ext: Pull in tinycrypt v0.2.6
Zephyr 1.9 moves to tinycrypt v0.2.7. This introduces a breaking API
change. This makes things challenging for mcuboot, which would like to
be able to work across multiple platforms.
To help with this, bring in the last working version of Tinycrypt v0.2.6
from https://github.com/01org/tinycrypt. Tinycrypt is released under a
3-clause BSD-style license, with parts under the micro-ecc license,
which is a 2-clause license. Please see ext/tinycrypt/LICENSE for
details.
Signed-off-by: David Brown <david.brown@linaro.org>
diff --git a/ext/tinycrypt/lib/source/ecc.c b/ext/tinycrypt/lib/source/ecc.c
new file mode 100644
index 0000000..bfe6c5f
--- /dev/null
+++ b/ext/tinycrypt/lib/source/ecc.c
@@ -0,0 +1,625 @@
+/* ecc.c - TinyCrypt implementation of ECC auxiliary functions */
+
+/*
+ *
+ * Copyright (c) 2013, Kenneth MacKay
+ * All rights reserved.
+ * https://github.com/kmackay/micro-ecc
+ *
+ * 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.
+ *
+ * Copyright (C) 2015 by Intel Corporation, 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.
+ *
+ * - Neither the name of Intel Corporation nor the names of its contributors
+ * may be used to endorse or promote products derived from this software
+ * without specific prior written permission.
+ *
+ * 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 OWNER 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 <tinycrypt/ecc.h>
+
+/* ------ Curve NIST P-256 constants: ------ */
+
+#define Curve_P {0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000000, \
+ 0x00000000, 0x00000000, 0x00000001, 0xFFFFFFFF}
+
+#define Curve_B {0x27D2604B, 0x3BCE3C3E, 0xCC53B0F6, 0x651D06B0, \
+ 0x769886BC, 0xB3EBBD55, 0xAA3A93E7, 0x5AC635D8}
+
+#define Curve_N {0xFC632551, 0xF3B9CAC2, 0xA7179E84, 0xBCE6FAAD, \
+ 0xFFFFFFFF, 0xFFFFFFFF, 0x00000000, 0xFFFFFFFF}
+
+#define Curve_G {{0xD898C296, 0xF4A13945, 0x2DEB33A0, 0x77037D81, \
+ 0x63A440F2, 0xF8BCE6E5, 0xE12C4247, 0x6B17D1F2}, \
+ {0x37BF51F5, 0xCBB64068, 0x6B315ECE, 0x2BCE3357, \
+ 0x7C0F9E16, 0x8EE7EB4A, 0xFE1A7F9B, 0x4FE342E2} }
+
+#define Curve_P_Barrett {0x00000003, 0x00000000, 0xFFFFFFFF, 0xFFFFFFFE, \
+ 0xFFFFFFFE, 0xFFFFFFFE, 0xFFFFFFFF, 0x00000000, 0x00000001}
+
+#define Curve_N_Barrett {0xEEDF9BFE, 0x012FFD85, 0xDF1A6C21, 0x43190552, \
+ 0xFFFFFFFF, 0xFFFFFFFE, 0xFFFFFFFF, 0x00000000, 0x00000001}
+
+uint32_t curve_p[NUM_ECC_DIGITS] = Curve_P;
+uint32_t curve_b[NUM_ECC_DIGITS] = Curve_B;
+EccPoint curve_G = Curve_G;
+uint32_t curve_n[NUM_ECC_DIGITS] = Curve_N;
+uint32_t curve_pb[NUM_ECC_DIGITS + 1] = Curve_P_Barrett;
+uint32_t curve_nb[NUM_ECC_DIGITS + 1] = Curve_N_Barrett;
+
+/* ------ Static functions: ------ */
+
+/* Zeroing out p_vli. */
+static void vli_clear(uint32_t *p_vli)
+{
+ uint32_t i;
+
+ for (i = 0; i < NUM_ECC_DIGITS; ++i) {
+ p_vli[i] = 0;
+ }
+}
+
+/* Returns nonzero if bit p_bit of p_vli is set.
