| /* |
| * Copyright (c) 2013, 2014 Kenneth MacKay. All rights reserved. |
| * Copyright (c) 2019 Vitaly Chikunov <vt@altlinux.org> |
| * |
| * 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 <crypto/ecc_curve.h> |
| #include <linux/module.h> |
| #include <linux/random.h> |
| #include <linux/slab.h> |
| #include <linux/swab.h> |
| #include <linux/fips.h> |
| #include <crypto/ecdh.h> |
| #include <crypto/rng.h> |
| #include <crypto/internal/ecc.h> |
| #include <asm/unaligned.h> |
| #include <linux/ratelimit.h> |
| |
| #include "ecc_curve_defs.h" |
| |
| typedef struct { |
| u64 m_low; |
| u64 m_high; |
| } uint128_t; |
| |
| /* Returns curv25519 curve param */ |
| const struct ecc_curve *ecc_get_curve25519(void) |
| { |
| return &ecc_25519; |
| } |
| EXPORT_SYMBOL(ecc_get_curve25519); |
| |
| 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; |
| case ECC_CURVE_NIST_P384: |
| return &nist_p384; |
| case ECC_CURVE_NIST_P521: |
| return &nist_p521; |
| default: |
| return NULL; |
| } |
| } |
| EXPORT_SYMBOL(ecc_get_curve); |
| |
| void ecc_digits_from_bytes(const u8 *in, unsigned int nbytes, |
| u64 *out, unsigned int ndigits) |
| { |
| int diff = ndigits - DIV_ROUND_UP(nbytes, sizeof(u64)); |
| unsigned int o = nbytes & 7; |
| __be64 msd = 0; |
| |
| /* diff > 0: not enough input bytes: set most significant digits to 0 */ |
| if (diff > 0) { |
| ndigits -= diff; |
| memset(&out[ndigits - 1], 0, diff * sizeof(u64)); |
| } |
| |
| if (o) { |
| memcpy((u8 *)&msd + sizeof(msd) - o, in, o); |
| out[--ndigits] = be64_to_cpu(msd); |
| in += o; |
| } |
| ecc_swap_digits(in, out, ndigits); |
| } |
| EXPORT_SYMBOL(ecc_digits_from_bytes); |
| |
| 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) |
| { |
| kfree_sensitive(space); |
| } |
| |
| 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; |
| } |
| EXPORT_SYMBOL(ecc_alloc_point); |
| |
| void ecc_free_point(struct ecc_point *p) |
| { |
| if (!p) |
| return; |
| |
| kfree_sensitive(p->x); |
| kfree_sensitive(p->y); |
| kfree_sensitive(p); |
| } |
| EXPORT_SYMBOL(ecc_free_point); |
| |
| 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. */ |
| 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; |
| } |
| EXPORT_SYMBOL(vli_is_zero); |
| |
| /* Returns nonzero if bit of vli is set. */ |
| static u64 vli_test_bit(const u64 *vli, unsigned int bit) |
| { |
| return (vli[bit / 64] & ((u64)1 << (bit % 64))); |
| } |
| |
| static bool vli_is_negative(const u64 *vli, unsigned int ndigits) |
| { |
| return vli_test_bit(vli, ndigits * 64 - 1); |
| } |
| |
| /* 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. */ |
| 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); |
| } |
| EXPORT_SYMBOL(vli_num_bits); |
| |
| /* Set dest from unaligned bit string src. */ |
| void vli_from_be64(u64 *dest, const void *src, unsigned int ndigits) |
| { |
| int i; |
| const u64 *from = src; |
| |
| for (i = 0; i < ndigits; i++) |
| dest[i] = get_unaligned_be64(&from[ndigits - 1 - i]); |
| } |
| EXPORT_SYMBOL(vli_from_be64); |
| |
| void vli_from_le64(u64 *dest, const void *src, unsigned int ndigits) |
| { |
| int i; |
| const u64 *from = src; |
| |
