Bluetooth: Add ECC library for LE Secure Connections

This patch adds a simple ECC library that will act as a fundamental
building block for LE Secure Connections. The library has a simple API
consisting of two functions: one for generating a public/private key
pair and another one for generating a Diffie-Hellman key from a local
private key and a remote public key.

The code has been taken from https://github.com/kmackay/easy-ecc and
modified to conform with the kernel coding style.
Signed-off-by: Johan Hedberg <johan.hedberg@intel.com>
Signed-off-by: Marcel Holtmann <marcel@holtmann.org>

net/bluetooth/Makefile

@@ -13,6 +13,6 @@ bluetooth_6lowpan-y := 6lowpan.o
 
 bluetooth-y := af_bluetooth.o hci_core.o hci_conn.o hci_event.o mgmt.o \
 	hci_sock.o hci_sysfs.o l2cap_core.o l2cap_sock.o smp.o sco.o lib.o \
-	a2mp.o amp.o
+	a2mp.o amp.o ecc.o
 
 subdir-ccflags-y += -D__CHECK_ENDIAN__

net/bluetooth/ecc.c

+/*
+ * Copyright (c) 2013, Kenneth MacKay
+ * All rights reserved.
+ *
+ * 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.
+ */
+
+#include <linux/random.h>
+
+#include "ecc.h"
+
+/* 256-bit curve */
+#define ECC_BYTES 32
+
+#define MAX_TRIES 16
+
+/* Number of u64's needed */
+#define NUM_ECC_DIGITS (ECC_BYTES / 8)
+
+struct ecc_point {
+	u64 x[NUM_ECC_DIGITS];
+	u64 y[NUM_ECC_DIGITS];
+};
+
+typedef struct {
+	u64 m_low;
+	u64 m_high;
+} uint128_t;
+
+#define CURVE_P_32 {	0xFFFFFFFFFFFFFFFFull, 0x00000000FFFFFFFFull, \
+			0x0000000000000000ull, 0xFFFFFFFF00000001ull }
+
+#define CURVE_G_32 { \
+		{	0xF4A13945D898C296ull, 0x77037D812DEB33A0ull,	\
+			0xF8BCE6E563A440F2ull, 0x6B17D1F2E12C4247ull }, \
+		{	0xCBB6406837BF51F5ull, 0x2BCE33576B315ECEull,	\
+			0x8EE7EB4A7C0F9E16ull, 0x4FE342E2FE1A7F9Bull }	\
+}
+
+#define CURVE_N_32 {	0xF3B9CAC2FC632551ull, 0xBCE6FAADA7179E84ull,	\
+			0xFFFFFFFFFFFFFFFFull, 0xFFFFFFFF00000000ull }
+
+static u64 curve_p[NUM_ECC_DIGITS] = CURVE_P_32;
+static struct ecc_point curve_g = CURVE_G_32;
+static u64 curve_n[NUM_ECC_DIGITS] = CURVE_N_32;
+
+static void vli_clear(u64 *vli)
+{
+	int i;
+
+	for (i = 0; i < NUM_ECC_DIGITS; i++)
+		vli[i] = 0;
+}
+
+/* Returns true if vli == 0, false otherwise. */
+static bool vli_is_zero(const u64 *vli)
+{
+	int i;
+
+	for (i = 0; i < NUM_ECC_DIGITS; i++) {
+		if (vli[i])
+			return false;
+	}
+
+	return true;
+}
+
+/* Returns nonzero if bit bit of vli is set. */
+static u64 vli_test_bit(const u64 *vli, unsigned int bit)
+{
+	return (vli[bit / 64] & ((u64) 1 << (bit % 64)));
+}
+
+/* Counts the number of 64-bit "digits" in vli. */
+static unsigned int vli_num_digits(const u64 *vli)
+{
+	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 = NUM_ECC_DIGITS - 1; i >= 0 && vli[i] == 0; i--);
+
+	return (i + 1);
+}
+
+/* Counts the number of bits required for vli. */
+static unsigned int vli_num_bits(const u64 *vli)
