
+				  tspace + size);
+
+		/* Add/copy product H. */
+		MPN_COPY(prodp + hsize, prodp + size, hsize);
+		cy = mpihelp_add_n(prodp + size, prodp + size,
+				   prodp + size + hsize, hsize);
+
+		/* Add product M (if NEGFLG M is a negative number) */
+		if (negflg)
+			cy -=
+			    mpihelp_sub_n(prodp + hsize, prodp + hsize, tspace,
+					  size);
+		else
+			cy +=
+			    mpihelp_add_n(prodp + hsize, prodp + hsize, tspace,
+					  size);
+
+		/* Product L.      ________________  ________________
+		 *                |________________||____U0 x V0_____|
+		 * Read temporary operands from low part of PROD.
+		 * Put result in low part of TSPACE using upper part of TSPACE
+		 * as new TSPACE.
+		 */
+		MPN_MUL_N_RECURSE(tspace, up, vp, hsize, tspace + size);
+
+		/* Add/copy Product L (twice) */
+
+		cy += mpihelp_add_n(prodp + hsize, prodp + hsize, tspace, size);
+		if (cy)
+			mpihelp_add_1(prodp + hsize + size,
+				      prodp + hsize + size, hsize, cy);
+
+		MPN_COPY(prodp, tspace, hsize);
+		cy = mpihelp_add_n(prodp + hsize, prodp + hsize, tspace + hsize,
+				   hsize);
+		if (cy)
+			mpihelp_add_1(prodp + size, prodp + size, size, 1);
+	}
+}
+
+void mpih_sqr_n_basecase(mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t size)
+{
+	mpi_size_t i;
+	mpi_limb_t cy_limb;
+	mpi_limb_t v_limb;
+
+	/* Multiply by the first limb in V separately, as the result can be
+	 * stored (not added) to PROD.  We also avoid a loop for zeroing.  */
+	v_limb = up[0];
+	if (v_limb <= 1) {
+		if (v_limb == 1)
+			MPN_COPY(prodp, up, size);
+		else
+			MPN_ZERO(prodp, size);
+		cy_limb = 0;
+	} else
+		cy_limb = mpihelp_mul_1(prodp, up, size, v_limb);
+
+	prodp[size] = cy_limb;
+	prodp++;
+
+	/* For each iteration in the outer loop, multiply one limb from
+	 * U with one limb from V, and add it to PROD.  */
+	for (i = 1; i < size; i++) {
+		v_limb = up[i];
+		if (v_limb <= 1) {
+			cy_limb = 0;
+			if (v_limb == 1)
+				cy_limb = mpihelp_add_n(prodp, prodp, up, size);
+		} else
+			cy_limb = mpihelp_addmul_1(prodp, up, size, v_limb);
+
+		prodp[size] = cy_limb;
+		prodp++;
+	}
+}
+
+void
+mpih_sqr_n(mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t size, mpi_ptr_t tspace)
+{
+	if (size & 1) {
+		/* The size is odd, and the code below doesn't handle that.
+		 * Multiply the least significant (size - 1) limbs with a recursive
+		 * call, and handle the most significant limb of S1 and S2
+		 * separately.
+		 * A slightly faster way to do this would be to make the Karatsuba
+		 * code below behave as if the size were even, and let it check for
+		 * odd size in the end.  I.e., in essence move this code to the end.
+		 * Doing so would save us a recursive call, and potentially make the
+		 * stack grow a lot less.
+		 */
+		mpi_size_t esize = size - 1;	/* even size */
+		mpi_limb_t cy_limb;
+
+		MPN_SQR_N_RECURSE(prodp, up, esize, tspace);
+		cy_limb = mpihelp_addmul_1(prodp + esize, up, esize, up[esize]);
+		prodp[esize + esize] = cy_limb;
+		cy_limb = mpihelp_addmul_1(prodp + esize, up, size, up[esize]);
+
+		prodp[esize + size] = cy_limb;
+	} else {
+		mpi_size_t hsize = size >> 1;
+		mpi_limb_t cy;
+
+		/* Product H.      ________________  ________________
+		 *                |_____U1 x U1____||____U0 x U0_____|