+ * It is assumed that the value provided in 'bit' is within
+ * the boundaries of the word-array 'p_vli'.*/
+static uint32_t vli_testBit(uint32_t *p_vli, uint32_t p_bit)
+{
+ return (p_vli[p_bit / 32] & (1 << (p_bit % 32)));
+}
+
+uint32_t vli_isZero(uint32_t *p_vli)
+{
+ uint32_t acc = 0;
+
+ for (uint32_t i = 0; i < NUM_ECC_DIGITS; ++i) {
+ acc |= p_vli[i];
+ }
+
+ return (!acc);
+}
+
+/*
+ * Find the right-most nonzero 32-bit "digits" in p_vli.
+ *
+ * Side-channel countermeasure: algorithm strengthened against timing attack.
+ */
+static uint32_t vli_numDigits(uint32_t *p_vli)
+{
+ int32_t i;
+ uint32_t digits = 0;
+
+ for (i = NUM_ECC_DIGITS - 1; i >= 0 ; --i) {
+ digits += p_vli[i] || digits;
+ }
+
+ return digits;
+}
+
+/*
+ * Find the left-most non-zero bit in p_vli.
+ *
+ * Side-channel countermeasure: algorithm strengthened against timing attack.
+ */
+static uint32_t vli_numBits(uint32_t *p_vli)
+{
+ uint32_t l_digit;
+ uint32_t i, acc = 32;
+ uint32_t l_numDigits = vli_numDigits(p_vli);
+
+ l_digit = p_vli[l_numDigits - 1];
+
+ for (i = 0; i < 32; ++i) {
+ acc -= !l_digit;
+ l_digit >>= 1;
+ }
+
+ return ((l_numDigits - 1) * 32 + acc);
+}
+
+/*
+ * Computes p_result = p_left + p_right, returns carry.
+ *
+ * Side-channel countermeasure: algorithm strengthened against timing attack.
+ */
+static uint32_t vli_add(uint32_t *p_result, uint32_t *p_left,
+ uint32_t *p_right)
+{
+
+ uint32_t l_carry = 0;
+
+ for (uint32_t i = 0; i < NUM_ECC_DIGITS; ++i) {
+ uint32_t l_sum = p_left[i] + p_right[i] + l_carry;
+
+ l_carry = (l_sum < p_left[i]) | ((l_sum == p_left[i]) && l_carry);
+ p_result[i] = l_sum;
+ }
+
+ return l_carry;
+}
+
+
+/* Computes p_result = p_left * p_right. */
+static void vli_mult(uint32_t *p_result, uint32_t *p_left,
+ uint32_t *p_right, uint32_t word_size)
+{
+
+ uint64_t r01 = 0;
+ uint32_t r2 = 0;
+
+ /* Compute each digit of p_result in sequence, maintaining the carries. */
+ for (uint32_t k = 0; k < word_size*2 - 1; ++k) {
+
+ uint32_t l_min = (k < word_size ? 0 : (k + 1) - word_size);
+
+ for (uint32_t i = l_min; i <= k && i < word_size; ++i) {
+
+ uint64_t l_product = (uint64_t)p_left[i] * p_right[k - i];
+
+ r01 += l_product;
+ r2 += (r01 < l_product);
+ }
+ p_result[k] = (uint32_t)r01;
+ r01 = (r01 >> 32) | (((uint64_t)r2) << 32);
+ r2 = 0;
+ }
+
+ p_result[word_size * 2 - 1] = (uint32_t)r01;
+}
+
+/* Computes p_result = p_left^2. */
+static void vli_square(uint32_t *p_result, uint32_t *p_left)
+{
+
+ uint64_t r01 = 0;
+ uint32_t r2 = 0;
+ uint32_t i, k;
+
+ for (k = 0; k < NUM_ECC_DIGITS * 2 - 1; ++k) {
+
+ uint32_t l_min = (k < NUM_ECC_DIGITS ? 0 : (k + 1) - NUM_ECC_DIGITS);
+
+ for (i = l_min; i <= k && i <= k - i; ++i) {
+
+ uint64_t l_product = (uint64_t)p_left[i] * p_left[k - i];
+
+ if (i < k - i) {
+
+ r2 += l_product >> 63;
