ecc.c 43.1 KB
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/*
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 * Copyright (c) 2013, 2014 Kenneth MacKay. All rights reserved.
 * Copyright (c) 2019 Vitaly Chikunov <vt@altlinux.org>
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 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are
 * met:
 *  * Redistributions of source code must retain the above copyright
 *   notice, this list of conditions and the following disclaimer.
 *  * Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
 * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
 * HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
 * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
 * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */

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#include <crypto/ecc_curve.h>
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#include <linux/module.h>
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#include <linux/random.h>
#include <linux/slab.h>
#include <linux/swab.h>
#include <linux/fips.h>
#include <crypto/ecdh.h>
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#include <crypto/rng.h>
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#include <crypto/internal/ecc.h>
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#include <asm/unaligned.h>
#include <linux/ratelimit.h>
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#include "ecc_curve_defs.h"

typedef struct {
	u64 m_low;
	u64 m_high;
} uint128_t;

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/* Returns curv25519 curve param */
const struct ecc_curve *ecc_get_curve25519(void)
{
	return &ecc_25519;
}
EXPORT_SYMBOL(ecc_get_curve25519);
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const struct ecc_curve *ecc_get_curve(unsigned int curve_id)
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{
	switch (curve_id) {
	/* In FIPS mode only allow P256 and higher */
	case ECC_CURVE_NIST_P192:
		return fips_enabled ? NULL : &nist_p192;
	case ECC_CURVE_NIST_P256:
		return &nist_p256;
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	case ECC_CURVE_NIST_P384:
		return &nist_p384;
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	default:
		return NULL;
	}
}
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EXPORT_SYMBOL(ecc_get_curve);
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static u64 *ecc_alloc_digits_space(unsigned int ndigits)
{
	size_t len = ndigits * sizeof(u64);

	if (!len)
		return NULL;

	return kmalloc(len, GFP_KERNEL);
}

static void ecc_free_digits_space(u64 *space)
{
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	kfree_sensitive(space);
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}

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struct ecc_point *ecc_alloc_point(unsigned int ndigits)
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{
	struct ecc_point *p = kmalloc(sizeof(*p), GFP_KERNEL);

	if (!p)
		return NULL;

	p->x = ecc_alloc_digits_space(ndigits);
	if (!p->x)
		goto err_alloc_x;

	p->y = ecc_alloc_digits_space(ndigits);
	if (!p->y)
		goto err_alloc_y;

	p->ndigits = ndigits;

	return p;

err_alloc_y:
	ecc_free_digits_space(p->x);
err_alloc_x:
	kfree(p);
	return NULL;
}
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EXPORT_SYMBOL(ecc_alloc_point);
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void ecc_free_point(struct ecc_point *p)
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{
	if (!p)
		return;

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	kfree_sensitive(p->x);
	kfree_sensitive(p->y);
	kfree_sensitive(p);
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}
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EXPORT_SYMBOL(ecc_free_point);
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static void vli_clear(u64 *vli, unsigned int ndigits)
{
	int i;

	for (i = 0; i < ndigits; i++)
		vli[i] = 0;
}

/* Returns true if vli == 0, false otherwise. */
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bool vli_is_zero(const u64 *vli, unsigned int ndigits)
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{
	int i;

	for (i = 0; i < ndigits; i++) {
		if (vli[i])
			return false;
	}

	return true;
}
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EXPORT_SYMBOL(vli_is_zero);
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/* Returns nonzero if bit of vli is set. */
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static u64 vli_test_bit(const u64 *vli, unsigned int bit)
{
	return (vli[bit / 64] & ((u64)1 << (bit % 64)));
}

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static bool vli_is_negative(const u64 *vli, unsigned int ndigits)
{
	return vli_test_bit(vli, ndigits * 64 - 1);
}

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/* Counts the number of 64-bit "digits" in vli. */
static unsigned int vli_num_digits(const u64 *vli, unsigned int ndigits)
{
	int i;

	/* Search from the end until we find a non-zero digit.
	 * We do it in reverse because we expect that most digits will
	 * be nonzero.
	 */
	for (i = ndigits - 1; i >= 0 && vli[i] == 0; i--);

	return (i + 1);
}

/* Counts the number of bits required for vli. */
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unsigned int vli_num_bits(const u64 *vli, unsigned int ndigits)
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{
	unsigned int i, num_digits;
	u64 digit;

	num_digits = vli_num_digits(vli, ndigits);
	if (num_digits == 0)
		return 0;

	digit = vli[num_digits - 1];
	for (i = 0; digit; i++)
		digit >>= 1;

	return ((num_digits - 1) * 64 + i);
}
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EXPORT_SYMBOL(vli_num_bits);
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/* Set dest from unaligned bit string src. */
void vli_from_be64(u64 *dest, const void *src, unsigned int ndigits)
{
	int i;
	const u64 *from = src;

	for (i = 0; i < ndigits; i++)
		dest[i] = get_unaligned_be64(&from[ndigits - 1 - i]);
}
EXPORT_SYMBOL(vli_from_be64);

void vli_from_le64(u64 *dest, const void *src, unsigned int ndigits)
{
	int i;
	const u64 *from = src;

	for (i = 0; i < ndigits; i++)
		dest[i] = get_unaligned_le64(&from[i]);
}
EXPORT_SYMBOL(vli_from_le64);

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/* Sets dest = src. */
static void vli_set(u64 *dest, const u64 *src, unsigned int ndigits)
{
	int i;

	for (i = 0; i < ndigits; i++)
		dest[i] = src[i];
}

/* Returns sign of left - right. */
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int vli_cmp(const u64 *left, const u64 *right, unsigned int ndigits)
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{
	int i;

	for (i = ndigits - 1; i >= 0; i--) {
		if (left[i] > right[i])
			return 1;
		else if (left[i] < right[i])
			return -1;
	}

	return 0;
}
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EXPORT_SYMBOL(vli_cmp);
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/* Computes result = in << c, returning carry. Can modify in place
 * (if result == in). 0 < shift < 64.
 */
static u64 vli_lshift(u64 *result, const u64 *in, unsigned int shift,
		      unsigned int ndigits)
{
	u64 carry = 0;
	int i;

	for (i = 0; i < ndigits; i++) {
		u64 temp = in[i];

		result[i] = (temp << shift) | carry;
		carry = temp >> (64 - shift);
	}

	return carry;
}

/* Computes vli = vli >> 1. */
static void vli_rshift1(u64 *vli, unsigned int ndigits)
{
	u64 *end = vli;
	u64 carry = 0;

	vli += ndigits;

	while (vli-- > end) {
		u64 temp = *vli;
		*vli = (temp >> 1) | carry;
		carry = temp << 63;
	}
}

/* Computes result = left + right, returning carry. Can modify in place. */
static u64 vli_add(u64 *result, const u64 *left, const u64 *right,
		   unsigned int ndigits)
{
	u64 carry = 0;
	int i;

	for (i = 0; i < ndigits; i++) {
		u64 sum;

		sum = left[i] + right[i] + carry;
		if (sum != left[i])
			carry = (sum < left[i]);

		result[i] = sum;
	}

	return carry;
}

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/* Computes result = left + right, returning carry. Can modify in place. */
static u64 vli_uadd(u64 *result, const u64 *left, u64 right,
		    unsigned int ndigits)
{
	u64 carry = right;
	int i;

	for (i = 0; i < ndigits; i++) {
		u64 sum;

		sum = left[i] + carry;
		if (sum != left[i])
			carry = (sum < left[i]);
		else
			carry = !!carry;

		result[i] = sum;
	}

	return carry;
}

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/* Computes result = left - right, returning borrow. Can modify in place. */
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u64 vli_sub(u64 *result, const u64 *left, const u64 *right,
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		   unsigned int ndigits)
{
	u64 borrow = 0;
	int i;

	for (i = 0; i < ndigits; i++) {
		u64 diff;

		diff = left[i] - right[i] - borrow;
		if (diff != left[i])
			borrow = (diff > left[i]);