+		 * Put result in upper part of PROD and pass low part of TSPACE
+		 * as new TSPACE.
+		 */
+		MPN_SQR_N_RECURSE(prodp + size, up + hsize, hsize, tspace);
+
+		/* Product M.      ________________
+		 *                |_(U1-U0)(U0-U1)_|
+		 */
+		if (mpihelp_cmp(up + hsize, up, hsize) >= 0)
+			mpihelp_sub_n(prodp, up + hsize, up, hsize);
+		else
+			mpihelp_sub_n(prodp, up, up + hsize, hsize);
+
+		/* Read temporary operands from low part of PROD.
+		 * Put result in low part of TSPACE using upper part of TSPACE
+		 * as new TSPACE.  */
+		MPN_SQR_N_RECURSE(tspace, prodp, hsize, tspace + size);
+
+		/* Add/copy product H  */
+		MPN_COPY(prodp + hsize, prodp + size, hsize);
+		cy = mpihelp_add_n(prodp + size, prodp + size,
+				   prodp + size + hsize, hsize);
+
+		/* Add product M (if NEGFLG M is a negative number).  */
+		cy -= mpihelp_sub_n(prodp + hsize, prodp + hsize, tspace, size);
+
+		/* Product L.      ________________  ________________
+		 *                |________________||____U0 x U0_____|
+		 * Read temporary operands from low part of PROD.
+		 * Put result in low part of TSPACE using upper part of TSPACE
+		 * as new TSPACE.  */
+		MPN_SQR_N_RECURSE(tspace, up, hsize, tspace + size);
+
+		/* Add/copy Product L (twice).  */
+		cy += mpihelp_add_n(prodp + hsize, prodp + hsize, tspace, size);
+		if (cy)
+			mpihelp_add_1(prodp + hsize + size,
+				      prodp + hsize + size, hsize, cy);
+
+		MPN_COPY(prodp, tspace, hsize);
+		cy = mpihelp_add_n(prodp + hsize, prodp + hsize, tspace + hsize,
+				   hsize);
+		if (cy)
+			mpihelp_add_1(prodp + size, prodp + size, size, 1);
+	}
+}
+
+/* This should be made into an inline function in gmp.h.  */
+int mpihelp_mul_n(mpi_ptr_t prodp, mpi_ptr_t up, mpi_ptr_t vp, mpi_size_t size)
+{
+	if (up == vp) {
+		if (size < KARATSUBA_THRESHOLD)
+			mpih_sqr_n_basecase(prodp, up, size);
+		else {
+			mpi_ptr_t tspace;
+			tspace = mpi_alloc_limb_space(2 * size);
+			if (!tspace)
+				return -ENOMEM;
+			mpih_sqr_n(prodp, up, size, tspace);
+			mpi_free_limb_space(tspace);
+		}
+	} else {
+		if (size < KARATSUBA_THRESHOLD)
+			mul_n_basecase(prodp, up, vp, size);
+		else {
+			mpi_ptr_t tspace;
+			tspace = mpi_alloc_limb_space(2 * size);
+			if (!tspace)
+				return -ENOMEM;
+			mul_n(prodp, up, vp, size, tspace);
+			mpi_free_limb_space(tspace);
+		}
+	}
+
+	return 0;
+}
+
+int
+mpihelp_mul_karatsuba_case(mpi_ptr_t prodp,
+			   mpi_ptr_t up, mpi_size_t usize,
+			   mpi_ptr_t vp, mpi_size_t vsize,
+			   struct karatsuba_ctx *ctx)
+{
+	mpi_limb_t cy;
+
+	if (!ctx->tspace || ctx->tspace_size < vsize) {
+		if (ctx->tspace)
+			mpi_free_limb_space(ctx->tspace);
+		ctx->tspace = mpi_alloc_limb_space(2 * vsize);
+		if (!ctx->tspace)
+			return -ENOMEM;
+		ctx->tspace_size = vsize;
+	}
+
+	MPN_MUL_N_RECURSE(prodp, up, vp, vsize, ctx->tspace);
+
+	prodp += vsize;
+	up += vsize;
+	usize -= vsize;
+	if (usize >= vsize) {
+		if (!ctx->tp || ctx->tp_size < vsize) {
+			if (ctx->tp)
+				mpi_free_limb_space(ctx->tp);
+			ctx->tp = mpi_alloc_limb_space(2 * vsize);
+			if (!ctx->tp) {
+				if (ctx->tspace)
+					mpi_free_limb_space(ctx->tspace);
+				ctx->tspace = NULL;
+				return -ENOMEM;
+			}
+			ctx->tp_size = vsize;
+		}
+
+		do {