+ l_product *= 2;
+ }
+ r01 += l_product;
+ r2 += (r01 < l_product);
+ }
+ p_result[k] = (uint32_t)r01;
+ r01 = (r01 >> 32) | (((uint64_t)r2) << 32);
+ r2 = 0;
+ }
+
+ p_result[NUM_ECC_DIGITS * 2 - 1] = (uint32_t)r01;
+}
+
+/* Computes p_result = p_product % curve_p using Barrett reduction. */
+void vli_mmod_barrett(uint32_t *p_result, uint32_t *p_product,
+ uint32_t *p_mod, uint32_t *p_barrett)
+{
+ uint32_t i;
+ uint32_t q1[NUM_ECC_DIGITS + 1];
+
+ for (i = NUM_ECC_DIGITS - 1; i < 2 * NUM_ECC_DIGITS; i++) {
+ q1[i - (NUM_ECC_DIGITS - 1)] = p_product[i];
+ }
+
+ uint32_t q2[2*NUM_ECC_DIGITS + 2];
+
+ vli_mult(q2, q1, p_barrett, NUM_ECC_DIGITS + 1);
+ for (i = NUM_ECC_DIGITS + 1; i < 2 * NUM_ECC_DIGITS + 2; i++) {
+ q1[i - (NUM_ECC_DIGITS + 1)] = q2[i];
+ }
+
+ uint32_t prime2[2*NUM_ECC_DIGITS];
+
+ for (i = 0; i < NUM_ECC_DIGITS; i++) {
+ prime2[i] = p_mod[i];
+ prime2[NUM_ECC_DIGITS + i] = 0;
+ }
+
+ vli_mult(q2, q1, prime2, NUM_ECC_DIGITS + 1);
+ vli_sub(p_product, p_product, q2, 2 * NUM_ECC_DIGITS);
+
+ uint32_t borrow;
+
+ borrow = vli_sub(q1, p_product, prime2, NUM_ECC_DIGITS + 1);
+ vli_cond_set(p_product, p_product, q1, borrow);
+ p_product[NUM_ECC_DIGITS] = q1[NUM_ECC_DIGITS] * (!borrow);
+ borrow = vli_sub(q1, p_product, prime2, NUM_ECC_DIGITS + 1);
+ vli_cond_set(p_product, p_product, q1, borrow);
+ p_product[NUM_ECC_DIGITS] = q1[NUM_ECC_DIGITS] * (!borrow);
+ borrow = vli_sub(q1, p_product, prime2, NUM_ECC_DIGITS + 1);
+ vli_cond_set(p_product, p_product, q1, borrow);
+ p_product[NUM_ECC_DIGITS] = q1[NUM_ECC_DIGITS] * (!borrow);
+
+ for (i = 0; i < NUM_ECC_DIGITS; i++) {
+ p_result[i] = p_product[i];
+ }
+}
+
+/*
+ * Computes modular exponentiation.
+ *
+ * Side-channel countermeasure: algorithm strengthened against timing attack.
+ */
+static void vli_modExp(uint32_t *p_result, uint32_t *p_base,
+ uint32_t *p_exp, uint32_t *p_mod, uint32_t *p_barrett)
+{
+
+ uint32_t acc[NUM_ECC_DIGITS], tmp[NUM_ECC_DIGITS], product[2 * NUM_ECC_DIGITS];
+ uint32_t j;
+ int32_t i;
+
+ vli_clear(acc);
+ acc[0] = 1;
+
+ for (i = NUM_ECC_DIGITS - 1; i >= 0; i--) {
+ for (j = 1 << 31; j > 0; j = j >> 1) {
+ vli_square(product, acc);
+ vli_mmod_barrett(acc, product, p_mod, p_barrett);
+ vli_mult(product, acc, p_base, NUM_ECC_DIGITS);
+ vli_mmod_barrett(tmp, product, p_mod, p_barrett);
+ vli_cond_set(acc, tmp, acc, j & p_exp[i]);
+ }
+ }
+
+ vli_set(p_result, acc);
+}
+
+/* Conversion from Affine coordinates to Jacobi coordinates. */
+static void EccPoint_fromAffine(EccPointJacobi *p_point_jacobi,
+ EccPoint *p_point) {
+
+ vli_set(p_point_jacobi->X, p_point->x);
+ vli_set(p_point_jacobi->Y, p_point->y);
+ vli_clear(p_point_jacobi->Z);
+ p_point_jacobi->Z[0] = 1;
+}
+
+/*
+ * Elliptic curve point doubling in Jacobi coordinates: P = P + P.
+ *
+ * Requires 4 squares and 4 multiplications.