		result[i] = diff;
	}

	return borrow;
}
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EXPORT_SYMBOL(vli_sub);
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/* Computes result = left - right, returning borrow. Can modify in place. */
static u64 vli_usub(u64 *result, const u64 *left, u64 right,
	     unsigned int ndigits)
{
	u64 borrow = right;
	int i;

	for (i = 0; i < ndigits; i++) {
		u64 diff;

		diff = left[i] - borrow;
		if (diff != left[i])
			borrow = (diff > left[i]);

		result[i] = diff;
	}

	return borrow;
}

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static uint128_t mul_64_64(u64 left, u64 right)
{
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	uint128_t result;
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#if defined(CONFIG_ARCH_SUPPORTS_INT128)
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	unsigned __int128 m = (unsigned __int128)left * right;

	result.m_low  = m;
	result.m_high = m >> 64;
#else
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	u64 a0 = left & 0xffffffffull;
	u64 a1 = left >> 32;
	u64 b0 = right & 0xffffffffull;
	u64 b1 = right >> 32;
	u64 m0 = a0 * b0;
	u64 m1 = a0 * b1;
	u64 m2 = a1 * b0;
	u64 m3 = a1 * b1;

	m2 += (m0 >> 32);
	m2 += m1;

	/* Overflow */
	if (m2 < m1)
		m3 += 0x100000000ull;

	result.m_low = (m0 & 0xffffffffull) | (m2 << 32);
	result.m_high = m3 + (m2 >> 32);
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#endif
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	return result;
}

static uint128_t add_128_128(uint128_t a, uint128_t b)
{
	uint128_t result;

	result.m_low = a.m_low + b.m_low;
	result.m_high = a.m_high + b.m_high + (result.m_low < a.m_low);

	return result;
}

static void vli_mult(u64 *result, const u64 *left, const u64 *right,
		     unsigned int ndigits)
{
	uint128_t r01 = { 0, 0 };
	u64 r2 = 0;
	unsigned int i, k;

	/* Compute each digit of result in sequence, maintaining the
	 * carries.
	 */
	for (k = 0; k < ndigits * 2 - 1; k++) {
		unsigned int min;

		if (k < ndigits)
			min = 0;
		else
			min = (k + 1) - ndigits;

		for (i = min; i <= k && i < ndigits; i++) {
			uint128_t product;

			product = mul_64_64(left[i], right[k - i]);

			r01 = add_128_128(r01, product);
			r2 += (r01.m_high < product.m_high);
		}

		result[k] = r01.m_low;
		r01.m_low = r01.m_high;
		r01.m_high = r2;
		r2 = 0;
	}

	result[ndigits * 2 - 1] = r01.m_low;
}

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/* Compute product = left * right, for a small right value. */
static void vli_umult(u64 *result, const u64 *left, u32 right,
		      unsigned int ndigits)
{
	uint128_t r01 = { 0 };
	unsigned int k;

	for (k = 0; k < ndigits; k++) {
		uint128_t product;

		product = mul_64_64(left[k], right);
		r01 = add_128_128(r01, product);
		/* no carry */
		result[k] = r01.m_low;
		r01.m_low = r01.m_high;
		r01.m_high = 0;
	}
	result[k] = r01.m_low;
	for (++k; k < ndigits * 2; k++)
		result[k] = 0;
}

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static void vli_square(u64 *result, const u64 *left, unsigned int ndigits)
{
	uint128_t r01 = { 0, 0 };
	u64 r2 = 0;
	int i, k;

	for (k = 0; k < ndigits * 2 - 1; k++) {
		unsigned int min;

		if (k < ndigits)
			min = 0;
		else
			min = (k + 1) - ndigits;

		for (i = min; i <= k && i <= k - i; i++) {
			uint128_t product;

			product = mul_64_64(left[i], left[k - i]);

			if (i < k - i) {
				r2 += product.m_high >> 63;
				product.m_high = (product.m_high << 1) |
						 (product.m_low >> 63);
				product.m_low <<= 1;
			}

			r01 = add_128_128(r01, product);
			r2 += (r01.m_high < product.m_high);
		}

		result[k] = r01.m_low;
		r01.m_low = r01.m_high;
		r01.m_high = r2;
		r2 = 0;
	}

	result[ndigits * 2 - 1] = r01.m_low;
}

/* Computes result = (left + right) % mod.
 * Assumes that left < mod and right < mod, result != mod.
 */
static void vli_mod_add(u64 *result, const u64 *left, const u64 *right,
			const u64 *mod, unsigned int ndigits)
{
	u64 carry;

	carry = vli_add(result, left, right, ndigits);

	/* result > mod (result = mod + remainder), so subtract mod to
	 * get remainder.
	 */
	if (carry || vli_cmp(result, mod, ndigits) >= 0)
		vli_sub(result, result, mod, ndigits);
}

/* Computes result = (left - right) % mod.
 * Assumes that left < mod and right < mod, result != mod.
 */
static void vli_mod_sub(u64 *result, const u64 *left, const u64 *right,
			const u64 *mod, unsigned int ndigits)
{
	u64 borrow = vli_sub(result, left, right, ndigits);

	/* In this case, p_result == -diff == (max int) - diff.
	 * Since -x % d == d - x, we can get the correct result from
	 * result + mod (with overflow).
	 */
	if (borrow)
		vli_add(result, result, mod, ndigits);
}

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/*
 * Computes result = product % mod
 * for special form moduli: p = 2^k-c, for small c (note the minus sign)
 *
 * References:
 * R. Crandall, C. Pomerance. Prime Numbers: A Computational Perspective.
 * 9 Fast Algorithms for Large-Integer Arithmetic. 9.2.3 Moduli of special form
 * Algorithm 9.2.13 (Fast mod operation for special-form moduli).
 */
static void vli_mmod_special(u64 *result, const u64 *product,
			      const u64 *mod, unsigned int ndigits)
{
	u64 c = -mod[0];
	u64 t[ECC_MAX_DIGITS * 2];
	u64 r[ECC_MAX_DIGITS * 2];

	vli_set(r, product, ndigits * 2);
	while (!vli_is_zero(r + ndigits, ndigits)) {
		vli_umult(t, r + ndigits, c, ndigits);
		vli_clear(r + ndigits, ndigits);
		vli_add(r, r, t, ndigits * 2);
	}
	vli_set(t, mod, ndigits);
	vli_clear(t + ndigits, ndigits);
	while (vli_cmp(r, t, ndigits * 2) >= 0)
		vli_sub(r, r, t, ndigits * 2);
	vli_set(result, r, ndigits);
}

/*
 * Computes result = product % mod
 * for special form moduli: p = 2^{k-1}+c, for small c (note the plus sign)
 * where k-1 does not fit into qword boundary by -1 bit (such as 255).

 * References (loosely based on):
 * A. Menezes, P. van Oorschot, S. Vanstone. Handbook of Applied Cryptography.
 * 14.3.4 Reduction methods for moduli of special form. Algorithm 14.47.
 * URL: http://cacr.uwaterloo.ca/hac/about/chap14.pdf
 *
 * H. Cohen, G. Frey, R. Avanzi, C. Doche, T. Lange, K. Nguyen, F. Vercauteren.
 * Handbook of Elliptic and Hyperelliptic Curve Cryptography.
 * Algorithm 10.25 Fast reduction for special form moduli
 */
static void vli_mmod_special2(u64 *result, const u64 *product,
			       const u64 *mod, unsigned int ndigits)
{
	u64 c2 = mod[0] * 2;
	u64 q[ECC_MAX_DIGITS];
	u64 r[ECC_MAX_DIGITS * 2];
	u64 m[ECC_MAX_DIGITS * 2]; /* expanded mod */
	int carry; /* last bit that doesn't fit into q */
	int i;

	vli_set(m, mod, ndigits);
	vli_clear(m + ndigits, ndigits);