+			MPN_MUL_N_RECURSE(ctx->tp, up, vp, vsize, ctx->tspace);
+			cy = mpihelp_add_n(prodp, prodp, ctx->tp, vsize);
+			mpihelp_add_1(prodp + vsize, ctx->tp + vsize, vsize,
+				      cy);
+			prodp += vsize;
+			up += vsize;
+			usize -= vsize;
+		} while (usize >= vsize);
+	}
+
+	if (usize) {
+		if (usize < KARATSUBA_THRESHOLD) {
+			mpi_limb_t tmp;
+			if (mpihelp_mul(ctx->tspace, vp, vsize, up, usize, &tmp)
+			    < 0)
+				return -ENOMEM;
+		} else {
+			if (!ctx->next) {
+				ctx->next = kzalloc(sizeof *ctx, GFP_KERNEL);
+				if (!ctx->next)
+					return -ENOMEM;
+			}
+			if (mpihelp_mul_karatsuba_case(ctx->tspace,
+						       vp, vsize,
+						       up, usize,
+						       ctx->next) < 0)
+				return -ENOMEM;
+		}
+
+		cy = mpihelp_add_n(prodp, prodp, ctx->tspace, vsize);
+		mpihelp_add_1(prodp + vsize, ctx->tspace + vsize, usize, cy);
+	}
+
+	return 0;
+}
+
+void mpihelp_release_karatsuba_ctx(struct karatsuba_ctx *ctx)
+{
+	struct karatsuba_ctx *ctx2;
+
+	if (ctx->tp)
+		mpi_free_limb_space(ctx->tp);
+	if (ctx->tspace)
+		mpi_free_limb_space(ctx->tspace);
+	for (ctx = ctx->next; ctx; ctx = ctx2) {
+		ctx2 = ctx->next;
+		if (ctx->tp)
+			mpi_free_limb_space(ctx->tp);
+		if (ctx->tspace)
+			mpi_free_limb_space(ctx->tspace);
+		kfree(ctx);
+	}
+}
+
+/* Multiply the natural numbers u (pointed to by UP, with USIZE limbs)
+ * and v (pointed to by VP, with VSIZE limbs), and store the result at
+ * PRODP.  USIZE + VSIZE limbs are always stored, but if the input
+ * operands are normalized.  Return the most significant limb of the
+ * result.
+ *
+ * NOTE: The space pointed to by PRODP is overwritten before finished
+ * with U and V, so overlap is an error.
+ *
+ * Argument constraints:
+ * 1. USIZE >= VSIZE.
+ * 2. PRODP != UP and PRODP != VP, i.e. the destination
+ *    must be distinct from the multiplier and the multiplicand.
+ */
+
+int
+mpihelp_mul(mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t usize,
+	    mpi_ptr_t vp, mpi_size_t vsize, mpi_limb_t *_result)
+{
+	mpi_ptr_t prod_endp = prodp + usize + vsize - 1;
+	mpi_limb_t cy;
+	struct karatsuba_ctx ctx;
+
+	if (vsize < KARATSUBA_THRESHOLD) {
+		mpi_size_t i;
+		mpi_limb_t v_limb;
+
+		if (!vsize) {
+			*_result = 0;
+			return 0;
+		}
+
+		/* Multiply by the first limb in V separately, as the result can be
+		 * stored (not added) to PROD.  We also avoid a loop for zeroing.  */
+		v_limb = vp[0];
+		if (v_limb <= 1) {
+			if (v_limb == 1)
+				MPN_COPY(prodp, up, usize);
+			else
+				MPN_ZERO(prodp, usize);
+			cy = 0;
+		} else
+			cy = mpihelp_mul_1(prodp, up, usize, v_limb);
+
+		prodp[usize] = cy;
+		prodp++;
+
+		/* For each iteration in the outer loop, multiply one limb from
+		 * U with one limb from V, and add it to PROD.  */
+		for (i = 1; i < vsize; i++) {
+			v_limb = vp[i];
+			if (v_limb <= 1) {
+				cy = 0;
+				if (v_limb == 1)
+					cy = mpihelp_add_n(prodp, prodp, up,
+							   usize);
+			} else
+				cy = mpihelp_addmul_1(prodp, up, usize, v_limb);
+
+			prodp[usize] = cy;
+			prodp++;
+		}
+
+		*_result = cy;
+		return 0;
+	}
+
+	memset(&ctx, 0, sizeof ctx);
+	if (mpihelp_mul_karatsuba_case(prodp, up, usize, vp, vsize, &ctx) < 0)
+		return -ENOMEM;
+	mpihelp_release_karatsuba_ctx(&ctx);
+	*_result = *prod_endp;
+	return 0;
+}