+{
+	unsigned int i, num_digits;
+	u64 digit;
+
+	num_digits = vli_num_digits(vli);
+	if (num_digits == 0)
+		return 0;
+
+	digit = vli[num_digits - 1];
+	for (i = 0; digit; i++)
+		digit >>= 1;
+
+	return ((num_digits - 1) * 64 + i);
+}
+
+/* Sets dest = src. */
+static void vli_set(u64 *dest, const u64 *src)
+{
+	int i;
+
+	for (i = 0; i < NUM_ECC_DIGITS; i++)
+		dest[i] = src[i];
+}
+
+/* Returns sign of left - right. */
+static int vli_cmp(const u64 *left, const u64 *right)
+{
+    int i;
+
+    for (i = NUM_ECC_DIGITS - 1; i >= 0; i--) {
+	    if (left[i] > right[i])
+		    return 1;
+	    else if (left[i] < right[i])
+		    return -1;
+    }
+
+    return 0;
+}
+
+/* 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)
+{
+	u64 carry = 0;
+	int i;
+
+	for (i = 0; i < NUM_ECC_DIGITS; 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)
+{
+	u64 *end = vli;
+	u64 carry = 0;
+
+	vli += NUM_ECC_DIGITS;
+
+	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)
+{
+	u64 carry = 0;
+	int i;
+
+	for (i = 0; i < NUM_ECC_DIGITS; i++) {
+		u64 sum;
+
+		sum = left[i] + right[i] + carry;
+		if (sum != left[i])
+			carry = (sum < left[i]);
+
+		result[i] = sum;
+	}
+
+	return carry;
+}
+
+/* Computes result = left - right, returning borrow. Can modify in place. */
+static u64 vli_sub(u64 *result, const u64 *left, const u64 *right)
+{
+	u64 borrow = 0;
+	int i;
+
+	for (i = 0; i < NUM_ECC_DIGITS; i++) {
+		u64 diff;
+
+		diff = left[i] - right[i] - borrow;
+		if (diff != left[i])
+			borrow = (diff > left[i]);
+
+		result[i] = diff;
+	}
+
+	return borrow;
+}
+
+static uint128_t mul_64_64(u64 left, u64 right)
+{
+	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;
+	uint128_t result;
+
+	m2 += (m0 >> 32);
+	m2 += m1;
+
+	/* Overflow */
+	if (m2 < m1)
+		m3 += 0x100000000ull;
+
+	result.m_low = (m0 & 0xffffffffull) | (m2 << 32);
+	result.m_high = m3 + (m2 >> 32);
+
+	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)
+{
+	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 < NUM_ECC_DIGITS * 2 - 1; k++) {
+		unsigned int min;
+
+		if (k < NUM_ECC_DIGITS)
+			min = 0;
+		else
+			min = (k + 1) - NUM_ECC_DIGITS;
+
+		for (i = min; i <= k && i < NUM_ECC_DIGITS; 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[NUM_ECC_DIGITS * 2 - 1] = r01.m_low;
+}
+
+static void vli_square(u64 *result, const u64 *left)
+{
+	uint128_t r01 = { 0, 0 };
+	u64 r2 = 0;
+	int i, k;
+
+	for (k = 0; k < NUM_ECC_DIGITS * 2 - 1; k++) {
+		unsigned int min;
+
+		if (k < NUM_ECC_DIGITS)
+			min = 0;
+		else
+			min = (k + 1) - NUM_ECC_DIGITS;
+
+		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[NUM_ECC_DIGITS * 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)
+{
+	u64 carry;
+
+	carry = vli_add(result, left, right);
+
+	/* result > mod (result = mod + remainder), so subtract mod to
+	 * get remainder.