| for (i = 0; i < ndigits; i++) |
| dest[i] = get_unaligned_le64(&from[i]); |
| } |
| EXPORT_SYMBOL(vli_from_le64); |
| |
| /* 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. */ |
| 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; |
| } |
| EXPORT_SYMBOL(vli_cmp); |
| |
| /* 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 carry. Can modify in place. */ |
| static u64 vli_uadd(u64 *result, const u64 *left, u64 right, |
| unsigned int ndigits) |
| { |
| u64 carry = right; |
| int i; |
| |
| for (i = 0; i < ndigits; i++) { |
| u64 sum; |
| |
| sum = left[i] + carry; |
| if (sum != left[i]) |
| carry = (sum < left[i]); |
| else |
| carry = !!carry; |
| |
| result[i] = sum; |
| } |
| |
| return carry; |
| } |
| |
| /* Computes result = left - right, returning borrow. Can modify in place. */ |
| 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; |
| } |
| EXPORT_SYMBOL(vli_sub); |
| |
| /* Computes result = left - right, returning borrow. Can modify in place. */ |
| static u64 vli_usub(u64 *result, const u64 *left, u64 right, |
| unsigned int ndigits) |
| { |
| u64 borrow = right; |
| int i; |
| |
| for (i = 0; i < ndigits; i++) { |
| u64 diff; |
| |
| diff = left[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) |
| { |
| uint128_t result; |
| #if defined(CONFIG_ARCH_SUPPORTS_INT128) |
| unsigned __int128 m = (unsigned __int128)left * right; |
| |
| result.m_low = m; |
| result.m_high = m >> 64; |
| #else |
| 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; |
| |
| m2 += (m0 >> 32); |
| m2 += m1; |
| |
| /* Overflow */ |
| if (m2 < m1) |
| m3 += 0x100000000ull; |
| |
| result.m_low = (m0 & 0xffffffffull) | (m2 << 32); |
| result.m_high = m3 + (m2 >> 32); |
| #endif |
| 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; |
| } |
| |
| /* Compute product = left * right, for a small right value. */ |
| static void vli_umult(u64 *result, const u64 *left, u32 right, |
| unsigned int ndigits) |
| { |
| uint128_t r01 = { 0 }; |
| unsigned int k; |
| |
| for (k = 0; k < ndigits; k++) { |
| uint128_t product; |
| |
| product = mul_64_64(left[k], right); |
| r01 = add_128_128(r01, product); |
| /* no carry */ |
| result[k] = r01.m_low; |
| r01.m_low = r01.m_high; |
| r01.m_high = 0; |
| } |
| result[k] = r01.m_low; |
| for (++k; k < ndigits * 2; k++) |
| result[k] = 0; |
| } |
| |
| 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 result = product % mod |
| * for special form moduli: p = 2^k-c, for small c (note the minus sign) |
| * |
| * References: |
| * R. Crandall, C. Pomerance. Prime Numbers: A Computational Perspective. |
| * 9 Fast Algorithms for Large-Integer Arithmetic. 9.2.3 Moduli of special form |
| * Algorithm 9.2.13 (Fast mod operation for special-form moduli). |
| */ |
| static void vli_mmod_special(u64 *result, const u64 *product, |
| const u64 *mod, unsigned int ndigits) |
| { |
| u64 c = -mod[0]; |
| u64 t[ECC_MAX_DIGITS * 2]; |
| u64 r[ECC_MAX_DIGITS * 2]; |
| |
| vli_set(r, product, ndigits * 2); |
| while (!vli_is_zero(r + ndigits, ndigits)) { |
| vli_umult(t, r + ndigits, c, ndigits); |
| vli_clear(r + ndigits, ndigits); |
| vli_add(r, r, t, ndigits * 2); |
| } |