lib/mpi/mpiutil.c

+/* mpiutil.ac  -  Utility functions for MPI
+ * Copyright (C) 1998, 1999 Free Software Foundation, Inc.
+ *
+ * This file is part of GnuPG.
+ *
+ * GnuPG is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * GnuPG is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
+ */
+
+#include "mpi-internal.h"
+
+/****************
+ * Note:  It was a bad idea to use the number of limbs to allocate
+ *	  because on a alpha the limbs are large but we normally need
+ *	  integers of n bits - So we should chnage this to bits (or bytes).
+ *
+ *	  But mpi_alloc is used in a lot of places :-)
+ */
+MPI mpi_alloc(unsigned nlimbs)
+{
+	MPI a;
+
+	a = kmalloc(sizeof *a, GFP_KERNEL);
+	if (!a)
+		return a;
+
+	if (nlimbs) {
+		a->d = mpi_alloc_limb_space(nlimbs);
+		if (!a->d) {
+			kfree(a);
+			return NULL;
+		}
+	} else {
+		a->d = NULL;
+	}
+
+	a->alloced = nlimbs;
+	a->nlimbs = 0;
+	a->sign = 0;
+	a->flags = 0;
+	a->nbits = 0;
+	return a;
+}
+EXPORT_SYMBOL_GPL(mpi_alloc);
+
+mpi_ptr_t mpi_alloc_limb_space(unsigned nlimbs)
+{
+	size_t len = nlimbs * sizeof(mpi_limb_t);
+
+	return kmalloc(len, GFP_KERNEL);
+}
+
+void mpi_free_limb_space(mpi_ptr_t a)
+{
+	if (!a)
+		return;
+
+	kfree(a);
+}
+
+void mpi_assign_limb_space(MPI a, mpi_ptr_t ap, unsigned nlimbs)
+{
+	mpi_free_limb_space(a->d);
+	a->d = ap;
+	a->alloced = nlimbs;
+}
+
+/****************
+ * Resize the array of A to NLIMBS. the additional space is cleared
+ * (set to 0) [done by m_realloc()]
+ */
+int mpi_resize(MPI a, unsigned nlimbs)
+{
+	void *p;
+
+	if (nlimbs <= a->alloced)
+		return 0;	/* no need to do it */
+
+	if (a->d) {
+		p = kmalloc(nlimbs * sizeof(mpi_limb_t), GFP_KERNEL);
+		if (!p)
+			return -ENOMEM;
+		memcpy(p, a->d, a->alloced * sizeof(mpi_limb_t));
+		kfree(a->d);
+		a->d = p;
+	} else {
+		a->d = kzalloc(nlimbs * sizeof(mpi_limb_t), GFP_KERNEL);
+		if (!a->d)
+			return -ENOMEM;
+	}
+	a->alloced = nlimbs;
+	return 0;
+}
+
+void mpi_clear(MPI a)
+{
+	a->nlimbs = 0;
+	a->nbits = 0;
+	a->flags = 0;
+}
+
+void mpi_free(MPI a)
+{
+	if (!a)
+		return;
+
+	if (a->flags & 4)
+		kfree(a->d);
+	else
+		mpi_free_limb_space(a->d);
+
+	if (a->flags & ~7)
+		pr_info("invalid flag value in mpi\n");
+	kfree(a);
+}
+EXPORT_SYMBOL_GPL(mpi_free);
+
+/****************
+ * Note: This copy function should not interpret the MPI
+ *	 but copy it transparently.
+ */
+int mpi_copy(MPI *copied, const MPI a)
+{
+	size_t i;
+	MPI b;
+
+	*copied = MPI_NULL;
+
+	if (a) {
+		b = mpi_alloc(a->nlimbs);
+		if (!b)
+			return -ENOMEM;
+
+		b->nlimbs = a->nlimbs;
+		b->sign = a->sign;
+		b->flags = a->flags;
+		b->nbits = a->nbits;
+
+		for (i = 0; i < b->nlimbs; i++)
+			b->d[i] = a->d[i];
+
+		*copied = b;
+	}
+
+	return 0;
+}
+
+int mpi_set(MPI w, const MPI u)
+{
+	mpi_ptr_t wp, up;
+	mpi_size_t usize = u->nlimbs;
+	int usign = u->sign;
+
+	if (RESIZE_IF_NEEDED(w, (size_t) usize) < 0)
+		return -ENOMEM;
+
+	wp = w->d;
+	up = u->d;
+	MPN_COPY(wp, up, usize);
+	w->nlimbs = usize;
+	w->nbits = u->nbits;
+	w->flags = u->flags;
+	w->sign = usign;
+	return 0;
+}
+
+int mpi_set_ui(MPI w, unsigned long u)
+{
+	if (RESIZE_IF_NEEDED(w, 1) < 0)
+		return -ENOMEM;
+	w->d[0] = u;
+	w->nlimbs = u ? 1 : 0;
+	w->sign = 0;
+	w->nbits = 0;
+	w->flags = 0;
+	return 0;
+}
+
+MPI mpi_alloc_set_ui(unsigned long u)
+{
+	MPI w = mpi_alloc(1);
+	if (!w)
+		return w;
+	w->d[0] = u;
+	w->nlimbs = u ? 1 : 0;
+	w->sign = 0;
+	return w;
+}
+
+void mpi_swap(MPI a, MPI b)
+{
+	struct gcry_mpi tmp;
+
+	tmp = *a;
+	*a = *b;
+	*b = tmp;
+}