+	 */
+	if (carry || vli_cmp(result, mod) >= 0)
+		vli_sub(result, result, mod);
+}
+
+/* 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)
+{
+	u64 borrow = vli_sub(result, left, right);
+
+	/* 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);
+}
+
+/* Computes result = product % curve_p
+   from http://www.nsa.gov/ia/_files/nist-routines.pdf */
+static void vli_mmod_fast(u64 *result, const u64 *product)
+{
+	u64 tmp[NUM_ECC_DIGITS];
+	int carry;
+
+	/* t */
+	vli_set(result, product);
+
+	/* s1 */
+	tmp[0] = 0;
+	tmp[1] = product[5] & 0xffffffff00000000ull;
+	tmp[2] = product[6];
+	tmp[3] = product[7];
+	carry = vli_lshift(tmp, tmp, 1);
+	carry += vli_add(result, result, tmp);
+
+	/* 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);
+	carry += vli_add(result, result, tmp);
+
+	/* s3 */
+	tmp[0] = product[4];
+	tmp[1] = product[5] & 0xffffffff;
+	tmp[2] = 0;
+	tmp[3] = product[7];
+	carry += vli_add(result, result, tmp);
+
+	/* 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);
+
+	/* 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);
+
+	/* 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);
+
+	/* 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);
+
+	/* 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);
+
+	if (carry < 0) {
+		do {
+			carry += vli_add(result, result, curve_p);
+		} while (carry < 0);
+	} else {
+		while (carry || vli_cmp(curve_p, result) != 1)
+			carry -= vli_sub(result, result, curve_p);
+	}
+}
+
+/* Computes result = (left * right) % curve_p. */
+static void vli_mod_mult_fast(u64 *result, const u64 *left, const u64 *right)
+{
+	u64 product[2 * NUM_ECC_DIGITS];
+
+	vli_mult(product, left, right);
+	vli_mmod_fast(result, product);
+}
+
+/* Computes result = left^2 % curve_p. */
+static void vli_mod_square_fast(u64 *result, const u64 *left)
+{
+	u64 product[2 * NUM_ECC_DIGITS];
+
+	vli_square(product, left);
+	vli_mmod_fast(result, product);
+}
+
+#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
+ */
+static void vli_mod_inv(u64 *result, const u64 *input, const u64 *mod)
+{
+	u64 a[NUM_ECC_DIGITS], b[NUM_ECC_DIGITS];
+	u64 u[NUM_ECC_DIGITS], v[NUM_ECC_DIGITS];
+	u64 carry;
+	int cmp_result;
+
+	if (vli_is_zero(input)) {
+		vli_clear(result);
+		return;
+	}
+
+	vli_set(a, input);
+	vli_set(b, mod);
+	vli_clear(u);
+	u[0] = 1;
+	vli_clear(v);
+
+	while ((cmp_result = vli_cmp(a, b)) != 0) {
+		carry = 0;
+
+		if (EVEN(a)) {
+			vli_rshift1(a);
+
+			if (!EVEN(u))
+				carry = vli_add(u, u, mod);
+
+			vli_rshift1(u);
+			if (carry)
+				u[NUM_ECC_DIGITS - 1] |= 0x8000000000000000ull;
+		} else if (EVEN(b)) {
+			vli_rshift1(b);
+
+			if (!EVEN(v))
+				carry = vli_add(v, v, mod);
+
+			vli_rshift1(v);
+			if (carry)
+				v[NUM_ECC_DIGITS - 1] |= 0x8000000000000000ull;
+		} else if (cmp_result > 0) {
+			vli_sub(a, a, b);
+			vli_rshift1(a);
+
+			if (vli_cmp(u, v) < 0)
+				vli_add(u, u, mod);
+
+			vli_sub(u, u, v);
+			if (!EVEN(u))
+				carry = vli_add(u, u, mod);
+
+			vli_rshift1(u);
+			if (carry)
+				u[NUM_ECC_DIGITS - 1] |= 0x8000000000000000ull;
+		} else {
+			vli_sub(b, b, a);
+			vli_rshift1(b);
+
+			if (vli_cmp(v, u) < 0)
+				vli_add(v, v, mod);
+
+			vli_sub(v, v, u);
+			if (!EVEN(v))
+				carry = vli_add(v, v, mod);
