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Diffstat (limited to 'crypto/ecc.c')
| -rw-r--r-- | crypto/ecc.c | 1018 |
1 files changed, 1018 insertions, 0 deletions
diff --git a/crypto/ecc.c b/crypto/ecc.c new file mode 100644 index 0000000..414c78a --- /dev/null +++ b/crypto/ecc.c @@ -0,0 +1,1018 @@ +/* + * 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 <linux/slab.h> +#include <linux/swab.h> +#include <linux/fips.h> +#include <crypto/ecdh.h> + +#include "ecc.h" +#include "ecc_curve_defs.h" + +typedef struct { + u64 m_low; + u64 m_high; +} uint128_t; + +static inline const struct ecc_curve *ecc_get_curve(unsigned int curve_id) +{ + switch (curve_id) { + /* In FIPS mode only allow P256 and higher */ + case ECC_CURVE_NIST_P192: + return fips_enabled ? NULL : &nist_p192; + case ECC_CURVE_NIST_P256: + return &nist_p256; + default: + return NULL; + } +} + +static u64 *ecc_alloc_digits_space(unsigned int ndigits) +{ + size_t len = ndigits * sizeof(u64); + + if (!len) + return NULL; + + return kmalloc(len, GFP_KERNEL); +} + +static void ecc_free_digits_space(u64 *space) +{ + kzfree(space); +} + +static struct ecc_point *ecc_alloc_point(unsigned int ndigits) +{ + struct ecc_point *p = kmalloc(sizeof(*p), GFP_KERNEL); + + if (!p) + return NULL; + + p->x = ecc_alloc_digits_space(ndigits); + if (!p->x) + goto err_alloc_x; + + p->y = ecc_alloc_digits_space(ndigits); + if (!p->y) + goto err_alloc_y; + + p->ndigits = ndigits; + + return p; + +err_alloc_y: + ecc_free_digits_space(p->x); +err_alloc_x: + kfree(p); + return NULL; +} + +static void ecc_free_point(struct ecc_point *p) +{ + if (!p) + return; + + kzfree(p->x); + kzfree(p->y); + kzfree(p); +} + +static void vli_clear(u64 *vli, unsigned int ndigits) +{ + int i; + + for (i = 0; i < ndigits; i++) + vli[i] = 0; +} + +/* Returns true if vli == 0, false otherwise. */ +static bool vli_is_zero(const u64 *vli, unsigned int ndigits) +{ + int i; + + for (i = 0; i < ndigits; 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, unsigned int ndigits) +{ + 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 = ndigits - 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 ndigits) +{ + unsigned int i, num_digits; + u64 digit; + + num_digits = vli_num_digits(vli, ndigits); + 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, unsigned int ndigits) +{ + int i; + + for (i = 0; i < ndigits; i++) + dest[i] = src[i]; +} + +/* Returns sign of left - right. */ +static int vli_cmp(const u64 *left, const u64 *right, unsigned int ndigits) +{ + int i; + + for (i = ndigits - 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, + unsigned int ndigits) +{ + u64 carry = 0; + int i; + + for (i = 0; i < ndigits; 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, unsigned int ndigits) +{ + u64 *end = vli; + u64 carry = 0; + + vli += ndigits; + + 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, + unsigned int ndigits) +{ + u64 carry = 0; + int i; + + for (i = 0; i < ndigits; 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, + unsigned int ndigits) +{ + u64 borrow = 0; + int i; + + for (i = 0; i < ndigits; 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, + unsigned int ndigits) +{ + 