+ */
+static void EccPoint_double(EccPointJacobi *P)
+{
+
+ uint32_t m[NUM_ECC_DIGITS], s[NUM_ECC_DIGITS], t[NUM_ECC_DIGITS];
+
+ vli_modSquare_fast(t, P->Z);
+ vli_modSub(m, P->X, t, curve_p);
+ vli_modAdd(s, P->X, t, curve_p);
+ vli_modMult_fast(m, m, s);
+ vli_modAdd(s, m, m, curve_p);
+ vli_modAdd(m, s, m, curve_p); /* m = 3X^2 - 3Z^4 */
+ vli_modSquare_fast(t, P->Y);
+ vli_modMult_fast(s, P->X, t);
+ vli_modAdd(s, s, s, curve_p);
+ vli_modAdd(s, s, s, curve_p); /* s = 4XY^2 */
+ vli_modMult_fast(P->Z, P->Y, P->Z);
+ vli_modAdd(P->Z, P->Z, P->Z, curve_p); /* Z' = 2YZ */
+ vli_modSquare_fast(P->X, m);
+ vli_modSub(P->X, P->X, s, curve_p);
+ vli_modSub(P->X, P->X, s, curve_p); /* X' = m^2 - 2s */
+ vli_modSquare_fast(P->Y, t);
+ vli_modAdd(P->Y, P->Y, P->Y, curve_p);
+ vli_modAdd(P->Y, P->Y, P->Y, curve_p);
+ vli_modAdd(P->Y, P->Y, P->Y, curve_p);
+ vli_modSub(t, s, P->X, curve_p);
+ vli_modMult_fast(t, t, m);
+ vli_modSub(P->Y, t, P->Y, curve_p); /* Y' = m(s - X') - 8Y^4 */
+
+}
+
+/* Copy input to target. */
+static void EccPointJacobi_set(EccPointJacobi *target, EccPointJacobi *input)
+{
+ vli_set(target->X, input->X);
+ vli_set(target->Y, input->Y);
+ vli_set(target->Z, input->Z);
+}
+
+/* ------ Externally visible functions (see header file for comments): ------ */
+
+void vli_set(uint32_t *p_dest, uint32_t *p_src)
+{
+
+ uint32_t i;
+
+ for (i = 0; i < NUM_ECC_DIGITS; ++i) {
+ p_dest[i] = p_src[i];
+ }
+}
+
+int32_t vli_cmp(uint32_t *p_left, uint32_t *p_right, int32_t word_size)
+{
+
+ int32_t i, cmp = 0;
+
+ for (i = word_size-1; i >= 0; --i) {
+ cmp |= ((p_left[i] > p_right[i]) - (p_left[i] < p_right[i])) * (!cmp);
+ }
+
+ return cmp;
+}
+
+uint32_t vli_sub(uint32_t *p_result, uint32_t *p_left, uint32_t *p_right,
+ uint32_t word_size)
+{
+
+ uint32_t l_borrow = 0;
+
+ for (uint32_t i = 0; i < word_size; ++i) {
+ uint32_t l_diff = p_left[i] - p_right[i] - l_borrow;
+
+ l_borrow = (l_diff > p_left[i]) | ((l_diff == p_left[i]) && l_borrow);
+ p_result[i] = l_diff;
+ }
+
+ return l_borrow;
+}
+
+void vli_cond_set(uint32_t *output, uint32_t *p_true, uint32_t *p_false,
+ uint32_t cond)
+{
+ uint32_t i;
+
+ cond = (!cond);
+
+ for (i = 0; i < NUM_ECC_DIGITS; i++) {
+ output[i] = (p_true[i]*(!cond)) | (p_false[i]*cond);
+ }
+}
+
+void vli_modAdd(uint32_t *p_result, uint32_t *p_left, uint32_t *p_right,
+ uint32_t *p_mod)
+{
+ uint32_t l_carry = vli_add(p_result, p_left, p_right);
+ uint32_t p_temp[NUM_ECC_DIGITS];
+
+ l_carry = l_carry == vli_sub(p_temp, p_result, p_mod, NUM_ECC_DIGITS);
+ vli_cond_set(p_result, p_temp, p_result, l_carry);
+}
+
+void vli_modSub(uint32_t *p_result, uint32_t *p_left, uint32_t *p_right,
+ uint32_t *p_mod)
+{
+ uint32_t l_borrow = vli_sub(p_result, p_left, p_right, NUM_ECC_DIGITS);
+ uint32_t p_temp[NUM_ECC_DIGITS];
+
+ vli_add(p_temp, p_result, p_mod);
+ vli_cond_set(p_result, p_temp, p_result, l_borrow);
+}
+
+void vli_modMult_fast(uint32_t *p_result, uint32_t *p_left,
+ uint32_t *p_right)
+{
+ uint32_t l_product[2 * NUM_ECC_DIGITS];
+
