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Diffstat (limited to 'src/libs/mynewt-nimble/ext/tinycrypt/src/ecc.c')
| -rw-r--r-- | src/libs/mynewt-nimble/ext/tinycrypt/src/ecc.c | 942 |
1 files changed, 942 insertions, 0 deletions
diff --git a/src/libs/mynewt-nimble/ext/tinycrypt/src/ecc.c b/src/libs/mynewt-nimble/ext/tinycrypt/src/ecc.c new file mode 100644 index 00000000..46080bf6 --- /dev/null +++ b/src/libs/mynewt-nimble/ext/tinycrypt/src/ecc.c @@ -0,0 +1,942 @@ +/* ecc.c - TinyCrypt implementation of common ECC functions */ + +/* + * Copyright (c) 2014, 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. + * + * Copyright (C) 2017 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> +#include <tinycrypt/ecc_platform_specific.h> +#include <string.h> + +/* IMPORTANT: Make sure a cryptographically-secure PRNG is set and the platform + * has access to enough entropy in order to feed the PRNG regularly. */ +#if default_RNG_defined +static uECC_RNG_Function g_rng_function = &default_CSPRNG; +#else +static uECC_RNG_Function g_rng_function = 0; +#endif + +void uECC_set_rng(uECC_RNG_Function rng_function) +{ + g_rng_function = rng_function; +} + +uECC_RNG_Function uECC_get_rng(void) +{ + return g_rng_function; +} + +int uECC_curve_private_key_size(uECC_Curve curve) +{ + return BITS_TO_BYTES(curve->num_n_bits); +} + +int uECC_curve_public_key_size(uECC_Curve curve) +{ + return 2 * curve->num_bytes; +} + +void uECC_vli_clear(uECC_word_t *vli, wordcount_t num_words) +{ + wordcount_t i; + for (i = 0; i < num_words; ++i) { + vli[i] = 0; + } +} + +uECC_word_t uECC_vli_isZero(const uECC_word_t *vli, wordcount_t num_words) +{ + uECC_word_t bits = 0; + wordcount_t i; + for (i = 0; i < num_words; ++i) { + bits |= vli[i]; + } + return (bits == 0); +} + +uECC_word_t uECC_vli_testBit(const uECC_word_t *vli, bitcount_t bit) +{ + return (vli[bit >> uECC_WORD_BITS_SHIFT] & + ((uECC_word_t)1 << (bit & uECC_WORD_BITS_MASK))); +} + +/* Counts the number of words in vli. */ +static wordcount_t vli_numDigits(const uECC_word_t *vli, + const wordcount_t max_words) +{ + + wordcount_t 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 = max_words - 1; i >= 0 && vli[i] == 0; --i) { + } + + return (i + 1); +} + +bitcount_t uECC_vli_numBits(const uECC_word_t *vli, + const wordcount_t max_words) +{ + + uECC_word_t i; + uECC_word_t digit; + + wordcount_t num_digits = vli_numDigits(vli, max_words); + if (num_digits == 0) { + return 0; + } + + digit = vli[num_digits - 1]; + for (i = 0; digit; ++i) { + digit >>= 1; + } + + return (((bitcount_t)(num_digits - 1) << uECC_WORD_BITS_SHIFT) + i); +} + +void uECC_vli_set(uECC_word_t *dest, const uECC_word_t *src, + wordcount_t num_words) +{ + wordcount_t i; + + for (i = 0; i < num_words; ++i) { + dest[i] = src[i]; + } +} + +cmpresult_t uECC_vli_cmp_unsafe(const uECC_word_t *left, + const uECC_word_t *right, + wordcount_t num_words) +{ + wordcount_t i; + + for (i = num_words - 1; i >= 0; --i) { + if (left[i] > right[i]) { + return 1; + } else if (left[i] < right[i]) { + return -1; + } + } + return 0; +} + +uECC_word_t uECC_vli_equal(const uECC_word_t *left, const uECC_word_t *right, + wordcount_t num_words) +{ + + uECC_word_t diff = 0; + wordcount_t i; + + for (i = num_words - 1; i >= 0; --i) { + diff |= (left[i] ^ right[i]); + } + return !