| vli_set(t, mod, ndigits); |
| vli_clear(t + ndigits, ndigits); |
| while (vli_cmp(r, t, ndigits * 2) >= 0) |
| vli_sub(r, r, t, ndigits * 2); |
| vli_set(result, r, ndigits); |
| } |
| |
| /* |
| * Computes result = product % mod |
| * for special form moduli: p = 2^{k-1}+c, for small c (note the plus sign) |
| * where k-1 does not fit into qword boundary by -1 bit (such as 255). |
| |
| * References (loosely based on): |
| * A. Menezes, P. van Oorschot, S. Vanstone. Handbook of Applied Cryptography. |
| * 14.3.4 Reduction methods for moduli of special form. Algorithm 14.47. |
| * URL: http://cacr.uwaterloo.ca/hac/about/chap14.pdf |
| * |
| * H. Cohen, G. Frey, R. Avanzi, C. Doche, T. Lange, K. Nguyen, F. Vercauteren. |
| * Handbook of Elliptic and Hyperelliptic Curve Cryptography. |
| * Algorithm 10.25 Fast reduction for special form moduli |
| */ |
| static void vli_mmod_special2(u64 *result, const u64 *product, |
| const u64 *mod, unsigned int ndigits) |
| { |
| u64 c2 = mod[0] * 2; |
| u64 q[ECC_MAX_DIGITS]; |
| u64 r[ECC_MAX_DIGITS * 2]; |
| u64 m[ECC_MAX_DIGITS * 2]; /* expanded mod */ |
| int carry; /* last bit that doesn't fit into q */ |
| int i; |
| |
| vli_set(m, mod, ndigits); |
| vli_clear(m + ndigits, ndigits); |
| |
| vli_set(r, product, ndigits); |
| /* q and carry are top bits */ |
| vli_set(q, product + ndigits, ndigits); |
| vli_clear(r + ndigits, ndigits); |
| carry = vli_is_negative(r, ndigits); |
| if (carry) |
| r[ndigits - 1] &= (1ull << 63) - 1; |
| for (i = 1; carry || !vli_is_zero(q, ndigits); i++) { |
| u64 qc[ECC_MAX_DIGITS * 2]; |
| |
| vli_umult(qc, q, c2, ndigits); |
| if (carry) |
| vli_uadd(qc, qc, mod[0], ndigits * 2); |
| vli_set(q, qc + ndigits, ndigits); |
| vli_clear(qc + ndigits, ndigits); |
| carry = vli_is_negative(qc, ndigits); |
| if (carry) |
| qc[ndigits - 1] &= (1ull << 63) - 1; |
| if (i & 1) |
| vli_sub(r, r, qc, ndigits * 2); |
| else |
| vli_add(r, r, qc, ndigits * 2); |
| } |
| while (vli_is_negative(r, ndigits * 2)) |
| vli_add(r, r, m, ndigits * 2); |
| while (vli_cmp(r, m, ndigits * 2) >= 0) |
| vli_sub(r, r, m, ndigits * 2); |
| |
| vli_set(result, r, ndigits); |
| } |
| |
| /* |
| * Computes result = product % mod, where product is 2N words long. |
| * Reference: Ken MacKay's micro-ecc. |
| * Currently only designed to work for curve_p or curve_n. |
| */ |
| static void vli_mmod_slow(u64 *result, u64 *product, const u64 *mod, |
| unsigned int ndigits) |
| { |
| u64 mod_m[2 * ECC_MAX_DIGITS]; |
| u64 tmp[2 * ECC_MAX_DIGITS]; |
| u64 *v[2] = { tmp, product }; |
| u64 carry = 0; |
| unsigned int i; |
| /* Shift mod so its highest set bit is at the maximum position. */ |
| int shift = (ndigits * 2 * 64) - vli_num_bits(mod, ndigits); |
| int word_shift = shift / 64; |
| int bit_shift = shift % 64; |
| |
| vli_clear(mod_m, word_shift); |
| if (bit_shift > 0) { |
| for (i = 0; i < ndigits; ++i) { |
| mod_m[word_shift + i] = (mod[i] << bit_shift) | carry; |
| carry = mod[i] >> (64 - bit_shift); |
| } |
| } else |
| vli_set(mod_m + word_shift, mod, ndigits); |
| |
| for (i = 1; shift >= 0; --shift) { |
| u64 borrow = 0; |
| unsigned int j; |
| |