+ vli_mult(l_product, p_left, p_right, NUM_ECC_DIGITS);
+ vli_mmod_barrett(p_result, l_product, curve_p, curve_pb);
+}
+
+void vli_modSquare_fast(uint32_t *p_result, uint32_t *p_left)
+{
+ uint32_t l_product[2 * NUM_ECC_DIGITS];
+
+ vli_square(l_product, p_left);
+ vli_mmod_barrett(p_result, l_product, curve_p, curve_pb);
+}
+
+void vli_modMult(uint32_t *p_result, uint32_t *p_left, uint32_t *p_right,
+ uint32_t *p_mod, uint32_t *p_barrett)
+{
+
+ uint32_t l_product[2 * NUM_ECC_DIGITS];
+
+ vli_mult(l_product, p_left, p_right, NUM_ECC_DIGITS);
+ vli_mmod_barrett(p_result, l_product, p_mod, p_barrett);
+}
+
+void vli_modInv(uint32_t *p_result, uint32_t *p_input, uint32_t *p_mod,
+ uint32_t *p_barrett)
+{
+ uint32_t p_power[NUM_ECC_DIGITS];
+
+ vli_set(p_power, p_mod);
+ p_power[0] -= 2;
+ vli_modExp(p_result, p_input, p_power, p_mod, p_barrett);
+}
+
+uint32_t EccPoint_isZero(EccPoint *p_point)
+{
+ return (vli_isZero(p_point->x) && vli_isZero(p_point->y));
+}
+
+uint32_t EccPointJacobi_isZero(EccPointJacobi *p_point_jacobi)
+{
+ return vli_isZero(p_point_jacobi->Z);
+}
+
+void EccPoint_toAffine(EccPoint *p_point, EccPointJacobi *p_point_jacobi)
+{
+
+ if (vli_isZero(p_point_jacobi->Z)) {
+ vli_clear(p_point->x);
+ vli_clear(p_point->y);
+ return;
+ }
+
+ uint32_t z[NUM_ECC_DIGITS];
+
+ vli_set(z, p_point_jacobi->Z);
+ vli_modInv(z, z, curve_p, curve_pb);
+ vli_modSquare_fast(p_point->x, z);
+ vli_modMult_fast(p_point->y, p_point->x, z);
+ vli_modMult_fast(p_point->x, p_point->x, p_point_jacobi->X);
+ vli_modMult_fast(p_point->y, p_point->y, p_point_jacobi->Y);
+}
+
+void EccPoint_add(EccPointJacobi *P1, EccPointJacobi *P2)
+{
+
+ uint32_t s1[NUM_ECC_DIGITS], u1[NUM_ECC_DIGITS], t[NUM_ECC_DIGITS];
+ uint32_t h[NUM_ECC_DIGITS], r[NUM_ECC_DIGITS];
+
+ vli_modSquare_fast(r, P1->Z);
+ vli_modSquare_fast(s1, P2->Z);
+ vli_modMult_fast(u1, P1->X, s1); /* u1 = X1 Z2^2 */
+ vli_modMult_fast(h, P2->X, r);
+ vli_modMult_fast(s1, P1->Y, s1);
+ vli_modMult_fast(s1, s1, P2->Z); /* s1 = Y1 Z2^3 */
+ vli_modMult_fast(r, P2->Y, r);
+ vli_modMult_fast(r, r, P1->Z);
+ vli_modSub(h, h, u1, curve_p); /* h = X2 Z1^2 - u1 */
+ vli_modSub(r, r, s1, curve_p); /* r = Y2 Z1^3 - s1 */
+
+ if (vli_isZero(h)) {
+ if (vli_isZero(r)) {
+ /* P1 = P2 */
+ EccPoint_double(P1);
+ return;
+ }
+ /* point at infinity */
+ vli_clear(P1->Z);
+ return;
+ }
+
+ vli_modMult_fast(P1->Z, P1->Z, P2->Z);
+ vli_modMult_fast(P1->Z, P1->Z, h); /* Z3 = h Z1 Z2 */
+ vli_modSquare_fast(t, h);
+ vli_modMult_fast(h, t, h);
+ vli_modMult_fast(u1, u1, t);
+ vli_modSquare_fast(P1->X, r);
+ vli_modSub(P1->X, P1->X, h, curve_p);
+ vli_modSub(P1->X, P1->X, u1, curve_p);
+ vli_modSub(P1->X, P1->X, u1, curve_p); /* X3 = r^2 - h^3 - 2 u1 h^2 */
+ vli_modMult_fast(t, s1, h);
+ vli_modSub(P1->Y, u1, P1->X, curve_p);
+ vli_modMult_fast(P1->Y, P1->Y, r);
+ vli_modSub(P1->Y, P1->Y, t, curve_p); /* Y3 = r(u1 h^2 - X3) - s1 h^3 */
+}
+
+/*
+ * Elliptic curve scalar multiplication with result in Jacobi coordinates:
+ *
+ * p_result = p_scalar * p_point.
