--- /dev/null
+/*
+ * 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);
+}
projects / cascardo / linux.git / commitdiff