security/integrity/Kconfig

@@ -3,5 +3,19 @@ config INTEGRITY
 	def_bool y
 	depends on IMA || EVM
 
+config INTEGRITY_DIGSIG
+	boolean "Digital signature verification using multiple keyrings"
+	depends on INTEGRITY
+	default n
+	select DIGSIG
+	help
+	  This option enables digital signature verification support
+	  using multiple keyrings. It defines separate keyrings for each
+	  of the different use cases - evm, ima, and modules.
+	  Different keyrings improves search performance, but also allow
+	  to "lock" certain keyring to prevent adding new keys.
+	  This is useful for evm and module keyrings, when keys are
+	  usually only added from initramfs.
+
 source security/integrity/ima/Kconfig
 source security/integrity/evm/Kconfig

security/integrity/Makefile

@@ -3,6 +3,7 @@
 #
 
 obj-$(CONFIG_INTEGRITY) += integrity.o
+obj-$(CONFIG_INTEGRITY_DIGSIG) += digsig.o
 
 integrity-y := iint.o
 

security/integrity/digsig.c

+/*
+ * Copyright (C) 2011 Intel Corporation
+ *
+ * Author:
+ * Dmitry Kasatkin <dmitry.kasatkin@intel.com>
+ *
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, version 2 of the License.
+ *
+ */
+
+#define pr_fmt(fmt) KBUILD_MODNAME ": " fmt
+
+#include <linux/err.h>
+#include <linux/rbtree.h>
+#include <linux/key-type.h>
+#include <linux/digsig.h>
+
+#include "integrity.h"
+
+static struct key *keyring[INTEGRITY_KEYRING_MAX];
+
+static const char *keyring_name[INTEGRITY_KEYRING_MAX] = {
+	"_evm",
+	"_module",
+	"_ima",
+};
+
+int integrity_digsig_verify(const unsigned int id, const char *sig, int siglen,
+					const char *digest, int digestlen)
+{
+	if (id >= INTEGRITY_KEYRING_MAX)
+		return -EINVAL;
+
+	if (!keyring[id]) {
+		keyring[id] =
+			request_key(&key_type_keyring, keyring_name[id], NULL);
+		if (IS_ERR(keyring[id])) {
+			int err = PTR_ERR(keyring[id]);
+			pr_err("no %s keyring: %d\n", keyring_name[id], err);
+			keyring[id] = NULL;
+			return err;
+		}
+	}
+
+	return digsig_verify(keyring[id], sig, siglen, digest, digestlen);
+}