(diff == 0); +} + +uECC_word_t cond_set(uECC_word_t p_true, uECC_word_t p_false, unsigned int cond) +{ + return (p_true*(cond)) | (p_false*(!cond)); +} + +/* Computes result = left - right, returning borrow, in constant time. + * Can modify in place. */ +uECC_word_t uECC_vli_sub(uECC_word_t *result, const uECC_word_t *left, + const uECC_word_t *right, wordcount_t num_words) +{ + uECC_word_t borrow = 0; + wordcount_t i; + for (i = 0; i < num_words; ++i) { + uECC_word_t diff = left[i] - right[i] - borrow; + uECC_word_t val = (diff > left[i]); + borrow = cond_set(val, borrow, (diff != left[i])); + + result[i] = diff; + } + return borrow; +} + +/* Computes result = left + right, returning carry, in constant time. + * Can modify in place. */ +static uECC_word_t uECC_vli_add(uECC_word_t *result, const uECC_word_t *left, + const uECC_word_t *right, wordcount_t num_words) +{ + uECC_word_t carry = 0; + wordcount_t i; + for (i = 0; i < num_words; ++i) { + uECC_word_t sum = left[i] + right[i] + carry; + uECC_word_t val = (sum < left[i]); + carry = cond_set(val, carry, (sum != left[i])); + result[i] = sum; + } + return carry; +} + +cmpresult_t uECC_vli_cmp(const uECC_word_t *left, const uECC_word_t *right, + wordcount_t num_words) +{ + uECC_word_t tmp[NUM_ECC_WORDS]; + uECC_word_t neg = !!uECC_vli_sub(tmp, left, right, num_words); + uECC_word_t equal = uECC_vli_isZero(tmp, num_words); + return (!equal - 2 * neg); +} + +/* Computes vli = vli >> 1. */ +static void uECC_vli_rshift1(uECC_word_t *vli, wordcount_t num_words) +{ + uECC_word_t *end = vli; + uECC_word_t carry = 0; + + vli += num_words; + while (vli-- > end) { + uECC_word_t temp = *vli; + *vli = (temp >> 1) | carry; + carry = temp << (uECC_WORD_BITS - 1); + } +} + +static void muladd(uECC_word_t a, uECC_word_t b, uECC_word_t *r0, + uECC_word_t *r1, uECC_word_t *r2) +{ + + uECC_dword_t p = (uECC_dword_t)a * b; + uECC_dword_t r01 = ((uECC_dword_t)(*r1) << uECC_WORD_BITS) | *r0; + r01 += p; + *r2 += (r01 < p); + *r1 = r01 >> uECC_WORD_BITS; + *r0 = (uECC_word_t)r01; + +} + +/* Computes result = left * right. Result must be 2 * num_words long. */ +static void uECC_vli_mult(uECC_word_t *result, const uECC_word_t *left, + const uECC_word_t *right, wordcount_t num_words) +{ + + uECC_word_t r0 = 0; + uECC_word_t r1 = 0; + uECC_word_t r2 = 0; + wordcount_t i, k; + + /* Compute each digit of result in sequence, maintaining the carries. */ + for (k = 0; k < num_words; ++k) { + + for (i = 0; i <= k; ++i) { + muladd(left[i], right[k - i], &r0, &r1, &r2); + } + + result[k] = r0; + r0 = r1; + r1 = r2; + r2 = 0; + } + + for (k = num_words; k < num_words * 2 - 1; ++k) { + + for (i = (k + 1) - num_words; i < num_words; ++i) { + muladd(left[i], right[k - i], &r0, &r1, &r2); + } + result[k] = r0; + r0 = r1; + r1 = r2; + r2 = 0; + } + result[num_words * 2 - 1] = r0; +} + +void uECC_vli_modAdd(uECC_word_t *result, const uECC_word_t *left, + const uECC_word_t *right, const uECC_word_t *mod, + wordcount_t num_words) +{ + uECC_word_t carry = uECC_vli_add(result, left, right, num_words); + if (carry || uECC_vli_cmp_unsafe(mod, result, num_words) != 1) { + /* result > mod (result = mod + remainder), so subtract mod to get + * remainder. */ + uECC_vli_sub(result, result, mod, num_words); + } +} + +void uECC_vli_modSub(uECC_word_t *result, const uECC_word_t *left, + const uECC_word_t *right, const uECC_word_t *mod, + wordcount_t num_words) +{ + uECC_word_t l_borrow = uECC_vli_sub(result, left, right, num_words); + if (l_borrow) { + /* In this case, result == -diff == (max int) - diff. Since -x % d == d - x, + * we can get the correct result from result + mod (with overflow). */ + uECC_vli_add(result, result, mod, num_words); + } +} + +/* Computes result = product % mod, where product is 2N words long. */ +/* Currently only designed to work for curve_p or curve_n. */ +void uECC_vli_mmod(uECC_word_t *result, uECC_word_t *product, + const uECC_word_t *mod, wordcount_t num_words) +{ + uECC_word_t mod_multiple[2 * NUM_ECC_WORDS]; + uECC_word_t tmp[2 * NUM_ECC_WORDS]; + uECC_word_t *v[2] = {tmp, product}; + uECC_word_t index; + + /* Shift mod so its highest set bit is at the maximum position. */ + bitcount_t shift = (num_words * 2 * uECC_WORD_BITS) - + uECC_vli_numBits(mod, num_words); + wordcount_t word_shift = shift / uECC_WORD_BITS; + wordcount_t bit_shift = shift % uECC_WORD_BITS; + uECC_word_t carry = 0; + uECC_vli_clear(mod_multiple, word_shift); + if (bit_shift > 0) { + for(index = 0; index < (uECC_word_t)num_words; ++index) { + mod_multiple[word_shift + index] = (mod[index] << bit_shift) | carry; + carry = mod[index] >> (uECC_WORD_BITS - bit_shift); + } + } else { + uECC_vli_set(mod_multiple + word_shift, mod, num_words); + } + + for (index = 1; shift >= 0; --shift) { + uECC_word_t borrow = 0; + wordcount_t i; + for (i = 0; i < num_words * 2; ++i) { + uECC_word_t diff = v[index][i] - mod_multiple[i] - borrow; + if (diff != v[index][i]) { + borrow = (diff > v[index][i]); + } + v[1 - index][i] = diff; + } + /* Swap the index if there was no borrow */ + index = !(index ^ borrow); + uECC_vli_rshift1(mod_multiple, num_words); + mod_multiple[num_words - 1] |= mod_multiple[num_words] << + (uECC_WORD_BITS - 1); + uECC_vli_rshift1(mod_multiple + num_words, num_words); + } + uECC_vli_set(result, v[index], num_words); +} + +void uECC_vli_modMult(uECC_word_t *result, const uECC_word_t *left, + const uECC_word_t *right, const uECC_word_t *mod, + wordcount_t num_words) +{ + uECC_word_t product[2 * NUM_ECC_WORDS]; + uECC_vli_mult(product, left, right, num_words); + uECC_vli_mmod(result, product, mod, num_words); +} + +void uECC_vli_modMult_fast(uECC_word_t *result, const uECC_word_t *left, + const uECC_word_t *right, uECC_Curve curve) +{ + uECC_word_t product[2 * NUM_ECC_WORDS]; + uECC_vli_mult(product, left, right, curve->num_words); + + curve->mmod_fast(result, product); +} + +static void uECC_vli_modSquare_fast(uECC_word_t *result, + const uECC_word_t *left, + uECC_Curve curve) +{ + uECC_vli_modMult_fast(result, left, left, curve); +} + + +#define EVEN(vli) (!