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 < ndigits * 2 - 1; k++) { + unsigned int min; + + if (k < ndigits) + min = 0; + else + min = (k + 1) - ndigits; + + for (i = min; i <= k && i < ndigits; 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[ndigits * 2 - 1] = r01.m_low; +} + +static void vli_square(u64 *result, const u64 *left, unsigned int ndigits) +{ + uint128_t r01 = { 0, 0 }; + u64 r2 = 0; + int i, k; + + for (k = 0; k < ndigits * 2 - 1; k++) { + unsigned int min; + + if (k < ndigits) + min = 0; + else + min = (k + 1) - ndigits; + + 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[ndigits * 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, unsigned int ndigits) +{ + u64 carry; + + carry = vli_add(result, left, right, ndigits); + + /* result > mod (result = mod + remainder), so subtract mod to + * get remainder. + */ + if (carry || vli_cmp(result, mod, ndigits) >= 0) + vli_sub(result, result, mod, ndigits); +} + +/* 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, unsigned int ndigits) +{ + u64 borrow = vli_sub(result, left, right, ndigits); + + /* 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, ndigits); +} + +/* Computes p_result = p_product % curve_p. + * See algorithm 5 and 6 from + * http://www.isys.uni-klu.ac.at/PDF/2001-0126-MT.pdf + */ +static void vli_mmod_fast_192(u64 *result, const u64 *product, + const u64 *curve_prime, u64 *tmp) +{ + const unsigned int ndigits = 3; + int carry; + + vli_set(result, product, ndigits); + + vli_set(tmp, &product[3], ndigits); + carry = vli_add(result, result, tmp, ndigits); + + tmp[0] = 0; + tmp[1] = product[3]; + tmp[2] = product[4]; + carry += vli_add(result, result, tmp, ndigits); + + tmp[0] = tmp[1] = product[5]; + tmp[2] = 0; + carry += vli_add(result, result, tmp, ndigits); + + while (carry || vli_cmp(curve_prime, result, ndigits) != 1) + carry -= vli_sub(result, result, curve_prime, ndigits); +} + +/* Computes result = product % curve_prime + * from http://www.nsa.gov/ia/_files/nist-routines.pdf + */ +static void vli_mmod_fast_256(u64 *result, const u64 *product, + const u64 *curve_prime, u64 *tmp) +{ + int carry; + const unsigned int ndigits = 4; + + /* t */ + vli_set(result, product, ndigits); + + /* s1 */ + tmp[0] = 0; + tmp[1] = product[5] & 0xffffffff00000000ull; + tmp[2] = product[6]; + tmp[3] = product[7]; + carry = vli_lshift(tmp, tmp, 1, ndigits); + carry += vli_add(result, result, tmp, ndigits); + + /* 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, ndigits); + carry += vli_add(result, result, tmp, ndigits); + + /* s3 */ + tmp[0] = product[4]; + tmp[1] = product[5] & 0xffffffff; + tmp[2] = 0; + tmp[3] = product[7]; + carry += vli_add(result, result, tmp, ndigits); + + /* 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, ndigits); + + /* 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, ndigits); + + /* 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, ndigits); + + /* 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, ndigits); + + /* 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, ndigits); + + if (carry < 0) { + do { + carry += vli_add(result, result, curve_prime, ndigits); + } while (carry < 0); + } else { + while (carry || vli_cmp(curve_prime, result, ndigits) != 1) + carry -= vli_sub(result, result, curve_prime, ndigits); + } +} + +/* Computes result = product % curve_prime + * from http://www.nsa.gov/ia/_files/nist-routines.pdf +*/ +static bool vli_mmod_fast(u64 *result, u64 *product, + const u64 *curve_prime, unsigned int ndigits) +{ + u64 tmp[2 * ndigits]; + + switch (ndigits) { + case 3: + vli_mmod_fast_192(result, product, curve_prime, tmp); + break; + case 4: + vli_mmod_fast_256(result, product, curve_prime, tmp); + break; + default: + pr_err("unsupports digits size!\n"); + return false; + } + + return true; +} + +/* Computes result = (left * right) % curve_prime. */ +static void vli_mod_mult_fast(u64 *result, const u64 *left, const u64 *right, + const u64 *curve_prime, unsigned int ndigits) +{ + u64 product[2 * ndigits]; + + vli_mult(product, left, right, ndigits); + vli_mmod_fast(result, product, curve_prime, ndigits); +} + +/* Computes result = left^2 % curve_prime. */ +static void vli_mod_square_fast(u64 *result, const u64 *left, + const u64 *curve_prime, unsigned int ndigits) +{ + u64 product[2 * ndigits]; + + vli_square(product, left, ndigits); + vli_mmod_fast(result, product, curve_prime, ndigits); +} + +#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, + unsigned int ndigits) +{ + u64 a[ndigits], b[ndigits]; + u64 u[ndigits], v[ndigits]; + u64 carry; + int cmp_result; + + if (vli_is_zero(input, ndigits)) { + vli_clear(result, ndigits); + return; + } + + vli_set(a, input, ndigits); + vli_set(b, mod, ndigits); + vli_clear(u, ndigits); + u[0] = 1; + vli_clear(v, ndigits); + + while ((cmp_result = vli_cmp(a, b, ndigits)) != 0) { + carry = 0; + + if (EVEN(a)) { + vli_rshift1(a, ndigits); + + if (!EVEN(u)) + carry = vli_add(u, u, mod, ndigits); + + vli_rshift1(u, ndigits); + if (carry) + u[ndigits - 1] |= 0x8000000000000000ull; + } else if (EVEN(b)) { + vli_rshift1(b, ndigits); + + if (!EVEN(v)) + carry = vli_add(v, v, mod, ndigits); + + vli_rshift1(v, ndigits); + if (carry) + v[ndigits - 1] |= 0x8000000000000000ull; + } else if (cmp_result > 0) { + vli_sub(a, a, b, ndigits); + vli_rshift1(a, ndigits); + + if (vli_cmp(u, v, ndigits) < 0) + vli_add(u, u, mod, ndigits); + + vli_sub(u, u, v, ndigits); + if (!EVEN(u)) + carry = vli_add(u, u, mod, ndigits); + + vli_rshift1(u, ndigits); + if (carry) + u[ndigits - 1] |= 0x8000000000000000ull; + } else { + vli_sub(b, b, a, ndigits); + vli_rshift1(b, ndigits); + + if (vli_cmp(v, u, ndigits) < 0) + vli_add(v, v, mod, ndigits); + + vli_sub(v, v, u, ndigits); + if (!EVEN(v)) + carry = vli_add(v, v, mod, ndigits); + + vli_rshift1(v, ndigits); + if (carry) + v[ndigits - 1] |= 0x8000000000000000ull; + } + } + + vli_set(result, u, ndigits); +} + +/* ------ 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, point->ndigits) && + vli_is_zero(point->y, point->ndigits)); +} + +/* 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, + u64 *curve_prime, unsigned int ndigits) +{ + /* t1 = x, t2 = y, t3 = z */ + u64 t4[ndigits]; + u64 t5[ndigits]; + + if (vli_is_zero(z1, ndigits)) + return; + + /* t4 = y1^2 */ + vli_mod_square_fast(t4, y1, curve_prime, ndigits); + /* t5 = x1*y1^2 = A */ + vli_mod_mult_fast(t5, x1, t4, curve_prime, ndigits); + /* t4 = y1^4 */ + vli_mod_square_fast(t4, t4, curve_prime, ndigits); + /* t2 = y1*z1 = z3 */ + vli_mod_mult_fast(y1, y1, z1, curve_prime, ndigits); + /* t3 = z1^2 */ + vli_mod_square_fast(z1, z1, curve_prime, ndigits); + + /* t1 = x1 + z1^2 */ + vli_mod_add(x1, x1, z1, curve_prime, ndigits); + /* t3 = 2*z1^2 */ + vli_mod_add(z1, z1, z1, curve_prime, ndigits); + /* t3 = x1 - z1^2 */ + vli_mod_sub(z1, x1, z1, curve_prime, ndigits); + /* t1 = x1^2 - z1^4 */ + vli_mod_mult_fast(x1, x1, z1, curve_prime, ndigits); + + /* t3 = 2*(x1^2 - z1^4) */ + vli_mod_add(z1, x1, x1, curve_prime, ndigits); + /* t1 = 3*(x1^2 - z1^4) */ + vli_mod_add(x1, x1, z1, curve_prime, ndigits); + if (vli_test_bit(x1, 0)) { + u64 carry = vli_add(x1, x1, curve_prime, ndigits); + + vli_rshift1(x1, ndigits); + x1[ndigits - 1] |= carry << 63; + } else { + vli_rshift1(x1, ndigits); + } + /* t1 = 3/2*(x1^2 - z1^4) = B */ + + /* t3 = B^2 */ + vli_mod_square_fast(z1, x1, curve_prime, ndigits); + /* t3 = B^2 - A */ + vli_mod_sub(z1, z1, t5, curve_prime, ndigits); + /* t3 = B^2 - 2A = x3 */ + vli_mod_sub(z1, z1, t5, curve_prime, ndigits); + /* t5 = A - x3 */ + vli_mod_sub(t5, t5, z1, curve_prime, ndigits); + /* t1 = B * (A - x3) */ + vli_mod_mult_fast(x1, x1, t5, curve_prime, ndigits); + /* t4 = B * (A - x3) - y1^4 = y3 */ + vli_mod_sub(t4, x1, t4, curve_prime, ndigits); + + vli_set(x1, z1, ndigits); + vli_set(z1, y1, ndigits); + vli_set(y1, t4, ndigits); +} + +/* Modify (x1, y1) => (x1 * z^2, y1 * z^3) */ +static void apply_z(u64 *x1, u64 *y1, u64 *z, u64 *curve_prime, + unsigned int ndigits) +{ + u64 t1[ndigits]; + + vli_mod_square_fast(t1, z, curve_prime, ndigits); /* z^2 */ + vli_mod_mult_fast(x1, x1, t1, curve_prime, ndigits); /* x1 * z^2 */ + vli_mod_mult_fast(t1, t1, z, curve_prime, ndigits); /* z^3 */ + vli_mod_mult_fast(y1, y1, t1, curve_prime, ndigits); /* 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 *curve_prime, + unsigned int ndigits) +{ + u64 z[ndigits]; + + vli_set(x2, x1, ndigits); + vli_set(y2, y1, ndigits); + + vli_clear(z, ndigits); + z[0] = 1; + + if (p_initial_z) + vli_set(z, p_initial_z, ndigits); + + apply_z(x1, y1, z, curve_prime, ndigits); + + ecc_point_double_jacobian(x1, y1, z, curve_prime, ndigits); + + apply_z(x2, y2, z, curve_prime, ndigits); +} + +/* 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, u64 *curve_prime, + unsigned int ndigits) +{ + /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */ + u64 t5[ndigits]; + + /* t5 = x2 - x1 */ + vli_mod_sub(t5, x2, x1, curve_prime, ndigits); + /* t5 = (x2 - x1)^2 = A */ + vli_mod_square_fast(t5, t5, curve_prime, ndigits); + /* t1 = x1*A = B */ + vli_mod_mult_fast(x1, x1, t5, curve_prime, ndigits); + /* t3 = x2*A = C */ + vli_mod_mult_fast(x2, x2, t5, curve_prime, ndigits); + /* t4 = y2 - y1 */ + vli_mod_sub(y2, y2, y1, curve_prime, ndigits); + /* t5 = (y2 - y1)^2 = D */ + vli_mod_square_fast(t5, y2, curve_prime, ndigits); + + /* t5 = D - B */ + vli_mod_sub(t5, t5, x1, curve_prime, ndigits); + /* t5 = D - B - C = x3 */ + vli_mod_sub(t5, t5, x2, curve_prime, ndigits); + /* t3 = C - B */ + vli_mod_sub(x2, x2, x1, curve_prime, ndigits); + /* t2 = y1*(C - B) */ + vli_mod_mult_fast(y1, y1, x2, curve_prime, ndigits); + /* t3 = B - x3 */ + vli_mod_sub(x2, x1, t5, curve_prime, ndigits); + /* t4 = (y2 - y1)*(B - x3) */ + vli_mod_mult_fast(y2, y2, x2, curve_prime, ndigits); + /* t4 = y3 */ + vli_mod_sub(y2, y2, y1, curve_prime, ndigits); + + vli_set(x2, t5, ndigits); +} + +/* 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, u64 *curve_prime, + unsigned int ndigits) +{ + /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */ + u64 t5[ndigits]; + u64 t6[ndigits]; + u64 t7[ndigits]; + + /* t5 = x2 - x1 */ + vli_mod_sub(t5, x2, x1, curve_prime, ndigits); + /* t5 = (x2 - x1)^2 = A */ + vli_mod_square_fast(t5, t5, curve_prime, ndigits); + /* t1 = x1*A = B */ + vli_mod_mult_fast(x1, x1, t5, curve_prime, ndigits); + /* t3 = x2*A = C */ + vli_mod_mult_fast(x2, x2, t5, curve_prime, ndigits); + /* t4 = y2 + y1 */ + vli_mod_add(t5, y2, y1, curve_prime, ndigits); + /* t4 = y2 - y1 */ + vli_mod_sub(y2, y2, y1, curve_prime, ndigits); + + /* t6 = C - B */ + vli_mod_sub(t6, x2, x1, curve_prime, ndigits); + /* t2 = y1 * (C - B) */ + vli_mod_mult_fast(y1, y1, t6, curve_prime, ndigits); + /* t6 = B + C */ + vli_mod_add(t6, x1, x2, curve_prime, ndigits); + /* t3 = (y2 - y1)^2 */ + vli_mod_square_fast(x2, y2, curve_prime, ndigits); + /* t3 = x3 */ + vli_mod_sub(x2, x2, t6, curve_prime, ndigits); + + /* t7 = B - x3 */ + vli_mod_sub(t7, x1, x2, curve_prime, ndigits); + /* t4 = (y2 - y1)*(B - x3) */ + vli_mod_mult_fast(y2, y2, t7, curve_prime, ndigits); + /* t4 = y3 */ + vli_mod_sub(y2, y2, y1, curve_prime, ndigits); + + /* t7 = (y2 + y1)^2 = F */ + vli_mod_square_fast(t7, t5, curve_prime, ndigits); + /* t7 = x3' */ + vli_mod_sub(t7, t7, t6, curve_prime, ndigits); + /* t6 = x3' - B */ + vli_mod_sub(t6, t7, x1, curve_prime, ndigits); + /* t6 = (y2 + y1)*(x3' - B) */ + vli_mod_mult_fast(t6, t6, t5, curve_prime, ndigits); + /* t2 = y3' */ + vli_mod_sub(y1, t6, y1, curve_prime, ndigits); + + vli_set(x1, t7, ndigits); +} + +static void ecc_point_mult(struct ecc_point *result, + const struct ecc_point *point, const u64 *scalar, + u64 *initial_z, u64 *curve_prime, + unsigned int ndigits) +{ + /* R0 and R1 */ + u64 rx[2][ndigits]; + u64 ry[2][ndigits]; + u64 z[ndigits]; + int i, nb; + int num_bits = vli_num_bits(scalar, ndigits); + + vli_set(rx[1], point->x, ndigits); + vli_set(ry[1], point->y, ndigits); + + xycz_initial_double(rx[1], ry[1], rx[0], ry[0], initial_z, curve_prime, + ndigits); + + 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], curve_prime, + ndigits); + xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve_prime, + ndigits); + } + + nb = !vli_test_bit(scalar, 0); + xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve_prime, + ndigits); + + /* Find final 1/Z value. */ + /* X1 - X0 */ + vli_mod_sub(z, rx[1], rx[0], curve_prime, ndigits); + /* Yb * (X1 - X0) */ + vli_mod_mult_fast(z, z, ry[1 - nb], curve_prime, ndigits); + /* xP * Yb * (X1 - X0) */ + vli_mod_mult_fast(z, z, point->x, curve_prime, ndigits); + + /* 1 / (xP * Yb * (X1 - X0)) */ + vli_mod_inv(z, z, curve_prime, point->ndigits); + + /* yP / (xP * Yb * (X1 - X0)) */ + vli_mod_mult_fast(z, z, point->y, curve_prime, ndigits); + /* Xb * yP / (xP * Yb * (X1 - X0)) */ + vli_mod_mult_fast(z, z, rx[1 - nb], curve_prime, ndigits); + /* End 1/Z calculation */ + + xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve_prime, ndigits); + + apply_z(rx[0], ry[0], z, curve_prime, ndigits); + + vli_set(result->x, rx[0], ndigits); + vli_set(result->y, ry[0], ndigits); +} + +static inline void ecc_swap_digits(const u64 *in, u64 *out, + unsigned int ndigits) +{ + int i; + + for (i = 0; i < ndigits; i++) + out[i] = __swab64(in[ndigits - 1 - i]); +} + +int ecc_is_key_valid(unsigned int curve_id, unsigned int ndigits, + const u8 *private_key, unsigned int private_key_len) +{ + int nbytes; + const struct ecc_curve *curve = ecc_get_curve(curve_id); + + if (!private_key) + return -EINVAL; + + nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT; + + if (private_key_len != nbytes) + return -EINVAL; + + if (vli_is_zero((const u64 *)&private_key[0], ndigits)) + return -EINVAL; + + /* Make sure the private key is in the range [1, n-1]. */ + if (vli_cmp(curve->n, (const u64 *)&private_key[0], ndigits) != 1) + return -EINVAL; + + return 0; +} + +int ecdh_make_pub_key(unsigned int curve_id, unsigned int ndigits, + const u8 *private_key, unsigned int private_key_len, + u8 *public_key, unsigned int public_key_len) +{ + int ret = 0; + struct ecc_point *pk; + u64 priv[ndigits]; + unsigned int nbytes; + const struct ecc_curve *curve = ecc_get_curve(curve_id); + + if (!private_key || !curve) { + ret = -EINVAL; + goto out; + } + + ecc_swap_digits((const u64 *)private_key, priv, ndigits); + + pk = ecc_alloc_point(ndigits); + if (!pk) { + ret = -ENOMEM; + goto out; + } + + ecc_point_mult(pk, &curve->g, priv, NULL, curve->p, ndigits); + if (ecc_point_is_zero(pk)) { + ret = -EAGAIN; + goto err_free_point; + } + + nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT; + ecc_swap_digits(pk->x, (u64 *)public_key, ndigits); + ecc_swap_digits(pk->y, (u64 *)&public_key[nbytes], ndigits); + +err_free_point: + ecc_free_point(pk); +out: + return ret; +} + +int crypto_ecdh_shared_secret(unsigned int curve_id, unsigned int ndigits, + const u8 *private_key, unsigned int private_key_len, + const u8 *public_key, unsigned int public_key_len, + u8 *secret, unsigned int secret_len) +{ + int ret = 0; + struct ecc_point *product, *pk; + u64 priv[ndigits]; + u64 rand_z[ndigits]; + unsigned int nbytes; + const struct ecc_curve *curve = ecc_get_curve(curve_id); + + if (!private_key || !public_key || !curve) { + ret = -EINVAL; + goto out; + } + + nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT; + + get_random_bytes(rand_z, nbytes); + + pk = ecc_alloc_point(ndigits); + if (!pk) { + ret = -ENOMEM; + goto out; + } + + product = ecc_alloc_point(ndigits); + if (!product) { + ret = -ENOMEM; + goto err_alloc_product; + } + + ecc_swap_digits((const u64 *)public_key, pk->x, ndigits); + ecc_swap_digits((const u64 *)&public_key[nbytes], pk->y, ndigits); + ecc_swap_digits((const u64 *)private_key, priv, ndigits); + + ecc_point_mult(product, pk, priv, rand_z, curve->p, ndigits); + + ecc_swap_digits(product->x, (u64 *)secret, ndigits); + + if (ecc_point_is_zero(product)) + ret = -EFAULT; + + ecc_free_point(product); +err_alloc_product: + ecc_free_point(pk); +out: + return ret; +} |