| for (j = 0; j < ndigits * 2; ++j) { |
| u64 diff = v[i][j] - mod_m[j] - borrow; |
| |
| if (diff != v[i][j]) |
| borrow = (diff > v[i][j]); |
| v[1 - i][j] = diff; |
| } |
| i = !(i ^ borrow); /* Swap the index if there was no borrow */ |
| vli_rshift1(mod_m, ndigits); |
| mod_m[ndigits - 1] |= mod_m[ndigits] << (64 - 1); |
| vli_rshift1(mod_m + ndigits, ndigits); |
| } |
| vli_set(result, v[i], ndigits); |
| } |
| |
| /* Computes result = product % mod using Barrett's reduction with precomputed |
| * value mu appended to the mod after ndigits, mu = (2^{2w} / mod) and have |
| * length ndigits + 1, where mu * (2^w - 1) should not overflow ndigits |
| * boundary. |
| * |
| * Reference: |
| * R. Brent, P. Zimmermann. Modern Computer Arithmetic. 2010. |
| * 2.4.1 Barrett's algorithm. Algorithm 2.5. |
| */ |
| static void vli_mmod_barrett(u64 *result, u64 *product, const u64 *mod, |
| unsigned int ndigits) |
| { |
| u64 q[ECC_MAX_DIGITS * 2]; |
| u64 r[ECC_MAX_DIGITS * 2]; |
| const u64 *mu = mod + ndigits; |
| |
| vli_mult(q, product + ndigits, mu, ndigits); |
| if (mu[ndigits]) |
| vli_add(q + ndigits, q + ndigits, product + ndigits, ndigits); |
| vli_mult(r, mod, q + ndigits, ndigits); |
| vli_sub(r, product, r, ndigits * 2); |
| while (!vli_is_zero(r + ndigits, ndigits) || |
| vli_cmp(r, mod, ndigits) != -1) { |
| u64 carry; |
| |
| carry = vli_sub(r, r, mod, ndigits); |
| vli_usub(r + ndigits, r + ndigits, carry, ndigits); |
| } |
| vli_set(result, r, 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 = ECC_CURVE_NIST_P192_DIGITS; |
| 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 = ECC_CURVE_NIST_P256_DIGITS; |
| |
| /* 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); |
| } |
| } |
| |
| #define SL32OR32(x32, y32) (((u64)x32 << 32) | y32) |
| #define AND64H(x64) (x64 & 0xffFFffFF00000000ull) |
| #define AND64L(x64) (x64 & 0x00000000ffFFffFFull) |
| |
| /* Computes result = product % curve_prime |
| * from "Mathematical routines for the NIST prime elliptic curves" |
| */ |
| static void vli_mmod_fast_384(u64 *result, const u64 *product, |
| const u64 *curve_prime, u64 *tmp) |
| { |
| int carry; |
| const unsigned int ndigits = ECC_CURVE_NIST_P384_DIGITS; |
| |
| /* t */ |
| vli_set(result, product, ndigits); |
| |
| /* s1 */ |
| tmp[0] = 0; // 0 || 0 |
| tmp[1] = 0; // 0 || 0 |
| tmp[2] = SL32OR32(product[11], (product[10]>>32)); //a22||a21 |
| tmp[3] = product[11]>>32; // 0 ||a23 |
| tmp[4] = 0; // 0 || 0 |
| tmp[5] = 0; // 0 || 0 |
| carry = vli_lshift(tmp, tmp, 1, ndigits); |
| carry += vli_add(result, result, tmp, ndigits); |
| |
| /* s2 */ |
| tmp[0] = product[6]; //a13||a12 |
| tmp[1] = product[7]; //a15||a14 |
| tmp[2] = product[8]; //a17||a16 |
| tmp[3] = product[9]; //a19||a18 |
| tmp[4] = product[10]; //a21||a20 |
| tmp[5] = product[11]; //a23||a22 |
| carry += vli_add(result, result, tmp, ndigits); |
| |
| /* s3 */ |
| tmp[0] = SL32OR32(product[11], (product[10]>>32)); //a22||a21 |
| tmp[1] = SL32OR32(product[6], (product[11]>>32)); //a12||a23 |
| tmp[2] = SL32OR32(product[7], (product[6])>>32); //a14||a13 |
| tmp[3] = SL32OR32(product[8], (product[7]>>32)); //a16||a15 |