+
+			vli_rshift1(v);
+			if (carry)
+				v[NUM_ECC_DIGITS - 1] |= 0x8000000000000000ull;
+		}
+	}
+
+	vli_set(result, u);
+}
+
+/* ------ Point operations ------ */
+
+/* Returns true if p_point is the point at infinity, false otherwise. */
+static bool ecc_point_is_zero(const struct ecc_point *point)
+{
+	return (vli_is_zero(point->x) && vli_is_zero(point->y));
+}
+
+/* Point multiplication algorithm using Montgomery's ladder with co-Z
+ * coordinates. From http://eprint.iacr.org/2011/338.pdf
+ */
+
+/* Double in place */
+static void ecc_point_double_jacobian(u64 *x1, u64 *y1, u64 *z1)
+{
+	/* t1 = x, t2 = y, t3 = z */
+	u64 t4[NUM_ECC_DIGITS];
+	u64 t5[NUM_ECC_DIGITS];
+
+	if (vli_is_zero(z1))
+		return;
+
+	vli_mod_square_fast(t4, y1);   /* t4 = y1^2 */
+	vli_mod_mult_fast(t5, x1, t4); /* t5 = x1*y1^2 = A */
+	vli_mod_square_fast(t4, t4);   /* t4 = y1^4 */
+	vli_mod_mult_fast(y1, y1, z1); /* t2 = y1*z1 = z3 */
+	vli_mod_square_fast(z1, z1);   /* t3 = z1^2 */
+
+	vli_mod_add(x1, x1, z1, curve_p); /* t1 = x1 + z1^2 */
+	vli_mod_add(z1, z1, z1, curve_p); /* t3 = 2*z1^2 */
+	vli_mod_sub(z1, x1, z1, curve_p); /* t3 = x1 - z1^2 */
+	vli_mod_mult_fast(x1, x1, z1);    /* t1 = x1^2 - z1^4 */
+
+	vli_mod_add(z1, x1, x1, curve_p); /* t3 = 2*(x1^2 - z1^4) */
+	vli_mod_add(x1, x1, z1, curve_p); /* t1 = 3*(x1^2 - z1^4) */
+	if (vli_test_bit(x1, 0)) {
+		u64 carry = vli_add(x1, x1, curve_p);
+		vli_rshift1(x1);
+		x1[NUM_ECC_DIGITS - 1] |= carry << 63;
+	} else {
+		vli_rshift1(x1);
+	}
+	/* t1 = 3/2*(x1^2 - z1^4) = B */
+
+	vli_mod_square_fast(z1, x1);      /* t3 = B^2 */
+	vli_mod_sub(z1, z1, t5, curve_p); /* t3 = B^2 - A */
+	vli_mod_sub(z1, z1, t5, curve_p); /* t3 = B^2 - 2A = x3 */
+	vli_mod_sub(t5, t5, z1, curve_p); /* t5 = A - x3 */
+	vli_mod_mult_fast(x1, x1, t5);    /* t1 = B * (A - x3) */
+	vli_mod_sub(t4, x1, t4, curve_p); /* t4 = B * (A - x3) - y1^4 = y3 */
+
+	vli_set(x1, z1);
+	vli_set(z1, y1);
+	vli_set(y1, t4);
+}
+
+/* Modify (x1, y1) => (x1 * z^2, y1 * z^3) */
+static void apply_z(u64 *x1, u64 *y1, u64 *z)
+{
+	u64 t1[NUM_ECC_DIGITS];
+
+	vli_mod_square_fast(t1, z);    /* z^2 */
+	vli_mod_mult_fast(x1, x1, t1); /* x1 * z^2 */
+	vli_mod_mult_fast(t1, t1, z);  /* z^3 */
+	vli_mod_mult_fast(y1, y1, t1); /* y1 * z^3 */
+}
+
+/* P = (x1, y1) => 2P, (x2, y2) => P' */
+static void xycz_initial_double(u64 *x1, u64 *y1, u64 *x2, u64 *y2,
+				u64 *p_initial_z)
+{
+	u64 z[NUM_ECC_DIGITS];
+
+	vli_set(x2, x1);
+	vli_set(y2, y1);
+
+	vli_clear(z);
+	z[0] = 1;
+
+	if (p_initial_z)
+		vli_set(z, p_initial_z);
+
+	apply_z(x1, y1, z);
+
+	ecc_point_double_jacobian(x1, y1, z);
+
+	apply_z(x2, y2, z);
+}
+
+/* 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
+ */
+static void xycz_add(u64 *x1, u64 *y1, u64 *x2, u64 *y2)
+{
+	/* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
+	u64 t5[NUM_ECC_DIGITS];
+
+	vli_mod_sub(t5, x2, x1, curve_p); /* t5 = x2 - x1 */
+	vli_mod_square_fast(t5, t5);      /* t5 = (x2 - x1)^2 = A */
+	vli_mod_mult_fast(x1, x1, t5);    /* t1 = x1*A = B */
+	vli_mod_mult_fast(x2, x2, t5);    /* t3 = x2*A = C */
+	vli_mod_sub(y2, y2, y1, curve_p); /* t4 = y2 - y1 */
+	vli_mod_square_fast(t5, y2);      /* t5 = (y2 - y1)^2 = D */
+
+	vli_mod_sub(t5, t5, x1, curve_p); /* t5 = D - B */