	vli_set(r, product, ndigits);
	/* q and carry are top bits */
	vli_set(q, product + ndigits, ndigits);
	vli_clear(r + ndigits, ndigits);
	carry = vli_is_negative(r, ndigits);
	if (carry)
		r[ndigits - 1] &= (1ull << 63) - 1;
	for (i = 1; carry || !vli_is_zero(q, ndigits); i++) {
		u64 qc[ECC_MAX_DIGITS * 2];

		vli_umult(qc, q, c2, ndigits);
		if (carry)
			vli_uadd(qc, qc, mod[0], ndigits * 2);
		vli_set(q, qc + ndigits, ndigits);
		vli_clear(qc + ndigits, ndigits);
		carry = vli_is_negative(qc, ndigits);
		if (carry)
			qc[ndigits - 1] &= (1ull << 63) - 1;
		if (i & 1)
			vli_sub(r, r, qc, ndigits * 2);
		else
			vli_add(r, r, qc, ndigits * 2);
	}
	while (vli_is_negative(r, ndigits * 2))
		vli_add(r, r, m, ndigits * 2);
	while (vli_cmp(r, m, ndigits * 2) >= 0)
		vli_sub(r, r, m, ndigits * 2);

	vli_set(result, r, ndigits);
}

/*
 * Computes result = product % mod, where product is 2N words long.
 * Reference: Ken MacKay's micro-ecc.
 * Currently only designed to work for curve_p or curve_n.
 */
static void vli_mmod_slow(u64 *result, u64 *product, const u64 *mod,
			  unsigned int ndigits)
{
	u64 mod_m[2 * ECC_MAX_DIGITS];
	u64 tmp[2 * ECC_MAX_DIGITS];
	u64 *v[2] = { tmp, product };
	u64 carry = 0;
	unsigned int i;
	/* Shift mod so its highest set bit is at the maximum position. */
	int shift = (ndigits * 2 * 64) - vli_num_bits(mod, ndigits);
	int word_shift = shift / 64;
	int bit_shift = shift % 64;

	vli_clear(mod_m, word_shift);
	if (bit_shift > 0) {
		for (i = 0; i < ndigits; ++i) {
			mod_m[word_shift + i] = (mod[i] << bit_shift) | carry;
			carry = mod[i] >> (64 - bit_shift);
		}
	} else
		vli_set(mod_m + word_shift, mod, ndigits);

	for (i = 1; shift >= 0; --shift) {
		u64 borrow = 0;
		unsigned int j;

		for (j = 0; j < ndigits * 2; ++j) {
			u64 diff = v[i][j] - mod_m[j] - borrow;

			if (diff != v[i][j])
				borrow = (diff > v[i][j]);
			v[1 - i][j] = diff;
		}
		i = !(i ^ borrow); /* Swap the index if there was no borrow */
		vli_rshift1(mod_m, ndigits);
		mod_m[ndigits - 1] |= mod_m[ndigits] << (64 - 1);
		vli_rshift1(mod_m + ndigits, ndigits);
	}
	vli_set(result, v[i], ndigits);
}

/* Computes result = product % mod using Barrett's reduction with precomputed
 * value mu appended to the mod after ndigits, mu = (2^{2w} / mod) and have
 * length ndigits + 1, where mu * (2^w - 1) should not overflow ndigits
 * boundary.
 *
 * Reference:
 * R. Brent, P. Zimmermann. Modern Computer Arithmetic. 2010.
 * 2.4.1 Barrett's algorithm. Algorithm 2.5.
 */
static void vli_mmod_barrett(u64 *result, u64 *product, const u64 *mod,
			     unsigned int ndigits)
{
	u64 q[ECC_MAX_DIGITS * 2];
	u64 r[ECC_MAX_DIGITS * 2];
	const u64 *mu = mod + ndigits;

	vli_mult(q, product + ndigits, mu, ndigits);
	if (mu[ndigits])
		vli_add(q + ndigits, q + ndigits, product + ndigits, ndigits);
	vli_mult(r, mod, q + ndigits, ndigits);
	vli_sub(r, product, r, ndigits * 2);
	while (!vli_is_zero(r + ndigits, ndigits) ||
	       vli_cmp(r, mod, ndigits) != -1) {
		u64 carry;

		carry = vli_sub(r, r, mod, ndigits);
		vli_usub(r + ndigits, r + ndigits, carry, ndigits);
	}
	vli_set(result, r, ndigits);
}

685 686 687 688 689 690 691
/* Computes p_result = p_product % curve_p.
 * See algorithm 5 and 6 from
 * http://www.isys.uni-klu.ac.at/PDF/2001-0126-MT.pdf
 */
static void vli_mmod_fast_192(u64 *result, const u64 *product,
			      const u64 *curve_prime, u64 *tmp)
{
692
	const unsigned int ndigits = ECC_CURVE_NIST_P192_DIGITS;
693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719
	int carry;

	vli_set(result, product, ndigits);

	vli_set(tmp, &product[3], ndigits);
	carry = vli_add(result, result, tmp, ndigits);

	tmp[0] = 0;
	tmp[1] = product[3];
	tmp[2] = product[4];
	carry += vli_add(result, result, tmp, ndigits);

	tmp[0] = tmp[1] = product[5];
	tmp[2] = 0;
	carry += vli_add(result, result, tmp, ndigits);

	while (carry || vli_cmp(curve_prime, result, ndigits) != 1)
		carry -= vli_sub(result, result, curve_prime, ndigits);
}

/* Computes result = product % curve_prime
 * from http://www.nsa.gov/ia/_files/nist-routines.pdf
 */
static void vli_mmod_fast_256(u64 *result, const u64 *product,
			      const u64 *curve_prime, u64 *tmp)
{
	int carry;
720
	const unsigned int ndigits = ECC_CURVE_NIST_P256_DIGITS;
721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791

	/* t */
	vli_set(result, product, ndigits);

	/* s1 */
	tmp[0] = 0;
	tmp[1] = product[5] & 0xffffffff00000000ull;
	tmp[2] = product[6];
	tmp[3] = product[7];
	carry = vli_lshift(tmp, tmp, 1, ndigits);
	carry += vli_add(result, result, tmp, ndigits);

	/* s2 */
	tmp[1] = product[6] << 32;
	tmp[2] = (product[6] >> 32) | (product[7] << 32);
	tmp[3] = product[7] >> 32;
	carry += vli_lshift(tmp, tmp, 1, ndigits);
	carry += vli_add(result, result, tmp, ndigits);

	/* s3 */
	tmp[0] = product[4];
	tmp[1] = product[5] & 0xffffffff;
	tmp[2] = 0;
	tmp[3] = product[7];
	carry += vli_add(result, result, tmp, ndigits);

	/* s4 */
	tmp[0] = (product[4] >> 32) | (product[5] << 32);
	tmp[1] = (product[5] >> 32) | (product[6] & 0xffffffff00000000ull);
	tmp[2] = product[7];
	tmp[3] = (product[6] >> 32) | (product[4] << 32);
	carry += vli_add(result, result, tmp, ndigits);

	/* d1 */
	tmp[0] = (product[5] >> 32) | (product[6] << 32);
	tmp[1] = (product[6] >> 32);
	tmp[2] = 0;
	tmp[3] = (product[4] & 0xffffffff) | (product[5] << 32);
	carry -= vli_sub(result, result, tmp, ndigits);

	/* d2 */
	tmp[0] = product[6];
	tmp[1] = product[7];
	tmp[2] = 0;
	tmp[3] = (product[4] >> 32) | (product[5] & 0xffffffff00000000ull);
	carry -= vli_sub(result, result, tmp, ndigits);

	/* d3 */
	tmp[0] = (product[6] >> 32) | (product[7] << 32);
	tmp[1] = (product[7] >> 32) | (product[4] << 32);
	tmp[2] = (product[4] >> 32) | (product[5] << 32);
	tmp[3] = (product[6] << 32);
	carry -= vli_sub(result, result, tmp, ndigits);