| tmp[4] = SL32OR32(product[9], (product[8]>>32)); //a18||a17 |
| tmp[5] = SL32OR32(product[10], (product[9]>>32)); //a20||a19 |
| carry += vli_add(result, result, tmp, ndigits); |
| |
| /* s4 */ |
| tmp[0] = AND64H(product[11]); //a23|| 0 |
| tmp[1] = (product[10]<<32); //a20|| 0 |
| tmp[2] = product[6]; //a13||a12 |
| tmp[3] = product[7]; //a15||a14 |
| tmp[4] = product[8]; //a17||a16 |
| tmp[5] = product[9]; //a19||a18 |
| carry += vli_add(result, result, tmp, ndigits); |
| |
| /* s5 */ |
| tmp[0] = 0; // 0|| 0 |
| tmp[1] = 0; // 0|| 0 |
| tmp[2] = product[10]; //a21||a20 |
| tmp[3] = product[11]; //a23||a22 |
| tmp[4] = 0; // 0|| 0 |
| tmp[5] = 0; // 0|| 0 |
| carry += vli_add(result, result, tmp, ndigits); |
| |
| /* s6 */ |
| tmp[0] = AND64L(product[10]); // 0 ||a20 |
| tmp[1] = AND64H(product[10]); //a21|| 0 |
| tmp[2] = product[11]; //a23||a22 |
| tmp[3] = 0; // 0 || 0 |
| tmp[4] = 0; // 0 || 0 |
| tmp[5] = 0; // 0 || 0 |
| carry += vli_add(result, result, tmp, ndigits); |
| |
| /* d1 */ |
| tmp[0] = SL32OR32(product[6], (product[11]>>32)); //a12||a23 |
| tmp[1] = SL32OR32(product[7], (product[6]>>32)); //a14||a13 |
| tmp[2] = SL32OR32(product[8], (product[7]>>32)); //a16||a15 |
| tmp[3] = SL32OR32(product[9], (product[8]>>32)); //a18||a17 |
| tmp[4] = SL32OR32(product[10], (product[9]>>32)); //a20||a19 |
| tmp[5] = SL32OR32(product[11], (product[10]>>32)); //a22||a21 |
| carry -= vli_sub(result, result, tmp, ndigits); |
| |
| /* d2 */ |
| tmp[0] = (product[10]<<32); //a20|| 0 |
| tmp[1] = SL32OR32(product[11], (product[10]>>32)); //a22||a21 |
| tmp[2] = (product[11]>>32); // 0 ||a23 |
| tmp[3] = 0; // 0 || 0 |
| tmp[4] = 0; // 0 || 0 |
| tmp[5] = 0; // 0 || 0 |
| carry -= vli_sub(result, result, tmp, ndigits); |
| |
| /* d3 */ |
| tmp[0] = 0; // 0 || 0 |
| tmp[1] = AND64H(product[11]); //a23|| 0 |
| tmp[2] = product[11]>>32; // 0 ||a23 |
| tmp[3] = 0; // 0 || 0 |
| tmp[4] = 0; // 0 || 0 |
| tmp[5] = 0; // 0 || 0 |
| 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); |
| } |
| |
| } |
| |
| #undef SL32OR32 |
| #undef AND64H |
| #undef AND64L |
| |
| /* |
| * Computes result = product % curve_prime |
| * from "Recommendations for Discrete Logarithm-Based Cryptography: |
| * Elliptic Curve Domain Parameters" section G.1.4 |
| */ |
| static void vli_mmod_fast_521(u64 *result, const u64 *product, |
| const u64 *curve_prime, u64 *tmp) |
| { |
| const unsigned int ndigits = ECC_CURVE_NIST_P521_DIGITS; |
| size_t i; |
| |
| /* Initialize result with lowest 521 bits from product */ |
| vli_set(result, product, ndigits); |
| result[8] &= 0x1ff; |
| |
| for (i = 0; i < ndigits; i++) |
| tmp[i] = (product[8 + i] >> 9) | (product[9 + i] << 55); |
| tmp[8] &= 0x1ff; |
| |
| vli_mod_add(result, result, tmp, curve_prime, ndigits); |
| } |
| |
| /* Computes result = product % curve_prime for different curve_primes. |
| * |
| * Note that curve_primes are distinguished just by heuristic check and |
| * not by complete conformance check. |
| */ |
| static bool vli_mmod_fast(u64 *result, u64 *product, |
| const struct ecc_curve *curve) |
| { |
| u64 tmp[2 * ECC_MAX_DIGITS]; |
| const u64 *curve_prime = curve->p; |