+	vli_mod_sub(t5, t5, x2, curve_p); /* t5 = D - B - C = x3 */
+	vli_mod_sub(x2, x2, x1, curve_p); /* t3 = C - B */
+	vli_mod_mult_fast(y1, y1, x2);    /* t2 = y1*(C - B) */
+	vli_mod_sub(x2, x1, t5, curve_p); /* t3 = B - x3 */
+	vli_mod_mult_fast(y2, y2, x2);    /* t4 = (y2 - y1)*(B - x3) */
+	vli_mod_sub(y2, y2, y1, curve_p); /* t4 = y3 */
+
+	vli_set(x2, t5);
+}
+
+/* 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
+ */
+static void xycz_add_c(u64 *x1, u64 *y1, u64 *x2, u64 *y2)
+{
+	/* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
+	u64 t5[NUM_ECC_DIGITS];
+	u64 t6[NUM_ECC_DIGITS];
+	u64 t7[NUM_ECC_DIGITS];
+
+	vli_mod_sub(t5, x2, x1, curve_p); /* t5 = x2 - x1 */
+	vli_mod_square_fast(t5, t5);      /* t5 = (x2 - x1)^2 = A */
+	vli_mod_mult_fast(x1, x1, t5);    /* t1 = x1*A = B */
+	vli_mod_mult_fast(x2, x2, t5);    /* t3 = x2*A = C */
+	vli_mod_add(t5, y2, y1, curve_p); /* t4 = y2 + y1 */
+	vli_mod_sub(y2, y2, y1, curve_p); /* t4 = y2 - y1 */
+
+	vli_mod_sub(t6, x2, x1, curve_p); /* t6 = C - B */
+	vli_mod_mult_fast(y1, y1, t6);    /* t2 = y1 * (C - B) */
+	vli_mod_add(t6, x1, x2, curve_p); /* t6 = B + C */
+	vli_mod_square_fast(x2, y2);      /* t3 = (y2 - y1)^2 */
+	vli_mod_sub(x2, x2, t6, curve_p); /* t3 = x3 */
+
+	vli_mod_sub(t7, x1, x2, curve_p); /* t7 = B - x3 */
+	vli_mod_mult_fast(y2, y2, t7);    /* t4 = (y2 - y1)*(B - x3) */
+	vli_mod_sub(y2, y2, y1, curve_p); /* t4 = y3 */
+
+	vli_mod_square_fast(t7, t5);      /* t7 = (y2 + y1)^2 = F */
+	vli_mod_sub(t7, t7, t6, curve_p); /* t7 = x3' */
+	vli_mod_sub(t6, t7, x1, curve_p); /* t6 = x3' - B */
+	vli_mod_mult_fast(t6, t6, t5);    /* t6 = (y2 + y1)*(x3' - B) */
+	vli_mod_sub(y1, t6, y1, curve_p); /* t2 = y3' */
+
+	vli_set(x1, t7);
+}
+
+static void ecc_point_mult(struct ecc_point *result,
+			   const struct ecc_point *point, u64 *scalar,
+			   u64 *initial_z, int num_bits)
+{
+	/* R0 and R1 */
+	u64 rx[2][NUM_ECC_DIGITS];
+	u64 ry[2][NUM_ECC_DIGITS];
+	u64 z[NUM_ECC_DIGITS];
+	int i, nb;
+
+	vli_set(rx[1], point->x);
+	vli_set(ry[1], point->y);
+
+	xycz_initial_double(rx[1], ry[1], rx[0], ry[0], initial_z);
+
+	for (i = num_bits - 2; i > 0; i--) {
+		nb = !vli_test_bit(scalar, i);
+		xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb]);
+		xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb]);
+	}
+
+	nb = !vli_test_bit(scalar, 0);
+	xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb]);
+
+	/* Find final 1/Z value. */
+	vli_mod_sub(z, rx[1], rx[0], curve_p); /* X1 - X0 */
+	vli_mod_mult_fast(z, z, ry[1 - nb]); /* Yb * (X1 - X0) */
+	vli_mod_mult_fast(z, z, point->x);   /* xP * Yb * (X1 - X0) */
+	vli_mod_inv(z, z, curve_p);          /* 1 / (xP * Yb * (X1 - X0)) */
+	vli_mod_mult_fast(z, z, point->y);   /* yP / (xP * Yb * (X1 - X0)) */
+	vli_mod_mult_fast(z, z, rx[1 - nb]); /* Xb * yP / (xP * Yb * (X1 - X0)) */
+	/* End 1/Z calculation */
+
+	xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb]);
+
+	apply_z(rx[0], ry[0], z);
+
+	vli_set(result->x, rx[0]);
+	vli_set(result->y, ry[0]);
+}
+
+static void ecc_bytes2native(const u8 bytes[ECC_BYTES],
+			     u64 native[NUM_ECC_DIGITS])
+{
+	int i;
+
+	for (i = 0; i < NUM_ECC_DIGITS; i++) {
+		const u8 *digit = bytes + 8 * (NUM_ECC_DIGITS - 1 - i);
