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57b51b9adb
linux/net/bluetooth/ecc.c
Johan Hedberg 05ddb47a91 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>
2014-12-03 16:51:16 +01:00

817 lines
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/*
* 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);
}
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