| const unsigned int ndigits = curve->g.ndigits; |
| |
| /* All NIST curves have name prefix 'nist_' */ |
| if (strncmp(curve->name, "nist_", 5) != 0) { |
| /* Try to handle Pseudo-Marsenne primes. */ |
| if (curve_prime[ndigits - 1] == -1ull) { |
| vli_mmod_special(result, product, curve_prime, |
| ndigits); |
| return true; |
| } else if (curve_prime[ndigits - 1] == 1ull << 63 && |
| curve_prime[ndigits - 2] == 0) { |
| vli_mmod_special2(result, product, curve_prime, |
| ndigits); |
| return true; |
| } |
| vli_mmod_barrett(result, product, curve_prime, ndigits); |
| return true; |
| } |
| |
| switch (ndigits) { |
| case ECC_CURVE_NIST_P192_DIGITS: |
| vli_mmod_fast_192(result, product, curve_prime, tmp); |
| break; |
| case ECC_CURVE_NIST_P256_DIGITS: |
| vli_mmod_fast_256(result, product, curve_prime, tmp); |
| break; |
| case ECC_CURVE_NIST_P384_DIGITS: |
| vli_mmod_fast_384(result, product, curve_prime, tmp); |
| break; |
| case ECC_CURVE_NIST_P521_DIGITS: |
| vli_mmod_fast_521(result, product, curve_prime, tmp); |
| break; |
| default: |
| pr_err_ratelimited("ecc: unsupported digits size!\n"); |
| return false; |
| } |
| |
| return true; |
| } |
| |
| /* Computes result = (left * right) % mod. |
| * Assumes that mod is big enough curve order. |
| */ |
| void vli_mod_mult_slow(u64 *result, const u64 *left, const u64 *right, |
| const u64 *mod, unsigned int ndigits) |
| { |
| u64 product[ECC_MAX_DIGITS * 2]; |
| |
| vli_mult(product, left, right, ndigits); |
| vli_mmod_slow(result, product, mod, ndigits); |
| } |
| EXPORT_SYMBOL(vli_mod_mult_slow); |
| |
| /* Computes result = (left * right) % curve_prime. */ |
| static void vli_mod_mult_fast(u64 *result, const u64 *left, const u64 *right, |
| const struct ecc_curve *curve) |
| { |
| u64 product[2 * ECC_MAX_DIGITS]; |
| |
| vli_mult(product, left, right, curve->g.ndigits); |
| vli_mmod_fast(result, product, curve); |
| } |
| |
| /* Computes result = left^2 % curve_prime. */ |
| static void vli_mod_square_fast(u64 *result, const u64 *left, |
| const struct ecc_curve *curve) |
| { |
| u64 product[2 * ECC_MAX_DIGITS]; |
| |
| vli_square(product, left, curve->g.ndigits); |
| vli_mmod_fast(result, product, curve); |
| } |
| |
| #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 |
| */ |
| void vli_mod_inv(u64 *result, const u64 *input, const u64 *mod, |
| unsigned int ndigits) |
| { |
| u64 a[ECC_MAX_DIGITS], b[ECC_MAX_DIGITS]; |
| u64 u[ECC_MAX_DIGITS], v[ECC_MAX_DIGITS]; |
| 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); |
| } |
| EXPORT_SYMBOL(vli_mod_inv); |
| |
| /* ------ Point operations ------ */ |
| |
| /* Returns true if p_point is the point at infinity, false otherwise. */ |
| 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)); |
| } |
| EXPORT_SYMBOL(ecc_point_is_zero); |
| |
| /* Point multiplication algorithm using Montgomery's ladder with co-Z |
| * coordinates. From https://eprint.iacr.org/2011/338.pdf |
| */ |
| |
| /* Double in place */ |
| static void ecc_point_double_jacobian(u64 *x1, u64 *y1, u64 *z1, |
| const struct ecc_curve *curve) |
| { |
| /* t1 = x, t2 = y, t3 = z */ |
| u64 t4[ECC_MAX_DIGITS]; |
| u64 t5[ECC_MAX_DIGITS]; |