	/* d4 */
	tmp[0] = product[7];
	tmp[1] = product[4] & 0xffffffff00000000ull;
	tmp[2] = product[5];
	tmp[3] = product[6] & 0xffffffff00000000ull;
	carry -= vli_sub(result, result, tmp, ndigits);

	if (carry < 0) {
		do {
			carry += vli_add(result, result, curve_prime, ndigits);
		} while (carry < 0);
	} else {
		while (carry || vli_cmp(curve_prime, result, ndigits) != 1)
			carry -= vli_sub(result, result, curve_prime, ndigits);
	}
}

792 793 794 795 796 797 798 799 800 801 802
#define SL32OR32(x32, y32) (((u64)x32 << 32) | y32)
#define AND64H(x64)  (x64 & 0xffFFffFF00000000ull)
#define AND64L(x64)  (x64 & 0x00000000ffFFffFFull)

/* Computes result = product % curve_prime
 * from "Mathematical routines for the NIST prime elliptic curves"
 */
static void vli_mmod_fast_384(u64 *result, const u64 *product,
				const u64 *curve_prime, u64 *tmp)
{
	int carry;
803
	const unsigned int ndigits = ECC_CURVE_NIST_P384_DIGITS;
804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904

	/* t */
	vli_set(result, product, ndigits);

	/* s1 */
	tmp[0] = 0;		// 0 || 0
	tmp[1] = 0;		// 0 || 0
	tmp[2] = SL32OR32(product[11], (product[10]>>32));	//a22||a21
	tmp[3] = product[11]>>32;	// 0 ||a23
	tmp[4] = 0;		// 0 || 0
	tmp[5] = 0;		// 0 || 0
	carry = vli_lshift(tmp, tmp, 1, ndigits);
	carry += vli_add(result, result, tmp, ndigits);

	/* s2 */
	tmp[0] = product[6];	//a13||a12
	tmp[1] = product[7];	//a15||a14
	tmp[2] = product[8];	//a17||a16
	tmp[3] = product[9];	//a19||a18
	tmp[4] = product[10];	//a21||a20
	tmp[5] = product[11];	//a23||a22
	carry += vli_add(result, result, tmp, ndigits);

	/* s3 */
	tmp[0] = SL32OR32(product[11], (product[10]>>32));	//a22||a21
	tmp[1] = SL32OR32(product[6], (product[11]>>32));	//a12||a23
	tmp[2] = SL32OR32(product[7], (product[6])>>32);	//a14||a13
	tmp[3] = SL32OR32(product[8], (product[7]>>32));	//a16||a15
	tmp[4] = SL32OR32(product[9], (product[8]>>32));	//a18||a17
	tmp[5] = SL32OR32(product[10], (product[9]>>32));	//a20||a19
	carry += vli_add(result, result, tmp, ndigits);

	/* s4 */
	tmp[0] = AND64H(product[11]);	//a23|| 0
	tmp[1] = (product[10]<<32);	//a20|| 0
	tmp[2] = product[6];	//a13||a12
	tmp[3] = product[7];	//a15||a14
	tmp[4] = product[8];	//a17||a16
	tmp[5] = product[9];	//a19||a18
	carry += vli_add(result, result, tmp, ndigits);

	/* s5 */
	tmp[0] = 0;		//  0|| 0
	tmp[1] = 0;		//  0|| 0
	tmp[2] = product[10];	//a21||a20
	tmp[3] = product[11];	//a23||a22
	tmp[4] = 0;		//  0|| 0
	tmp[5] = 0;		//  0|| 0
	carry += vli_add(result, result, tmp, ndigits);

	/* s6 */
	tmp[0] = AND64L(product[10]);	// 0 ||a20
	tmp[1] = AND64H(product[10]);	//a21|| 0
	tmp[2] = product[11];	//a23||a22
	tmp[3] = 0;		// 0 || 0
	tmp[4] = 0;		// 0 || 0
	tmp[5] = 0;		// 0 || 0
	carry += vli_add(result, result, tmp, ndigits);

	/* d1 */
	tmp[0] = SL32OR32(product[6], (product[11]>>32));	//a12||a23
	tmp[1] = SL32OR32(product[7], (product[6]>>32));	//a14||a13
	tmp[2] = SL32OR32(product[8], (product[7]>>32));	//a16||a15
	tmp[3] = SL32OR32(product[9], (product[8]>>32));	//a18||a17
	tmp[4] = SL32OR32(product[10], (product[9]>>32));	//a20||a19
	tmp[5] = SL32OR32(product[11], (product[10]>>32));	//a22||a21
	carry -= vli_sub(result, result, tmp, ndigits);

	/* d2 */
	tmp[0] = (product[10]<<32);	//a20|| 0
	tmp[1] = SL32OR32(product[11], (product[10]>>32));	//a22||a21
	tmp[2] = (product[11]>>32);	// 0 ||a23
	tmp[3] = 0;		// 0 || 0
	tmp[4] = 0;		// 0 || 0
	tmp[5] = 0;		// 0 || 0
	carry -= vli_sub(result, result, tmp, ndigits);

	/* d3 */
	tmp[0] = 0;		// 0 || 0
	tmp[1] = AND64H(product[11]);	//a23|| 0
	tmp[2] = product[11]>>32;	// 0 ||a23
	tmp[3] = 0;		// 0 || 0
	tmp[4] = 0;		// 0 || 0
	tmp[5] = 0;		// 0 || 0
	carry -= vli_sub(result, result, tmp, ndigits);

	if (carry < 0) {
		do {
			carry += vli_add(result, result, curve_prime, ndigits);
		} while (carry < 0);
	} else {
		while (carry || vli_cmp(curve_prime, result, ndigits) != 1)
			carry -= vli_sub(result, result, curve_prime, ndigits);
	}

}

#undef SL32OR32
#undef AND64H
#undef AND64L

905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926
/*
 * Computes result = product % curve_prime
 * from "Recommendations for Discrete Logarithm-Based Cryptography:
 *       Elliptic Curve Domain Parameters" section G.1.4
 */
static void vli_mmod_fast_521(u64 *result, const u64 *product,
			      const u64 *curve_prime, u64 *tmp)
{
	const unsigned int ndigits = ECC_CURVE_NIST_P521_DIGITS;
	size_t i;

	/* Initialize result with lowest 521 bits from product */
	vli_set(result, product, ndigits);
	result[8] &= 0x1ff;

	for (i = 0; i < ndigits; i++)
		tmp[i] = (product[8 + i] >> 9) | (product[9 + i] << 55);
	tmp[8] &= 0x1ff;

	vli_mod_add(result, result, tmp, curve_prime, ndigits);
}

927 928 929 930 931
/* Computes result = product % curve_prime for different curve_primes.
 *
 * Note that curve_primes are distinguished just by heuristic check and
 * not by complete conformance check.
 */
932
static bool vli_mmod_fast(u64 *result, u64 *product,
933
			  const struct ecc_curve *curve)
934
{
935
	u64 tmp[2 * ECC_MAX_DIGITS];
936 937
	const u64 *curve_prime = curve->p;
	const unsigned int ndigits = curve->g.ndigits;
938

939 940
	/* All NIST curves have name prefix 'nist_' */
	if (strncmp(curve->name, "nist_", 5) != 0) {
941 942 943 944 945 946 947 948 949 950 951 952 953 954 955
		/* Try to handle Pseudo-Marsenne primes. */
		if (curve_prime[ndigits - 1] == -1ull) {
			vli_mmod_special(result, product, curve_prime,
					 ndigits);
			return true;
		} else if (curve_prime[ndigits - 1] == 1ull << 63 &&
			   curve_prime[ndigits - 2] == 0) {
			vli_mmod_special2(result, product, curve_prime,
					  ndigits);
			return true;
		}
		vli_mmod_barrett(result, product, curve_prime, ndigits);
		return true;
	}