security/integrity/evm/evm.h

@@ -12,14 +12,21 @@
  * File: evm.h
  *
  */
+
+#ifndef __INTEGRITY_EVM_H
+#define __INTEGRITY_EVM_H
+
 #include <linux/xattr.h>
 #include <linux/security.h>
+
 #include "../integrity.h"
 
 extern int evm_initialized;
 extern char *evm_hmac;
+extern char *evm_hash;
 
 extern struct crypto_shash *hmac_tfm;
+extern struct crypto_shash *hash_tfm;
 
 /* List of EVM protected security xattrs */
 extern char *evm_config_xattrnames[];
@@ -32,7 +39,12 @@ extern int evm_update_evmxattr(struct dentry *dentry,
 extern int evm_calc_hmac(struct dentry *dentry, const char *req_xattr_name,
 			 const char *req_xattr_value,
 			 size_t req_xattr_value_len, char *digest);
+extern int evm_calc_hash(struct dentry *dentry, const char *req_xattr_name,
+			 const char *req_xattr_value,
+			 size_t req_xattr_value_len, char *digest);
 extern int evm_init_hmac(struct inode *inode, const struct xattr *xattr,
 			 char *hmac_val);
 extern int evm_init_secfs(void);
 extern void evm_cleanup_secfs(void);
+
+#endif

security/integrity/evm/evm_crypto.c

@@ -26,34 +26,48 @@ static unsigned char evmkey[MAX_KEY_SIZE];
 static int evmkey_len = MAX_KEY_SIZE;
 
 struct crypto_shash *hmac_tfm;
+struct crypto_shash *hash_tfm;
 
-static struct shash_desc *init_desc(void)
+static struct shash_desc *init_desc(const char type)
 {
 	int rc;
+	char *algo;
+	struct crypto_shash **tfm;
 	struct shash_desc *desc;
 
-	if (hmac_tfm == NULL) {
-		hmac_tfm = crypto_alloc_shash(evm_hmac, 0, CRYPTO_ALG_ASYNC);
-		if (IS_ERR(hmac_tfm)) {
+	if (type == EVM_XATTR_HMAC) {
+		tfm = &hmac_tfm;
+		algo = evm_hmac;
+	} else {
+		tfm = &hash_tfm;
+		algo = evm_hash;
+	}
+
+	if (*tfm == NULL) {
+		*tfm = crypto_alloc_shash(algo, 0, CRYPTO_ALG_ASYNC);
+		if (IS_ERR(*tfm)) {
 			pr_err("Can not allocate %s (reason: %ld)\n",
-			       evm_hmac, PTR_ERR(hmac_tfm));
-			rc = PTR_ERR(hmac_tfm);
-			hmac_tfm = NULL;
+			       algo, PTR_ERR(*tfm));
+			rc = PTR_ERR(*tfm);
+			*tfm = NULL;
 			return ERR_PTR(rc);
 		}
 	}
 
-	desc = kmalloc(sizeof(*desc) + crypto_shash_descsize(hmac_tfm),
+	desc = kmalloc(sizeof(*desc) + crypto_shash_descsize(*tfm),
 			GFP_KERNEL);
 	if (!desc)
 		return ERR_PTR(-ENOMEM);
 
-	desc->tfm = hmac_tfm;
+	desc->tfm = *tfm;
 	desc->flags = CRYPTO_TFM_REQ_MAY_SLEEP;
 