(vli[0] & 1)) + +static void vli_modInv_update(uECC_word_t *uv, + const uECC_word_t *mod, + wordcount_t num_words) +{ + + uECC_word_t carry = 0; + + if (!EVEN(uv)) { + carry = uECC_vli_add(uv, uv, mod, num_words); + } + uECC_vli_rshift1(uv, num_words); + if (carry) { + uv[num_words - 1] |= HIGH_BIT_SET; + } +} + +void uECC_vli_modInv(uECC_word_t *result, const uECC_word_t *input, + const uECC_word_t *mod, wordcount_t num_words) +{ + uECC_word_t a[NUM_ECC_WORDS], b[NUM_ECC_WORDS]; + uECC_word_t u[NUM_ECC_WORDS], v[NUM_ECC_WORDS]; + cmpresult_t cmpResult; + + if (uECC_vli_isZero(input, num_words)) { + uECC_vli_clear(result, num_words); + return; + } + + uECC_vli_set(a, input, num_words); + uECC_vli_set(b, mod, num_words); + uECC_vli_clear(u, num_words); + u[0] = 1; + uECC_vli_clear(v, num_words); + while ((cmpResult = uECC_vli_cmp_unsafe(a, b, num_words)) != 0) { + if (EVEN(a)) { + uECC_vli_rshift1(a, num_words); + vli_modInv_update(u, mod, num_words); + } else if (EVEN(b)) { + uECC_vli_rshift1(b, num_words); + vli_modInv_update(v, mod, num_words); + } else if (cmpResult > 0) { + uECC_vli_sub(a, a, b, num_words); + uECC_vli_rshift1(a, num_words); + if (uECC_vli_cmp_unsafe(u, v, num_words) < 0) { + uECC_vli_add(u, u, mod, num_words); + } + uECC_vli_sub(u, u, v, num_words); + vli_modInv_update(u, mod, num_words); + } else { + uECC_vli_sub(b, b, a, num_words); + uECC_vli_rshift1(b, num_words); + if (uECC_vli_cmp_unsafe(v, u, num_words) < 0) { + uECC_vli_add(v, v, mod, num_words); + } + uECC_vli_sub(v, v, u, num_words); + vli_modInv_update(v, mod, num_words); + } + } + uECC_vli_set(result, u, num_words); +} + +/* ------ Point operations ------ */ + +void double_jacobian_default(uECC_word_t * X1, uECC_word_t * Y1, + uECC_word_t * Z1, uECC_Curve curve) +{ + /* t1 = X, t2 = Y, t3 = Z */ + uECC_word_t t4[NUM_ECC_WORDS]; + uECC_word_t t5[NUM_ECC_WORDS]; + wordcount_t num_words = curve->num_words; + + if (uECC_vli_isZero(Z1, num_words)) { + return; + } + + uECC_vli_modSquare_fast(t4, Y1, curve); /* t4 = y1^2 */ + uECC_vli_modMult_fast(t5, X1, t4, curve); /* t5 = x1*y1^2 = A */ + uECC_vli_modSquare_fast(t4, t4, curve); /* t4 = y1^4 */ + uECC_vli_modMult_fast(Y1, Y1, Z1, curve); /* t2 = y1*z1 = z3 */ + uECC_vli_modSquare_fast(Z1, Z1, curve); /* t3 = z1^2 */ + + uECC_vli_modAdd(X1, X1, Z1, curve->p, num_words); /* t1 = x1 + z1^2 */ + uECC_vli_modAdd(Z1, Z1, Z1, curve->p, num_words); /* t3 = 2*z1^2 */ + uECC_vli_modSub(Z1, X1, Z1, curve->p, num_words); /* t3 = x1 - z1^2 */ + uECC_vli_modMult_fast(X1, X1, Z1, curve); /* t1 = x1^2 - z1^4 */ + + uECC_vli_modAdd(Z1, X1, X1, curve->p, num_words); /* t3 = 2*(x1^2 - z1^4) */ + uECC_vli_modAdd(X1, X1, Z1, curve->p, num_words); /* t1 = 3*(x1^2 - z1^4) */ + if (uECC_vli_testBit(X1, 0)) { + uECC_word_t l_carry = uECC_vli_add(X1, X1, curve->p, num_words); + uECC_vli_rshift1(X1, num_words); + X1[num_words - 1] |= l_carry << (uECC_WORD_BITS - 1); + } else { + uECC_vli_rshift1(X1, num_words); + } + + /* t1 = 3/2*(x1^2 - z1^4) = B */ + uECC_vli_modSquare_fast(Z1, X1, curve); /* t3 = B^2 */ + uECC_vli_modSub(Z1, Z1, t5, curve->p, num_words); /* t3 = B^2 - A */ + uECC_vli_modSub(Z1, Z1, t5, curve->p, num_words); /* t3 = B^2 - 2A = x3 */ + uECC_vli_modSub(t5, t5, Z1, curve->p, num_words); /* t5 = A - x3 */ + uECC_vli_modMult_fast(X1, X1, t5, curve); /* t1 = B * (A - x3) */ + /* t4 = B * (A - x3) - y1^4 = y3: */ + uECC_vli_modSub(t4, X1, t4, curve->p, num_words); + + uECC_vli_set(X1, Z1, num_words); + uECC_vli_set(Z1, Y1, num_words); + uECC_vli_set(Y1, t4, num_words); +} + +void x_side_default(uECC_word_t *result, + const uECC_word_t *x, + uECC_Curve curve) +{ + uECC_word_t _3[NUM_ECC_WORDS] = {3}; /* -a = 3 */ + wordcount_t num_words = curve->num_words; + + uECC_vli_modSquare_fast(result, x, curve); /* r = x^2 */ + uECC_vli_modSub(result, result, _3, curve->p, num_words); /* r = x^2 - 3 */ + uECC_vli_modMult_fast(result, result, x, curve); /* r = x^3 - 3x */ + /* r = x^3 - 3x + b: */ + uECC_vli_modAdd(result, result, curve->b, curve->p, num_words); +} + +uECC_Curve uECC_secp256r1(void) +{ + return &curve_secp256r1; +} + +void vli_mmod_fast_secp256r1(unsigned int *result, unsigned int*product) +{ + unsigned int tmp[NUM_ECC_WORDS]; + int carry; + + /* t */ + uECC_vli_set(result, product, NUM_ECC_WORDS); + + /* s1 */ + tmp[0] = tmp[1] = tmp[2] = 0; + tmp[3] = product[11]; + tmp[4] = product[12]; + tmp[5] = product[13]; + tmp[6] = product[14]; + tmp[7] = product[15]; + carry = uECC_vli_add(tmp, tmp, tmp, NUM_ECC_WORDS); + carry += uECC_vli_add(result, result, tmp, NUM_ECC_WORDS); + + /* s2 */ + tmp[3] = product[12]; + tmp[4] = product[13]; + tmp[5] = product[14]; + tmp[6] = product[15]; + tmp[7] = 0; + carry += uECC_vli_add(tmp, tmp, tmp, NUM_ECC_WORDS); + carry += uECC_vli_add(result, result, tmp, NUM_ECC_WORDS); + + /* s3 */ + tmp[0] = product[8]; + tmp[1] = product[9]; + tmp[2] = product[10]; + tmp[3] = tmp[4] = tmp[5] = 0; + tmp[6] = product[14]; + tmp[7] = product[15]; + carry += uECC_vli_add(result, result, tmp, NUM_ECC_WORDS); + + /* s4 */ + tmp[0] = product[9]; + tmp[1] = product[10]; + tmp[2] = product[11]; + tmp[3] = product[13]; + tmp[4] = product[14]; + tmp[5] = product[15]; + tmp[6] = product[13]; + tmp[7] = product[8]; + carry += uECC_vli_add(result, result, tmp, NUM_ECC_WORDS); + + /* d1 */ + tmp[0] = product[11]; + tmp[1] = product[12]; + tmp[2] = product[13]; + tmp[3] = tmp[4] = tmp[5] = 0; + tmp[6] = product[8]; + tmp[7] = product[10]; + carry -= uECC_vli_sub(result, result, tmp, NUM_ECC_WORDS); + + /* d2 */ + tmp[0] = product[12]; + tmp[1] = product[13]; + tmp[2] = product[14]; + tmp[3] = product[15]; + tmp[4] = tmp[5] = 0; + tmp[6] = product[9]; + tmp[7] = product[11]; + carry -= uECC_vli_sub(result, result, tmp, NUM_ECC_WORDS); + + /* d3 */ + tmp[0] = product[13]; + tmp[1] = product[14]; + tmp[2] = product[15]; + tmp[3] = product[8]; + tmp[4] = product[9]; + tmp[5] = product[10]; + tmp[6] = 0; + tmp[7] = product[12]; + carry -= uECC_vli_sub(result, result, tmp, NUM_ECC_WORDS); + + /* d4 */ + tmp[0] = product[14]; + tmp[1] = product[15]; + tmp[2] = 0; + tmp[3] = product[9]; + tmp[4] = product[10]; + tmp[5] = product[11]; + tmp[6] = 0; + tmp[7] = product[13]; + carry -= uECC_vli_sub(result, result, tmp, NUM_ECC_WORDS); + + if (carry < 0) { + do { + carry += uECC_vli_add(result, result, curve_secp256r1.p, NUM_ECC_WORDS); + } + while (carry < 0); + } else { + while (carry || + uECC_vli_cmp_unsafe(curve_secp256r1.p, result, NUM_ECC_WORDS) != 1) { + carry -= uECC_vli_sub(result, result, curve_secp256r1.p, NUM_ECC_WORDS); + } + } +} + +uECC_word_t EccPoint_isZero(const uECC_word_t *point, uECC_Curve curve) +{ + return uECC_vli_isZero(point, curve->num_words * 2); +} + +void apply_z(uECC_word_t * X1, uECC_word_t * Y1, const uECC_word_t * const Z, + uECC_Curve curve) +{ + uECC_word_t t1[NUM_ECC_WORDS]; + + uECC_vli_modSquare_fast(t1, Z, curve); /* z^2 */ + uECC_vli_modMult_fast(X1, X1, t1, curve); /* x1 * z^2 */ + uECC_vli_modMult_fast(t1, t1, Z, curve); /* z^3 */ + uECC_vli_modMult_fast(Y1, Y1, t1, curve); /* y1 * z^3 */ +} + +/* P = (x1, y1) => 2P, (x2, y2) => P' */ +static void XYcZ_initial_double(uECC_word_t * X1, uECC_word_t * Y1, + uECC_word_t * X2, uECC_word_t * Y2, + const uECC_word_t * const initial_Z, + uECC_Curve curve) +{ + uECC_word_t z[NUM_ECC_WORDS]; + wordcount_t num_words = curve->num_words; + if (initial_Z) { + uECC_vli_set(z, initial_Z, num_words); + } else { + uECC_vli_clear(z, num_words); + z[0] = 1; + } + + uECC_vli_set(X2, X1, num_words); + uECC_vli_set(Y2, Y1, num_words); + + apply_z(X1, Y1, z, curve); + curve->double_jacobian(X1, Y1, z, curve); + apply_z(X2, Y2, z, curve); +} + +void XYcZ_add(uECC_word_t * X1, uECC_word_t * Y1, + uECC_word_t * X2, uECC_word_t * Y2, + uECC_Curve curve) +{ + /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */ + uECC_word_t t5[NUM_ECC_WORDS]; + wordcount_t num_words = curve->num_words; + + uECC_vli_modSub(t5, X2, X1, curve->p, num_words); /* t5 = x2 - x1 */ + uECC_vli_modSquare_fast(t5, t5, curve); /* t5 = (x2 - x1)^2 = A */ + uECC_vli_modMult_fast(X1, X1, t5, curve); /* t1 = x1*A = B */ + uECC_vli_modMult_fast(X2, X2, t5, curve); /* t3 = x2*A = C */ + uECC_vli_modSub(Y2, Y2, Y1, curve->p, num_words); /* t4 = y2 - y1 */ + uECC_vli_modSquare_fast(t5, Y2, curve); /* t5 = (y2 - y1)^2 = D */ + + uECC_vli_modSub(t5, t5, X1, curve->p, num_words); /* t5 = D - B */ + uECC_vli_modSub(t5, t5, X2, curve->p, num_words); /* t5 = D - B - C = x3 */ + uECC_vli_modSub(X2, X2, X1, curve->p, num_words); /* t3 = C - B */ + uECC_vli_modMult_fast(Y1, Y1, X2, curve); /* t2 = y1*(C - B) */ + uECC_vli_modSub(X2, X1, t5, curve->p, num_words); /* t3 = B - x3 */ + uECC_vli_modMult_fast(Y2, Y2, X2, curve); /* t4 = (y2 - y1)*(B - x3) */ + uECC_vli_modSub(Y2, Y2, Y1, curve->p, num_words); /* t4 = y3 */ + + uECC_vli_set(X2, t5, num_words); +} + +/* 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_addC(uECC_word_t * X1, uECC_word_t * Y1, + uECC_word_t * X2, uECC_word_t * Y2, + uECC_Curve curve) +{ + /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */ + uECC_word_t t5[NUM_ECC_WORDS]; + uECC_word_t t6[NUM_ECC_WORDS]; + uECC_word_t t7[NUM_ECC_WORDS]; + wordcount_t num_words = curve->num_words; + + uECC_vli_modSub(t5, X2, X1, curve->p, num_words); /* t5 = x2 - x1 */ + uECC_vli_modSquare_fast(t5, t5, curve); /* t5 = (x2 - x1)^2 = A */ + uECC_vli_modMult_fast(X1, X1, t5, curve); /* t1 = x1*A = B */ + uECC_vli_modMult_fast(X2, X2, t5, curve); /* t3 = x2*A = C */ + uECC_vli_modAdd(t5, Y2, Y1, curve->p, num_words); /* t5 = y2 + y1 */ + uECC_vli_modSub(Y2, Y2, Y1, curve->p, num_words); /* t4 = y2 - y1 */ + + uECC_vli_modSub(t6, X2, X1, curve->p, num_words); /* t6 = C - B */ + uECC_vli_modMult_fast(Y1, Y1, t6, curve); /* t2 = y1 * (C - B) = E */ + uECC_vli_modAdd(t6, X1, X2, curve->p, num_words); /* t6 = B + C */ + uECC_vli_modSquare_fast(X2, Y2, curve); /* t3 = (y2 - y1)^2 = D */ + uECC_vli_modSub(X2, X2, t6, curve->p, num_words); /* t3 = D - (B + C) = x3 */ + + uECC_vli_modSub(t7, X1, X2, curve->p, num_words); /* t7 = B - x3 */ + uECC_vli_modMult_fast(Y2, Y2, t7, curve); /* t4 = (y2 - y1)*(B - x3) */ + /* t4 = (y2 - y1)*(B - x3) - E = y3: */ + uECC_vli_modSub(Y2, Y2, Y1, curve->p, num_words); + + uECC_vli_modSquare_fast(t7, t5, curve); /* t7 = (y2 + y1)^2 = F */ + uECC_vli_modSub(t7, t7, t6, curve->p, num_words); /* t7 = F - (B + C) = x3' */ + uECC_vli_modSub(t6, t7, X1, curve->p, num_words); /* t6 = x3' - B */ + uECC_vli_modMult_fast(t6, t6, t5, curve); /* t6 = (y2+y1)*(x3' - B) */ + /* t2 = (y2+y1)*(x3' - B) - E = y3': */ + uECC_vli_modSub(Y1, t6, Y1, curve->p, num_words); + + uECC_vli_set(X1, t7, num_words); +} + +void EccPoint_mult(uECC_word_t * result, const uECC_word_t * point, + const uECC_word_t * scalar, + const uECC_word_t * initial_Z, + bitcount_t num_bits, uECC_Curve curve) +{ + /* R0 and R1 */ + uECC_word_t Rx[2][NUM_ECC_WORDS]; + uECC_word_t Ry[2][NUM_ECC_WORDS]; + uECC_word_t z[NUM_ECC_WORDS]; + bitcount_t i; + uECC_word_t nb; + wordcount_t num_words = curve->num_words; + + uECC_vli_set(Rx[1], point, num_words); + uECC_vli_set(Ry[1], point + num_words, num_words); + + XYcZ_initial_double(Rx[1], Ry[1], Rx[0], Ry[0], initial_Z, curve); + + for (i = num_bits - 2; i > 0; --i) { + nb = !uECC_vli_testBit(scalar, i); + XYcZ_addC(Rx[1 - nb], Ry[1 - nb], Rx[nb], Ry[nb], curve); + XYcZ_add(Rx[nb], Ry[nb], Rx[1 - nb], Ry[1 - nb], curve); + } + + nb = !uECC_vli_testBit(scalar, 0); + XYcZ_addC(Rx[1 - nb], Ry[1 - nb], Rx[nb], Ry[nb], curve); + + /* Find final 1/Z value. */ + uECC_vli_modSub(z, Rx[1], Rx[0], curve->p, num_words); /* X1 - X0 */ + uECC_vli_modMult_fast(z, z, Ry[1 - nb], curve); /* Yb * (X1 - X0) */ + uECC_vli_modMult_fast(z, z, point, curve); /* xP * Yb * (X1 - X0) */ + uECC_vli_modInv(z, z, curve->p, num_words); /* 1 / (xP * Yb * (X1 - X0))*/ + /* yP / (xP * Yb * (X1 - X0)) */ + uECC_vli_modMult_fast(z, z, point + num_words, curve); + /* Xb * yP / (xP * Yb * (X1 - X0)) */ + uECC_vli_modMult_fast(z, z, Rx[1 - nb], curve); + /* End 1/Z calculation */ + + XYcZ_add(Rx[nb], Ry[nb], Rx[1 - nb], Ry[1 - nb], curve); + apply_z(Rx[0], Ry[0], z, curve); + + uECC_vli_set(result, Rx[0], num_words); + uECC_vli_set(result + num_words, Ry[0], num_words); +} + +uECC_word_t regularize_k(const uECC_word_t * const k, uECC_word_t *k0, + uECC_word_t *k1, uECC_Curve curve) +{ + + wordcount_t num_n_words = BITS_TO_WORDS(curve->num_n_bits); + + bitcount_t num_n_bits = curve->num_n_bits; + + uECC_word_t carry = uECC_vli_add(k0, k, curve->n, num_n_words) || + (num_n_bits < ((bitcount_t)num_n_words * uECC_WORD_SIZE * 8) && + uECC_vli_testBit(k0, num_n_bits)); + + uECC_vli_add(k1, k0, curve->n, num_n_words); + + return carry; +} + +uECC_word_t EccPoint_compute_public_key(uECC_word_t *result, + uECC_word_t *private_key, + uECC_Curve curve) +{ + + uECC_word_t tmp1[NUM_ECC_WORDS]; + uECC_word_t tmp2[NUM_ECC_WORDS]; + uECC_word_t *p2[2] = {tmp1, tmp2}; + uECC_word_t carry; + + /* Regularize the bitcount for the private key so that attackers cannot + * use a side channel attack to learn the number of leading zeros. */ + carry = regularize_k(private_key, tmp1, tmp2, curve); + + EccPoint_mult(result, curve->G, p2[!carry], 0, curve->num_n_bits + 1, curve); + + if (EccPoint_isZero(result, curve)) { + return 0; + } + return 1; +} + +/* Converts an integer in uECC native format to big-endian bytes. */ +void uECC_vli_nativeToBytes(uint8_t *bytes, int