956
	switch (ndigits) {
957
	case ECC_CURVE_NIST_P192_DIGITS:
958 959
		vli_mmod_fast_192(result, product, curve_prime, tmp);
		break;
960
	case ECC_CURVE_NIST_P256_DIGITS:
961 962
		vli_mmod_fast_256(result, product, curve_prime, tmp);
		break;
963
	case ECC_CURVE_NIST_P384_DIGITS:
964 965
		vli_mmod_fast_384(result, product, curve_prime, tmp);
		break;
966 967 968
	case ECC_CURVE_NIST_P521_DIGITS:
		vli_mmod_fast_521(result, product, curve_prime, tmp);
		break;
969
	default:
970
		pr_err_ratelimited("ecc: unsupported digits size!\n");
971 972 973 974 975 976
		return false;
	}

	return true;
}

977 978 979 980 981 982 983 984 985 986 987 988 989
/* Computes result = (left * right) % mod.
 * Assumes that mod is big enough curve order.
 */
void vli_mod_mult_slow(u64 *result, const u64 *left, const u64 *right,
		       const u64 *mod, unsigned int ndigits)
{
	u64 product[ECC_MAX_DIGITS * 2];

	vli_mult(product, left, right, ndigits);
	vli_mmod_slow(result, product, mod, ndigits);
}
EXPORT_SYMBOL(vli_mod_mult_slow);

990 991
/* Computes result = (left * right) % curve_prime. */
static void vli_mod_mult_fast(u64 *result, const u64 *left, const u64 *right,
992
			      const struct ecc_curve *curve)
993
{
994
	u64 product[2 * ECC_MAX_DIGITS];
995

996 997
	vli_mult(product, left, right, curve->g.ndigits);
	vli_mmod_fast(result, product, curve);
998 999 1000 1001
}

/* Computes result = left^2 % curve_prime. */
static void vli_mod_square_fast(u64 *result, const u64 *left,
1002
				const struct ecc_curve *curve)
1003
{
1004
	u64 product[2 * ECC_MAX_DIGITS];
1005

1006 1007
	vli_square(product, left, curve->g.ndigits);
	vli_mmod_fast(result, product, curve);
1008 1009 1010 1011 1012 1013 1014
}

#define EVEN(vli) (!(vli[0] & 1))
/* Computes result = (1 / p_input) % mod. All VLIs are the same size.
 * See "From Euclid's GCD to Montgomery Multiplication to the Great Divide"
 * https://labs.oracle.com/techrep/2001/smli_tr-2001-95.pdf
 */
1015
void vli_mod_inv(u64 *result, const u64 *input, const u64 *mod,
1016 1017
			unsigned int ndigits)
{
1018 1019
	u64 a[ECC_MAX_DIGITS], b[ECC_MAX_DIGITS];
	u64 u[ECC_MAX_DIGITS], v[ECC_MAX_DIGITS];
1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087
	u64 carry;
	int cmp_result;

	if (vli_is_zero(input, ndigits)) {
		vli_clear(result, ndigits);
		return;
	}

	vli_set(a, input, ndigits);
	vli_set(b, mod, ndigits);
	vli_clear(u, ndigits);
	u[0] = 1;
	vli_clear(v, ndigits);

	while ((cmp_result = vli_cmp(a, b, ndigits)) != 0) {
		carry = 0;

		if (EVEN(a)) {
			vli_rshift1(a, ndigits);

			if (!EVEN(u))
				carry = vli_add(u, u, mod, ndigits);

			vli_rshift1(u, ndigits);
			if (carry)
				u[ndigits - 1] |= 0x8000000000000000ull;
		} else if (EVEN(b)) {
			vli_rshift1(b, ndigits);

			if (!EVEN(v))
				carry = vli_add(v, v, mod, ndigits);

			vli_rshift1(v, ndigits);
			if (carry)
				v[ndigits - 1] |= 0x8000000000000000ull;
		} else if (cmp_result > 0) {
			vli_sub(a, a, b, ndigits);
			vli_rshift1(a, ndigits);

			if (vli_cmp(u, v, ndigits) < 0)
				vli_add(u, u, mod, ndigits);

			vli_sub(u, u, v, ndigits);
			if (!EVEN(u))
				carry = vli_add(u, u, mod, ndigits);

			vli_rshift1(u, ndigits);
			if (carry)
				u[ndigits - 1] |= 0x8000000000000000ull;
		} else {
			vli_sub(b, b, a, ndigits);
			vli_rshift1(b, ndigits);

			if (vli_cmp(v, u, ndigits) < 0)
				vli_add(v, v, mod, ndigits);

			vli_sub(v, v, u, ndigits);
			if (!EVEN(v))
				carry = vli_add(v, v, mod, ndigits);

			vli_rshift1(v, ndigits);
			if (carry)
				v[ndigits - 1] |= 0x8000000000000000ull;
		}
	}

	vli_set(result, u, ndigits);
}
1088
EXPORT_SYMBOL(vli_mod_inv);
1089 1090 1091 1092

/* ------ Point operations ------ */

/* Returns true if p_point is the point at infinity, false otherwise. */
1093
bool ecc_point_is_zero(const struct ecc_point *point)
1094 1095 1096 1097
{
	return (vli_is_zero(point->x, point->ndigits) &&
		vli_is_zero(point->y, point->ndigits));
}
1098
EXPORT_SYMBOL(ecc_point_is_zero);
1099 1100

/* Point multiplication algorithm using Montgomery's ladder with co-Z
1101
 * coordinates. From https://eprint.iacr.org/2011/338.pdf
1102 1103 1104 1105
 */

/* Double in place */
static void ecc_point_double_jacobian(u64 *x1, u64 *y1, u64 *z1,
1106
					const struct ecc_curve *curve)
1107 1108
{
	/* t1 = x, t2 = y, t3 = z */
1109 1110
	u64 t4[ECC_MAX_DIGITS];
	u64 t5[ECC_MAX_DIGITS];
1111 1112
	const u64 *curve_prime = curve->p;
	const unsigned int ndigits = curve->g.ndigits;
1113 1114 1115 1116 1117

	if (vli_is_zero(z1, ndigits))
		return;

	/* t4 = y1^2 */
1118
	vli_mod_square_fast(t4, y1, curve);
1119
	/* t5 = x1*y1^2 = A */
1120
	vli_mod_mult_fast(t5, x1, t4, curve);
1121
	/* t4 = y1^4 */
1122
	vli_mod_square_fast(t4, t4, curve);
1123
	/* t2 = y1*z1 = z3 */
1124
	vli_mod_mult_fast(y1, y1, z1, curve);
1125
	/* t3 = z1^2 */
1126
	vli_mod_square_fast(z1, z1, curve);
1127 1128 1129 1130 1131 1132 1133 1134

	/* t1 = x1 + z1^2 */
	vli_mod_add(x1, x1, z1, curve_prime, ndigits);
	/* t3 = 2*z1^2 */
	vli_mod_add(z1, z1, z1, curve_prime, ndigits);
	/* t3 = x1 - z1^2 */
	vli_mod_sub(z1, x1, z1, curve_prime, ndigits);
	/* t1 = x1^2 - z1^4 */
1135
	vli_mod_mult_fast(x1, x1, z1, curve);
1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151

	/* t3 = 2*(x1^2 - z1^4) */
	vli_mod_add(z1, x1, x1, curve_prime, ndigits);
	/* t1 = 3*(x1^2 - z1^4) */
	vli_mod_add(x1, x1, z1, curve_prime, ndigits);
	if (vli_test_bit(x1, 0)) {
		u64 carry = vli_add(x1, x1, curve_prime, ndigits);

		vli_rshift1(x1, ndigits);
		x1[ndigits - 1] |= carry << 63;
	} else {
		vli_rshift1(x1, ndigits);
	}
	/* t1 = 3/2*(x1^2 - z1^4) = B */

	/* t3 = B^2 */
1152
	vli_mod_square_fast(z1, x1, curve);
1153 1154 1155 1156 1157 1158 1159
	/* t3 = B^2 - A */
	vli_mod_sub(z1, z1, t5, curve_prime, ndigits);
	/* t3 = B^2 - 2A = x3 */
	vli_mod_sub(z1, z1, t5, curve_prime, ndigits);
	/* t5 = A - x3 */
	vli_mod_sub(t5, t5, z1, curve_prime, ndigits);
	/* t1 = B * (A - x3) */
1160
	vli_mod_mult_fast(x1, x1, t5, curve);
1161 1162 1163 1164 1165 1166 1167 1168 1169
	/* t4 = B * (A - x3) - y1^4 = y3 */
	vli_mod_sub(t4, x1, t4, curve_prime, ndigits);

	vli_set(x1, z1, ndigits);
	vli_set(z1, y1, ndigits);
	vli_set(y1, t4, ndigits);
}