+ */
+void EccPoint_mult_safe(EccPointJacobi *p_result, EccPoint *p_point, uint32_t *p_scalar)
+{
+
+ int32_t i;
+ uint32_t bit;
+ EccPointJacobi p_point_jacobi, p_tmp;
+
+ EccPoint_fromAffine(p_result, p_point);
+ EccPoint_fromAffine(&p_point_jacobi, p_point);
+
+ for (i = vli_numBits(p_scalar) - 2; i >= 0; i--) {
+ EccPoint_double(p_result);
+ EccPointJacobi_set(&p_tmp, p_result);
+ EccPoint_add(&p_tmp, &p_point_jacobi);
+ bit = vli_testBit(p_scalar, i);
+ vli_cond_set(p_result->X, p_tmp.X, p_result->X, bit);
+ vli_cond_set(p_result->Y, p_tmp.Y, p_result->Y, bit);
+ vli_cond_set(p_result->Z, p_tmp.Z, p_result->Z, bit);
+ }
+}
+
+/* Ellptic curve scalar multiplication with result in Jacobi coordinates */
+/* p_result = p_scalar * p_point */
+void EccPoint_mult_unsafe(EccPointJacobi *p_result, EccPoint *p_point, uint32_t *p_scalar)
+{
+ int i;
+ EccPointJacobi p_point_jacobi;
+ EccPoint_fromAffine(p_result, p_point);
+ EccPoint_fromAffine(&p_point_jacobi, p_point);
+
+ for(i = vli_numBits(p_scalar) - 2; i >= 0; i--)
+ {
+ EccPoint_double(p_result);
+ if (vli_testBit(p_scalar, i))
+ {
+ EccPoint_add(p_result, &p_point_jacobi);
+ }
+ }
+}
+
+/* -------- Conversions between big endian and little endian: -------- */
+
+void ecc_bytes2native(uint32_t p_native[NUM_ECC_DIGITS],
+ uint8_t p_bytes[NUM_ECC_DIGITS * 4])
+{
+
+ uint32_t i;
+
+ for (i = 0; i < NUM_ECC_DIGITS; ++i) {
+ uint8_t *p_digit = p_bytes + 4 * (NUM_ECC_DIGITS - 1 - i);
+
+ p_native[i] = ((uint32_t)p_digit[0] << 24) |
+ ((uint32_t)p_digit[1] << 16) |
+ ((uint32_t)p_digit[2] << 8) |
+ (uint32_t)p_digit[3];
+ }
+}
+
+void ecc_native2bytes(uint8_t p_bytes[NUM_ECC_DIGITS * 4],
+ uint32_t p_native[NUM_ECC_DIGITS])
+{
+
+ uint32_t i;
+
+ for (i = 0; i < NUM_ECC_DIGITS; ++i) {
+ uint8_t *p_digit = p_bytes + 4 * (NUM_ECC_DIGITS - 1 - i);
+
+ p_digit[0] = p_native[i] >> 24;
+ p_digit[1] = p_native[i] >> 16;
+ p_digit[2] = p_native[i] >> 8;
+ p_digit[3] = p_native[i];
+ }
+}
+