-	rc = crypto_shash_setkey(hmac_tfm, evmkey, evmkey_len);
-	if (rc)
-		goto out;
+	if (type == EVM_XATTR_HMAC) {
+		rc = crypto_shash_setkey(*tfm, evmkey, evmkey_len);
+		if (rc)
+			goto out;
+	}
+
 	rc = crypto_shash_init(desc);
 out:
 	if (rc) {
@@ -97,9 +111,11 @@ static void hmac_add_misc(struct shash_desc *desc, struct inode *inode,
  * the hmac using the requested xattr value. Don't alloc/free memory for
  * each xattr, but attempt to re-use the previously allocated memory.
  */
-int evm_calc_hmac(struct dentry *dentry, const char *req_xattr_name,
-		  const char *req_xattr_value, size_t req_xattr_value_len,
-		  char *digest)
+static int evm_calc_hmac_or_hash(struct dentry *dentry,
+				const char *req_xattr_name,
+				const char *req_xattr_value,
+				size_t req_xattr_value_len,
+				char type, char *digest)
 {
 	struct inode *inode = dentry->d_inode;
 	struct shash_desc *desc;
@@ -111,7 +127,7 @@ int evm_calc_hmac(struct dentry *dentry, const char *req_xattr_name,
 
 	if (!inode->i_op || !inode->i_op->getxattr)
 		return -EOPNOTSUPP;
-	desc = init_desc();
+	desc = init_desc(type);
 	if (IS_ERR(desc))
 		return PTR_ERR(desc);
 
@@ -145,6 +161,22 @@ int evm_calc_hmac(struct dentry *dentry, const char *req_xattr_name,
 	return error;
 }
 
+int evm_calc_hmac(struct dentry *dentry, const char *req_xattr_name,
+		  const char *req_xattr_value, size_t req_xattr_value_len,
+		  char *digest)
+{
+	return evm_calc_hmac_or_hash(dentry, req_xattr_name, req_xattr_value,
+				req_xattr_value_len, EVM_XATTR_HMAC, digest);
+}
+
+int evm_calc_hash(struct dentry *dentry, const char *req_xattr_name,
+		  const char *req_xattr_value, size_t req_xattr_value_len,
+		  char *digest)
+{
+	return evm_calc_hmac_or_hash(dentry, req_xattr_name, req_xattr_value,
+				req_xattr_value_len, IMA_XATTR_DIGEST, digest);
+}
+
 /*
  * Calculate the hmac and update security.evm xattr
  *
@@ -175,7 +207,7 @@ int evm_init_hmac(struct inode *inode, const struct xattr *lsm_xattr,
 {
 	struct shash_desc *desc;
 
-	desc = init_desc();
+	desc = init_desc(EVM_XATTR_HMAC);
 	if (IS_ERR(desc)) {
 		printk(KERN_INFO "init_desc failed\n");
 		return PTR_ERR(desc);

security/integrity/evm/evm_main.c

@@ -25,6 +25,7 @@
 int evm_initialized;
 
 char *evm_hmac = "hmac(sha1)";
+char *evm_hash = "sha1";
 
 char *evm_config_xattrnames[] = {
 #ifdef CONFIG_SECURITY_SELINUX
@@ -46,6 +47,29 @@ static int __init evm_set_fixmode(char *str)
 }
 __setup("evm=", evm_set_fixmode);
 
+static int evm_find_protected_xattrs(struct dentry *dentry)
+{
+	struct inode *inode = dentry->d_inode;
+	char **xattr;
+	int error;
+	int count = 0;
+
+	if (!inode->i_op || !inode->i_op->getxattr)
+		return -EOPNOTSUPP;
+
+	for (xattr = evm_config_xattrnames; *xattr != NULL; xattr++) {
+		error = inode->i_op->getxattr(dentry, *xattr, NULL, 0);
+		if (error < 0) {
+			if (error == -ENODATA)
+				continue;
+			return error;
+		}
+		count++;
+	}
+
+	return count;
+}
+
 /*
  * evm_verify_hmac - calculate and compare the HMAC with the EVM xattr
  *
@@ -65,32 +89,72 @@ static enum integrity_status evm_verify_hmac(struct dentry *dentry,
 					     size_t xattr_value_len,
 					     struct integrity_iint_cache *iint)
 {
-	struct evm_ima_xattr_data xattr_data;
+	struct evm_ima_xattr_data *xattr_data = NULL;
+	struct evm_ima_xattr_data calc;
 	enum integrity_status evm_status = INTEGRITY_PASS;
-	int rc;
+	int rc, xattr_len;
 
 	if (iint && iint->evm_status == INTEGRITY_PASS)
 		return iint->evm_status;
 