+
+		native[NUM_ECC_DIGITS - 1 - i] =
+				((u64) digit[0] << 0) |
+				((u64) digit[1] << 8) |
+				((u64) digit[2] << 16) |
+				((u64) digit[3] << 24) |
+				((u64) digit[4] << 32) |
+				((u64) digit[5] << 40) |
+				((u64) digit[6] << 48) |
+				((u64) digit[7] << 56);
+	}
+}
+
+static void ecc_native2bytes(const u64 native[NUM_ECC_DIGITS],
+			     u8 bytes[ECC_BYTES])
+{
+	int i;
+
+	for (i = 0; i < NUM_ECC_DIGITS; i++) {
+		u8 *digit = bytes + 8 * (NUM_ECC_DIGITS - 1 - i);
+
+		digit[0] = native[NUM_ECC_DIGITS - 1 - i] >> 0;
+		digit[1] = native[NUM_ECC_DIGITS - 1 - i] >> 8;
+		digit[2] = native[NUM_ECC_DIGITS - 1 - i] >> 16;
+		digit[3] = native[NUM_ECC_DIGITS - 1 - i] >> 24;
+		digit[4] = native[NUM_ECC_DIGITS - 1 - i] >> 32;
+		digit[5] = native[NUM_ECC_DIGITS - 1 - i] >> 40;
+		digit[6] = native[NUM_ECC_DIGITS - 1 - i] >> 48;
+		digit[7] = native[NUM_ECC_DIGITS - 1 - i] >> 56;
+	}
+}
+
+bool ecc_make_key(u8 public_key[64], u8 private_key[32])
+{
+	struct ecc_point pk;
+	u64 priv[NUM_ECC_DIGITS];
+	unsigned int tries = 0;
+
+	do {
+		if (tries++ >= MAX_TRIES)
+			return false;
+
+		get_random_bytes(priv, ECC_BYTES);
+
+		if (vli_is_zero(priv))
+			continue;
+
+		/* Make sure the private key is in the range [1, n-1]. */
+		if (vli_cmp(curve_n, priv) != 1)
+			continue;
+
+		ecc_point_mult(&pk, &curve_g, priv, NULL, vli_num_bits(priv));
+	} while (ecc_point_is_zero(&pk));
+
+	ecc_native2bytes(priv, private_key);
+	ecc_native2bytes(pk.x, public_key);
+	ecc_native2bytes(pk.y, &public_key[32]);
+
+	return true;
+}
+
+bool ecdh_shared_secret(const u8 public_key[64], const u8 private_key[32],
+		        u8 secret[32])
+{
+	u64 priv[NUM_ECC_DIGITS];
+	u64 rand[NUM_ECC_DIGITS];
+	struct ecc_point product, pk;
+
+	get_random_bytes(rand, ECC_BYTES);
+
+	ecc_bytes2native(public_key, pk.x);
+	ecc_bytes2native(&public_key[32], pk.y);
+	ecc_bytes2native(private_key, priv);
+
+	ecc_point_mult(&product, &pk, priv, rand, vli_num_bits(priv));
+
+	ecc_native2bytes(product.x, secret);
+
+	return !ecc_point_is_zero(&product);
+}

net/bluetooth/ecc.h

+/*
+ * Copyright (c) 2013, Kenneth MacKay
+ * All rights reserved.
+ *
+ * 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.
+ */
+
+/* Create a public/private key pair.
+ * Outputs:
+ *	public_key  - Will be filled in with the public key.
+ *	private_key - Will be filled in with the private key.
+ *
+ * Returns true if the key pair was generated successfully, false
+ * if an error occurred. The keys are with the LSB first.
+ */
+bool ecc_make_key(u8 public_key[64], u8 private_key[32]);
+
+/* Compute a shared secret given your secret key and someone else's
+ * public key.
+ * Note: It is recommended that you hash the result of ecdh_shared_secret
+ * before using it for symmetric encryption or HMAC.
+ *
+ * Inputs:
+ *	public_key  - The public key of the remote party
+ *	private_key - Your private key.
+ *
+ * Outputs:
+ *	secret - Will be filled in with the shared secret value.
+ *
+ * Returns true if the shared secret was generated successfully, false
+ * if an error occurred. Both input and output parameters are with the
+ * LSB first.
+ */
+bool ecdh_shared_secret(const u8 public_key[64], const u8 private_key[32],
+		        u8 secret[32]);