/* Modify (x1, y1) => (x1 * z^2, y1 * z^3) */
1170
static void apply_z(u64 *x1, u64 *y1, u64 *z, const struct ecc_curve *curve)
1171
{
1172
	u64 t1[ECC_MAX_DIGITS];
1173

1174 1175 1176 1177
	vli_mod_square_fast(t1, z, curve);		/* z^2 */
	vli_mod_mult_fast(x1, x1, t1, curve);	/* x1 * z^2 */
	vli_mod_mult_fast(t1, t1, z, curve);	/* z^3 */
	vli_mod_mult_fast(y1, y1, t1, curve);	/* y1 * z^3 */
1178 1179 1180 1181
}

/* P = (x1, y1) => 2P, (x2, y2) => P' */
static void xycz_initial_double(u64 *x1, u64 *y1, u64 *x2, u64 *y2,
1182
				u64 *p_initial_z, const struct ecc_curve *curve)
1183
{
1184
	u64 z[ECC_MAX_DIGITS];
1185
	const unsigned int ndigits = curve->g.ndigits;
1186 1187 1188 1189 1190 1191 1192 1193 1194 1195

	vli_set(x2, x1, ndigits);
	vli_set(y2, y1, ndigits);

	vli_clear(z, ndigits);
	z[0] = 1;

	if (p_initial_z)
		vli_set(z, p_initial_z, ndigits);

1196
	apply_z(x1, y1, z, curve);
1197

1198
	ecc_point_double_jacobian(x1, y1, z, curve);
1199

1200
	apply_z(x2, y2, z, curve);
1201 1202 1203 1204 1205 1206
}

/* Input P = (x1, y1, Z), Q = (x2, y2, Z)
 * Output P' = (x1', y1', Z3), P + Q = (x3, y3, Z3)
 * or P => P', Q => P + Q
 */
1207 1208
static void xycz_add(u64 *x1, u64 *y1, u64 *x2, u64 *y2,
			const struct ecc_curve *curve)
1209 1210
{
	/* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
1211
	u64 t5[ECC_MAX_DIGITS];
1212 1213
	const u64 *curve_prime = curve->p;
	const unsigned int ndigits = curve->g.ndigits;
1214 1215 1216 1217

	/* t5 = x2 - x1 */
	vli_mod_sub(t5, x2, x1, curve_prime, ndigits);
	/* t5 = (x2 - x1)^2 = A */
1218
	vli_mod_square_fast(t5, t5, curve);
1219
	/* t1 = x1*A = B */
1220
	vli_mod_mult_fast(x1, x1, t5, curve);
1221
	/* t3 = x2*A = C */
1222
	vli_mod_mult_fast(x2, x2, t5, curve);
1223 1224 1225
	/* t4 = y2 - y1 */
	vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
	/* t5 = (y2 - y1)^2 = D */
1226
	vli_mod_square_fast(t5, y2, curve);
1227 1228 1229 1230 1231 1232 1233 1234

	/* t5 = D - B */
	vli_mod_sub(t5, t5, x1, curve_prime, ndigits);
	/* t5 = D - B - C = x3 */
	vli_mod_sub(t5, t5, x2, curve_prime, ndigits);
	/* t3 = C - B */
	vli_mod_sub(x2, x2, x1, curve_prime, ndigits);
	/* t2 = y1*(C - B) */
1235
	vli_mod_mult_fast(y1, y1, x2, curve);
1236 1237 1238
	/* t3 = B - x3 */
	vli_mod_sub(x2, x1, t5, curve_prime, ndigits);
	/* t4 = (y2 - y1)*(B - x3) */
1239
	vli_mod_mult_fast(y2, y2, x2, curve);
1240 1241 1242 1243 1244 1245 1246 1247 1248 1249
	/* t4 = y3 */
	vli_mod_sub(y2, y2, y1, curve_prime, ndigits);

	vli_set(x2, t5, ndigits);
}

/* Input P = (x1, y1, Z), Q = (x2, y2, Z)
 * Output P + Q = (x3, y3, Z3), P - Q = (x3', y3', Z3)
 * or P => P - Q, Q => P + Q
 */
1250 1251
static void xycz_add_c(u64 *x1, u64 *y1, u64 *x2, u64 *y2,
			const struct ecc_curve *curve)
1252 1253
{
	/* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
1254 1255 1256
	u64 t5[ECC_MAX_DIGITS];
	u64 t6[ECC_MAX_DIGITS];
	u64 t7[ECC_MAX_DIGITS];
1257 1258
	const u64 *curve_prime = curve->p;
	const unsigned int ndigits = curve->g.ndigits;
1259 1260 1261 1262

	/* t5 = x2 - x1 */
	vli_mod_sub(t5, x2, x1, curve_prime, ndigits);
	/* t5 = (x2 - x1)^2 = A */
1263
	vli_mod_square_fast(t5, t5, curve);
1264
	/* t1 = x1*A = B */
1265
	vli_mod_mult_fast(x1, x1, t5, curve);
1266
	/* t3 = x2*A = C */
1267
	vli_mod_mult_fast(x2, x2, t5, curve);
1268 1269 1270 1271 1272 1273 1274 1275
	/* t4 = y2 + y1 */
	vli_mod_add(t5, y2, y1, curve_prime, ndigits);
	/* t4 = y2 - y1 */
	vli_mod_sub(y2, y2, y1, curve_prime, ndigits);

	/* t6 = C - B */
	vli_mod_sub(t6, x2, x1, curve_prime, ndigits);
	/* t2 = y1 * (C - B) */
1276
	vli_mod_mult_fast(y1, y1, t6, curve);
1277 1278 1279
	/* t6 = B + C */
	vli_mod_add(t6, x1, x2, curve_prime, ndigits);
	/* t3 = (y2 - y1)^2 */
1280
	vli_mod_square_fast(x2, y2, curve);
1281 1282 1283 1284 1285 1286
	/* t3 = x3 */
	vli_mod_sub(x2, x2, t6, curve_prime, ndigits);

	/* t7 = B - x3 */
	vli_mod_sub(t7, x1, x2, curve_prime, ndigits);
	/* t4 = (y2 - y1)*(B - x3) */
1287
	vli_mod_mult_fast(y2, y2, t7, curve);
1288 1289 1290 1291
	/* t4 = y3 */
	vli_mod_sub(y2, y2, y1, curve_prime, ndigits);

	/* t7 = (y2 + y1)^2 = F */
1292
	vli_mod_square_fast(t7, t5, curve);
1293 1294 1295 1296 1297
	/* t7 = x3' */
	vli_mod_sub(t7, t7, t6, curve_prime, ndigits);
	/* t6 = x3' - B */
	vli_mod_sub(t6, t7, x1, curve_prime, ndigits);
	/* t6 = (y2 + y1)*(x3' - B) */
1298
	vli_mod_mult_fast(t6, t6, t5, curve);
1299 1300 1301 1302 1303 1304 1305 1306
	/* t2 = y3' */
	vli_mod_sub(y1, t6, y1, curve_prime, ndigits);

	vli_set(x1, t7, ndigits);
}

static void ecc_point_mult(struct ecc_point *result,
			   const struct ecc_point *point, const u64 *scalar,
1307
			   u64 *initial_z, const struct ecc_curve *curve,
1308 1309 1310
			   unsigned int ndigits)
{
	/* R0 and R1 */
1311 1312 1313
	u64 rx[2][ECC_MAX_DIGITS];
	u64 ry[2][ECC_MAX_DIGITS];
	u64 z[ECC_MAX_DIGITS];
1314 1315
	u64 sk[2][ECC_MAX_DIGITS];
	u64 *curve_prime = curve->p;
1316
	int i, nb;
1317 1318 1319 1320 1321 1322 1323
	int num_bits;
	int carry;

	carry = vli_add(sk[0], scalar, curve->n, ndigits);
	vli_add(sk[1], sk[0], curve->n, ndigits);
	scalar = sk[!carry];
	num_bits = sizeof(u64) * ndigits * 8 + 1;
1324 1325 1326 1327

	vli_set(rx[1], point->x, ndigits);
	vli_set(ry[1], point->y, ndigits);