 	/* if status is not PASS, try to check again - against -ENOMEM */
 
-	rc = evm_calc_hmac(dentry, xattr_name, xattr_value,
-			   xattr_value_len, xattr_data.digest);
-	if (rc < 0) {
-		evm_status = (rc == -ENODATA)
-		    ? INTEGRITY_NOXATTRS : INTEGRITY_FAIL;
+	/* first need to know the sig type */
+	rc = vfs_getxattr_alloc(dentry, XATTR_NAME_EVM, (char **)&xattr_data, 0,
+				GFP_NOFS);
+	if (rc <= 0) {
+		if (rc == 0)
+			evm_status = INTEGRITY_FAIL; /* empty */
+		else if (rc == -ENODATA) {
+			rc = evm_find_protected_xattrs(dentry);
+			if (rc > 0)
+				evm_status = INTEGRITY_NOLABEL;
+			else if (rc == 0)
+				evm_status = INTEGRITY_NOXATTRS; /* new file */
+		}
 		goto out;
 	}
 
-	xattr_data.type = EVM_XATTR_HMAC;
-	rc = vfs_xattr_cmp(dentry, XATTR_NAME_EVM, (u8 *)&xattr_data,
-			   sizeof xattr_data, GFP_NOFS);
-	if (rc < 0)
-		evm_status = (rc == -ENODATA)
-		    ? INTEGRITY_NOLABEL : INTEGRITY_FAIL;
+	xattr_len = rc - 1;
+
+	/* check value type */
+	switch (xattr_data->type) {
+	case EVM_XATTR_HMAC:
+		rc = evm_calc_hmac(dentry, xattr_name, xattr_value,
+				   xattr_value_len, calc.digest);
+		if (rc)
+			break;
+		rc = memcmp(xattr_data->digest, calc.digest,
+			    sizeof(calc.digest));
+		if (rc)
+			rc = -EINVAL;
+		break;
+	case EVM_IMA_XATTR_DIGSIG:
+		rc = evm_calc_hash(dentry, xattr_name, xattr_value,
+				xattr_value_len, calc.digest);
+		if (rc)
+			break;
+		rc = integrity_digsig_verify(INTEGRITY_KEYRING_EVM,
+					xattr_data->digest, xattr_len,
+					calc.digest, sizeof(calc.digest));
+		if (!rc) {
+			/* we probably want to replace rsa with hmac here */
+			evm_update_evmxattr(dentry, xattr_name, xattr_value,
+				   xattr_value_len);
+		}
+		break;
+	default:
+		rc = -EINVAL;
+		break;
+	}
+
+	if (rc)
+		evm_status = (rc == -ENODATA) ?
+				INTEGRITY_NOXATTRS : INTEGRITY_FAIL;
 out:
 	if (iint)
 		iint->evm_status = evm_status;
+	kfree(xattr_data);
 	return evm_status;
 }
 
@@ -354,6 +418,8 @@ static int __init init_evm(void)
 		printk(KERN_INFO "EVM: Error registering secfs\n");
 		goto err;
 	}
+
+	return 0;
 err:
 	return error;
 }
@@ -363,6 +429,8 @@ static void __exit cleanup_evm(void)
 	evm_cleanup_secfs();
 	if (hmac_tfm)
 		crypto_free_shash(hmac_tfm);
+	if (hash_tfm)
+		crypto_free_shash(hash_tfm);
 }
 
 /*

security/integrity/integrity.h

@@ -46,5 +46,26 @@ struct integrity_iint_cache {
 struct integrity_iint_cache *integrity_iint_insert(struct inode *inode);
 struct integrity_iint_cache *integrity_iint_find(struct inode *inode);
 
+#define INTEGRITY_KEYRING_EVM		0
+#define INTEGRITY_KEYRING_MODULE	1
+#define INTEGRITY_KEYRING_IMA		2
+#define INTEGRITY_KEYRING_MAX		3
+
+#ifdef CONFIG_INTEGRITY_DIGSIG
+
+int integrity_digsig_verify(const unsigned int id, const char *sig, int siglen,
+					const char *digest, int digestlen);
+
+#else
+
+static inline int integrity_digsig_verify(const unsigned int id,
+					  const char *sig, int siglen,
+					  const char *digest, int digestlen)
+{
+	return -EOPNOTSUPP;
+}
+
+#endif /* CONFIG_INTEGRITY_DIGSIG */
+
 /* set during initialization */
 extern int iint_initialized;