num_bytes, + const unsigned int *native) +{ + wordcount_t i; + for (i = 0; i < num_bytes; ++i) { + unsigned b = num_bytes - 1 - i; + bytes[i] = native[b / uECC_WORD_SIZE] >> (8 * (b % uECC_WORD_SIZE)); + } +} + +/* Converts big-endian bytes to an integer in uECC native format. */ +void uECC_vli_bytesToNative(unsigned int *native, const uint8_t *bytes, + int num_bytes) +{ + wordcount_t i; + uECC_vli_clear(native, (num_bytes + (uECC_WORD_SIZE - 1)) / uECC_WORD_SIZE); + for (i = 0; i < num_bytes; ++i) { + unsigned b = num_bytes - 1 - i; + native[b / uECC_WORD_SIZE] |= + (uECC_word_t)bytes[i] << (8 * (b % uECC_WORD_SIZE)); + } +} + +int uECC_generate_random_int(uECC_word_t *random, const uECC_word_t *top, + wordcount_t num_words) +{ + uECC_word_t mask = (uECC_word_t)-1; + uECC_word_t tries; + bitcount_t num_bits = uECC_vli_numBits(top, num_words); + + if (!g_rng_function) { + return 0; + } + + for (tries = 0; tries < uECC_RNG_MAX_TRIES; ++tries) { + if (!g_rng_function((uint8_t *)random, num_words * uECC_WORD_SIZE)) { + return 0; + } + random[num_words - 1] &= + mask >> ((bitcount_t)(num_words * uECC_WORD_SIZE * 8 - num_bits)); + if (!uECC_vli_isZero(random, num_words) && + uECC_vli_cmp(top, random, num_words) == 1) { + return 1; + } + } + return 0; +} + + +int uECC_valid_point(const uECC_word_t *point, uECC_Curve curve) +{ + uECC_word_t tmp1[NUM_ECC_WORDS]; + uECC_word_t tmp2[NUM_ECC_WORDS]; + wordcount_t num_words = curve->num_words; + + /* The point at infinity is invalid. */ + if (EccPoint_isZero(point, curve)) { + return -1; + } + + /* x and y must be smaller than p. */ + if (uECC_vli_cmp_unsafe(curve->p, point, num_words) != 1 || + uECC_vli_cmp_unsafe(curve->p, point + num_words, num_words) != 1) { + return -2; + } + + uECC_vli_modSquare_fast(tmp1, point + num_words, curve); + curve->x_side(tmp2, point, curve); /* tmp2 = x^3 + ax + b */ + + /* Make sure that y^2 == x^3 + ax + b */ + if (uECC_vli_equal(tmp1, tmp2, num_words) != 0) + return -3; + + return 0; +} + +int uECC_valid_public_key(const uint8_t *public_key, uECC_Curve curve) +{ + + uECC_word_t _public[NUM_ECC_WORDS * 2]; + + uECC_vli_bytesToNative(_public, public_key, curve->num_bytes); + uECC_vli_bytesToNative( + _public + curve->num_words, + public_key + curve->num_bytes, + curve->num_bytes); + + if (uECC_vli_cmp_unsafe(_public, curve->G, NUM_ECC_WORDS * 2) == 0) { + return -4; + } + + return uECC_valid_point(_public, curve); +} + +int uECC_compute_public_key(const uint8_t *private_key, uint8_t *public_key, + uECC_Curve curve) +{ + + uECC_word_t _private[NUM_ECC_WORDS]; + uECC_word_t _public[NUM_ECC_WORDS * 2]; + + uECC_vli_bytesToNative( + _private, + private_key, + BITS_TO_BYTES(curve->num_n_bits)); + + /* Make sure the private key is in the range [1, n-1]. */ + if (uECC_vli_isZero(_private, BITS_TO_WORDS(curve->num_n_bits))) { + return 0; + } + + if (uECC_vli_cmp(curve->n, _private, BITS_TO_WORDS(curve->num_n_bits)) != 1) { + return 0; + } + + /* Compute public key. */ + if (!EccPoint_compute_public_key(_public, _private, curve)) { + return 0; + } + + uECC_vli_nativeToBytes(public_key, curve->num_bytes, _public); + uECC_vli_nativeToBytes( + public_key + + curve->num_bytes, curve->num_bytes, _public + curve->num_words); + return 1; +} + + + |