1328
	xycz_initial_double(rx[1], ry[1], rx[0], ry[0], initial_z, curve);
1329 1330 1331

	for (i = num_bits - 2; i > 0; i--) {
		nb = !vli_test_bit(scalar, i);
1332 1333
		xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve);
		xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve);
1334 1335 1336
	}

	nb = !vli_test_bit(scalar, 0);
1337
	xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve);
1338 1339 1340 1341 1342

	/* Find final 1/Z value. */
	/* X1 - X0 */
	vli_mod_sub(z, rx[1], rx[0], curve_prime, ndigits);
	/* Yb * (X1 - X0) */
1343
	vli_mod_mult_fast(z, z, ry[1 - nb], curve);
1344
	/* xP * Yb * (X1 - X0) */
1345
	vli_mod_mult_fast(z, z, point->x, curve);
1346 1347 1348 1349 1350

	/* 1 / (xP * Yb * (X1 - X0)) */
	vli_mod_inv(z, z, curve_prime, point->ndigits);

	/* yP / (xP * Yb * (X1 - X0)) */
1351
	vli_mod_mult_fast(z, z, point->y, curve);
1352
	/* Xb * yP / (xP * Yb * (X1 - X0)) */
1353
	vli_mod_mult_fast(z, z, rx[1 - nb], curve);
1354 1355
	/* End 1/Z calculation */

1356
	xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve);
1357

1358
	apply_z(rx[0], ry[0], z, curve);
1359 1360 1361 1362 1363

	vli_set(result->x, rx[0], ndigits);
	vli_set(result->y, ry[0], ndigits);
}

1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378
/* Computes R = P + Q mod p */
static void ecc_point_add(const struct ecc_point *result,
		   const struct ecc_point *p, const struct ecc_point *q,
		   const struct ecc_curve *curve)
{
	u64 z[ECC_MAX_DIGITS];
	u64 px[ECC_MAX_DIGITS];
	u64 py[ECC_MAX_DIGITS];
	unsigned int ndigits = curve->g.ndigits;

	vli_set(result->x, q->x, ndigits);
	vli_set(result->y, q->y, ndigits);
	vli_mod_sub(z, result->x, p->x, curve->p, ndigits);
	vli_set(px, p->x, ndigits);
	vli_set(py, p->y, ndigits);
1379
	xycz_add(px, py, result->x, result->y, curve);
1380
	vli_mod_inv(z, z, curve->p, ndigits);
1381
	apply_z(result->x, result->y, z, curve);
1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409
}

/* Computes R = u1P + u2Q mod p using Shamir's trick.
 * Based on: Kenneth MacKay's micro-ecc (2014).
 */
void ecc_point_mult_shamir(const struct ecc_point *result,
			   const u64 *u1, const struct ecc_point *p,
			   const u64 *u2, const struct ecc_point *q,
			   const struct ecc_curve *curve)
{
	u64 z[ECC_MAX_DIGITS];
	u64 sump[2][ECC_MAX_DIGITS];
	u64 *rx = result->x;
	u64 *ry = result->y;
	unsigned int ndigits = curve->g.ndigits;
	unsigned int num_bits;
	struct ecc_point sum = ECC_POINT_INIT(sump[0], sump[1], ndigits);
	const struct ecc_point *points[4];
	const struct ecc_point *point;
	unsigned int idx;
	int i;

	ecc_point_add(&sum, p, q, curve);
	points[0] = NULL;
	points[1] = p;
	points[2] = q;
	points[3] = &sum;

1410
	num_bits = max(vli_num_bits(u1, ndigits), vli_num_bits(u2, ndigits));
1411
	i = num_bits - 1;
1412 1413
	idx = !!vli_test_bit(u1, i);
	idx |= (!!vli_test_bit(u2, i)) << 1;
1414 1415 1416 1417 1418 1419 1420 1421
	point = points[idx];

	vli_set(rx, point->x, ndigits);
	vli_set(ry, point->y, ndigits);
	vli_clear(z + 1, ndigits - 1);
	z[0] = 1;

	for (--i; i >= 0; i--) {
1422
		ecc_point_double_jacobian(rx, ry, z, curve);
1423 1424
		idx = !!vli_test_bit(u1, i);
		idx |= (!!vli_test_bit(u2, i)) << 1;
1425 1426 1427 1428 1429 1430 1431 1432
		point = points[idx];
		if (point) {
			u64 tx[ECC_MAX_DIGITS];
			u64 ty[ECC_MAX_DIGITS];
			u64 tz[ECC_MAX_DIGITS];

			vli_set(tx, point->x, ndigits);
			vli_set(ty, point->y, ndigits);
1433
			apply_z(tx, ty, z, curve);
1434
			vli_mod_sub(tz, rx, tx, curve->p, ndigits);
1435 1436
			xycz_add(tx, ty, rx, ry, curve);
			vli_mod_mult_fast(z, z, tz, curve);
1437 1438 1439
		}
	}
	vli_mod_inv(z, z, curve->p, ndigits);
1440
	apply_z(rx, ry, z, curve);
1441 1442 1443
}
EXPORT_SYMBOL(ecc_point_mult_shamir);

1444 1445 1446 1447 1448 1449
/*
 * This function performs checks equivalent to Appendix A.4.2 of FIPS 186-5.
 * Whereas A.4.2 results in an integer in the interval [1, n-1], this function
 * ensures that the integer is in the range of [2, n-3]. We are slightly
 * stricter because of the currently used scalar multiplication algorithm.
 */
1450 1451
static int __ecc_is_key_valid(const struct ecc_curve *curve,
			      const u64 *private_key, unsigned int ndigits)
1452
{
1453 1454
	u64 one[ECC_MAX_DIGITS] = { 1, };
	u64 res[ECC_MAX_DIGITS];
1455 1456 1457 1458

	if (!private_key)
		return -EINVAL;

1459
	if (curve->g.ndigits != ndigits)
1460 1461
		return -EINVAL;

1462 1463
	/* Make sure the private key is in the range [2, n-3]. */
	if (vli_cmp(one, private_key, ndigits) != -1)
1464
		return -EINVAL;
1465 1466 1467
	vli_sub(res, curve->n, one, ndigits);
	vli_sub(res, res, one, ndigits);
	if (vli_cmp(res, private_key, ndigits) != 1)
1468 1469 1470 1471 1472
		return -EINVAL;

	return 0;
}

1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485
int ecc_is_key_valid(unsigned int curve_id, unsigned int ndigits,
		     const u64 *private_key, unsigned int private_key_len)
{
	int nbytes;
	const struct ecc_curve *curve = ecc_get_curve(curve_id);

	nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;

	if (private_key_len != nbytes)
		return -EINVAL;

	return __ecc_is_key_valid(curve, private_key, ndigits);
}
1486
EXPORT_SYMBOL(ecc_is_key_valid);
1487

1488
/*
1489 1490
 * ECC private keys are generated using the method of rejection sampling,
 * equivalent to that described in FIPS 186-5, Appendix A.2.2.
1491 1492
 *
 * This method generates a private key uniformly distributed in the range
1493
 * [2, n-3].
1494 1495 1496 1497
 */
int ecc_gen_privkey(unsigned int curve_id, unsigned int ndigits, u64 *privkey)
{
	const struct ecc_curve *curve = ecc_get_curve(curve_id);
1498
	u64 priv[ECC_MAX_DIGITS];
1499 1500 1501 1502
	unsigned int nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
	unsigned int nbits = vli_num_bits(curve->n, ndigits);
	int err;

