diff options
author | David S. Miller <davem@davemloft.net> | 2017-05-01 14:34:46 -0400 |
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committer | David S. Miller <davem@davemloft.net> | 2017-05-01 14:34:46 -0400 |
commit | f9ed236c2aed30eef4b2c8025973631714655301 (patch) | |
tree | 649a50975caa3c26c42f42eebbd3158c7e3d3f23 /net/bluetooth/ecc.c | |
parent | d5066c467ee3b8eb8716e776584b3953a0bb218a (diff) | |
parent | 71653eb64bcca6110c42aadfd50b8d54d3a88079 (diff) |
Merge branch 'for-upstream' of git://git.kernel.org/pub/scm/linux/kernel/git/bluetooth/bluetooth-next
Johan Hedberg says:
====================
pull request: bluetooth-next 2017-04-30
Here's one last batch of Bluetooth patches in the bluetooth-next tree
targeting the 4.12 kernel.
- Remove custom ECDH implementation and use new KPP API instead
- Add protocol checks to hci_ldisc
- Add module license to HCI UART Nokia H4+ driver
- Minor fix for 32bit user space - 64 bit kernel combination
Please let me know if there are any issues pulling. Thanks.
====================
Signed-off-by: David S. Miller <davem@davemloft.net>
Diffstat (limited to 'net/bluetooth/ecc.c')
-rw-r--r-- | net/bluetooth/ecc.c | 816 |
1 files changed, 0 insertions, 816 deletions
diff --git a/net/bluetooth/ecc.c b/net/bluetooth/ecc.c deleted file mode 100644 index e1709f8467ac..000000000000 --- a/net/bluetooth/ecc.c +++ /dev/null @@ -1,816 +0,0 @@ -/* - * 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); -} |