1503 1504 1505 1506 1507
	/*
	 * Step 1 & 2: check that N is included in Table 1 of FIPS 186-5,
	 * section 6.1.1.
	 */
	if (nbits < 224 || ndigits > ARRAY_SIZE(priv))
1508 1509 1510
		return -EINVAL;

	/*
1511
	 * FIPS 186-5 recommends that the private key should be obtained from a
1512 1513 1514 1515 1516 1517 1518 1519 1520 1521
	 * RBG with a security strength equal to or greater than the security
	 * strength associated with N.
	 *
	 * The maximum security strength identified by NIST SP800-57pt1r4 for
	 * ECC is 256 (N >= 512).
	 *
	 * This condition is met by the default RNG because it selects a favored
	 * DRBG with a security strength of 256.
	 */
	if (crypto_get_default_rng())
1522
		return -EFAULT;
1523

1524
	/* Step 3: obtain N returned_bits from the DRBG. */
1525 1526 1527 1528 1529
	err = crypto_rng_get_bytes(crypto_default_rng, (u8 *)priv, nbytes);
	crypto_put_default_rng();
	if (err)
		return err;

1530
	/* Step 4: make sure the private key is in the valid range. */
1531
	if (__ecc_is_key_valid(curve, priv, ndigits))
1532 1533 1534 1535 1536 1537
		return -EINVAL;

	ecc_swap_digits(priv, privkey, ndigits);

	return 0;
}
1538
EXPORT_SYMBOL(ecc_gen_privkey);
1539

1540 1541
int ecc_make_pub_key(unsigned int curve_id, unsigned int ndigits,
		     const u64 *private_key, u64 *public_key)
1542 1543 1544
{
	int ret = 0;
	struct ecc_point *pk;
1545
	u64 priv[ECC_MAX_DIGITS];
1546 1547
	const struct ecc_curve *curve = ecc_get_curve(curve_id);

1548
	if (!private_key || ndigits > ARRAY_SIZE(priv)) {
1549 1550 1551 1552
		ret = -EINVAL;
		goto out;
	}

1553
	ecc_swap_digits(private_key, priv, ndigits);
1554 1555 1556 1557 1558 1559 1560

	pk = ecc_alloc_point(ndigits);
	if (!pk) {
		ret = -ENOMEM;
		goto out;
	}

1561
	ecc_point_mult(pk, &curve->g, priv, NULL, curve, ndigits);
1562 1563 1564

	/* SP800-56A rev 3 5.6.2.1.3 key check */
	if (ecc_is_pubkey_valid_full(curve, pk)) {
1565 1566 1567 1568
		ret = -EAGAIN;
		goto err_free_point;
	}

1569 1570
	ecc_swap_digits(pk->x, public_key, ndigits);
	ecc_swap_digits(pk->y, &public_key[ndigits], ndigits);
1571 1572 1573 1574 1575 1576

err_free_point:
	ecc_free_point(pk);
out:
	return ret;
}
1577
EXPORT_SYMBOL(ecc_make_pub_key);
1578

1579
/* SP800-56A section 5.6.2.3.4 partial verification: ephemeral keys only */
1580 1581
int ecc_is_pubkey_valid_partial(const struct ecc_curve *curve,
				struct ecc_point *pk)
1582 1583 1584
{
	u64 yy[ECC_MAX_DIGITS], xxx[ECC_MAX_DIGITS], w[ECC_MAX_DIGITS];

1585 1586 1587
	if (WARN_ON(pk->ndigits != curve->g.ndigits))
		return -EINVAL;

1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598
	/* Check 1: Verify key is not the zero point. */
	if (ecc_point_is_zero(pk))
		return -EINVAL;

	/* Check 2: Verify key is in the range [1, p-1]. */
	if (vli_cmp(curve->p, pk->x, pk->ndigits) != 1)
		return -EINVAL;
	if (vli_cmp(curve->p, pk->y, pk->ndigits) != 1)
		return -EINVAL;

	/* Check 3: Verify that y^2 == (x^3 + a·x + b) mod p */
1599 1600 1601 1602
	vli_mod_square_fast(yy, pk->y, curve); /* y^2 */
	vli_mod_square_fast(xxx, pk->x, curve); /* x^2 */
	vli_mod_mult_fast(xxx, xxx, pk->x, curve); /* x^3 */
	vli_mod_mult_fast(w, curve->a, pk->x, curve); /* a·x */
1603 1604 1605 1606 1607 1608 1609
	vli_mod_add(w, w, curve->b, curve->p, pk->ndigits); /* a·x + b */
	vli_mod_add(w, w, xxx, curve->p, pk->ndigits); /* x^3 + a·x + b */
	if (vli_cmp(yy, w, pk->ndigits) != 0) /* Equation */
		return -EINVAL;

	return 0;
}
1610
EXPORT_SYMBOL(ecc_is_pubkey_valid_partial);
1611

1612 1613 1614 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638
/* SP800-56A section 5.6.2.3.3 full verification */
int ecc_is_pubkey_valid_full(const struct ecc_curve *curve,
			     struct ecc_point *pk)
{
	struct ecc_point *nQ;

	/* Checks 1 through 3 */
	int ret = ecc_is_pubkey_valid_partial(curve, pk);

	if (ret)
		return ret;

	/* Check 4: Verify that nQ is the zero point. */
	nQ = ecc_alloc_point(pk->ndigits);
	if (!nQ)
		return -ENOMEM;

	ecc_point_mult(nQ, pk, curve->n, NULL, curve, pk->ndigits);
	if (!ecc_point_is_zero(nQ))
		ret = -EINVAL;

	ecc_free_point(nQ);

	return ret;
}
EXPORT_SYMBOL(ecc_is_pubkey_valid_full);

1639
int crypto_ecdh_shared_secret(unsigned int curve_id, unsigned int ndigits,
1640 1641
			      const u64 *private_key, const u64 *public_key,
			      u64 *secret)
1642 1643 1644
{
	int ret = 0;
	struct ecc_point *product, *pk;
1645 1646 1647
	u64 priv[ECC_MAX_DIGITS];
	u64 rand_z[ECC_MAX_DIGITS];
	unsigned int nbytes;
1648 1649
	const struct ecc_curve *curve = ecc_get_curve(curve_id);

1650
	if (!private_key || !public_key ||
1651
	    ndigits > ARRAY_SIZE(priv) || ndigits > ARRAY_SIZE(rand_z)) {
1652 1653 1654 1655
		ret = -EINVAL;
		goto out;
	}

1656
	nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
1657

1658
	get_random_bytes(rand_z, nbytes);
1659 1660 1661 1662

	pk = ecc_alloc_point(ndigits);
	if (!pk) {
		ret = -ENOMEM;
1663
		goto out;
1664 1665
	}

1666 1667 1668 1669 1670 1671 1672 1673
	ecc_swap_digits(public_key, pk->x, ndigits);
	ecc_swap_digits(&public_key[ndigits], pk->y, ndigits);
	ret = ecc_is_pubkey_valid_partial(curve, pk);
	if (ret)
		goto err_alloc_product;

	ecc_swap_digits(private_key, priv, ndigits);

1674 1675 1676 1677 1678 1679
	product = ecc_alloc_point(ndigits);
	if (!product) {
		ret = -ENOMEM;
		goto err_alloc_product;
	}

1680
	ecc_point_mult(product, pk, priv, rand_z, curve, ndigits);
1681

1682
	if (ecc_point_is_zero(product)) {
1683
		ret = -EFAULT;
1684 1685 1686 1687
		goto err_validity;
	}

	ecc_swap_digits(product->x, secret, ndigits);
1688

1689 1690 1691
err_validity:
	memzero_explicit(priv, sizeof(priv));
	memzero_explicit(rand_z, sizeof(rand_z));
1692 1693 1694 1695 1696 1697
	ecc_free_point(product);
err_alloc_product:
	ecc_free_point(pk);
out:
	return ret;
}
1698 1699 1700
EXPORT_SYMBOL(crypto_ecdh_shared_secret);

MODULE_LICENSE("Dual BSD/GPL");