| const u64 *curve_prime = curve->p; |
| const unsigned int ndigits = curve->g.ndigits; |
| |
| if (vli_is_zero(z1, ndigits)) |
| return; |
| |
| /* t4 = y1^2 */ |
| vli_mod_square_fast(t4, y1, curve); |
| /* t5 = x1*y1^2 = A */ |
| vli_mod_mult_fast(t5, x1, t4, curve); |
| /* t4 = y1^4 */ |
| vli_mod_square_fast(t4, t4, curve); |
| /* t2 = y1*z1 = z3 */ |
| vli_mod_mult_fast(y1, y1, z1, curve); |
| /* t3 = z1^2 */ |
| vli_mod_square_fast(z1, z1, curve); |
| |
| /* 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); |
| |
| /* 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); |
| /* 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); |
| /* 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, const struct ecc_curve *curve) |
| { |
| u64 t1[ECC_MAX_DIGITS]; |
| |
| vli_mod_square_fast(t1, z, curve); /* z^2 */ |
| vli_mod_mult_fast(x1, x1, t1, curve); /* x1 * z^2 */ |
| vli_mod_mult_fast(t1, t1, z, curve); /* z^3 */ |
| vli_mod_mult_fast(y1, y1, t1, curve); /* 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, const struct ecc_curve *curve) |
| { |
| u64 z[ECC_MAX_DIGITS]; |
| const unsigned int ndigits = curve->g.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); |
| |
| ecc_point_double_jacobian(x1, y1, z, curve); |
| |
| apply_z(x2, y2, z, curve); |
| } |
| |
| /* 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, |
| const struct ecc_curve *curve) |
| { |
| /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */ |
| u64 t5[ECC_MAX_DIGITS]; |
| const u64 *curve_prime = curve->p; |
| const unsigned int ndigits = curve->g.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); |
| /* t1 = x1*A = B */ |
| vli_mod_mult_fast(x1, x1, t5, curve); |
| /* t3 = x2*A = C */ |
| vli_mod_mult_fast(x2, x2, t5, curve); |
| /* t4 = y2 - y1 */ |
| vli_mod_sub(y2, y2, y1, curve_prime, ndigits); |
| /* t5 = (y2 - y1)^2 = D */ |
| vli_mod_square_fast(t5, y2, curve); |
| |
| /* 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); |
| /* 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); |
| /* 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, |
| const struct ecc_curve *curve) |
| { |
| /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */ |
| u64 t5[ECC_MAX_DIGITS]; |
| u64 t6[ECC_MAX_DIGITS]; |
| u64 t7[ECC_MAX_DIGITS]; |
| const u64 *curve_prime = curve->p; |
| const unsigned int ndigits = curve->g.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); |
| /* t1 = x1*A = B */ |
| vli_mod_mult_fast(x1, x1, t5, curve); |
| /* t3 = x2*A = C */ |
| vli_mod_mult_fast(x2, x2, t5, curve); |
| /* 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); |
| /* t6 = B + C */ |
| vli_mod_add(t6, x1, x2, curve_prime, ndigits); |
| /* t3 = (y2 - y1)^2 */ |
| vli_mod_square_fast(x2, y2, curve); |
| /* 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); |
| /* t4 = y3 */ |
| vli_mod_sub(y2, y2, y1, curve_prime, ndigits); |
| |
| /* t7 = (y2 + y1)^2 = F */ |
| vli_mod_square_fast(t7, t5, curve); |
| /* 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); |
| /* 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, const struct ecc_curve *curve, |
| unsigned int ndigits) |
| { |
| /* R0 and R1 */ |
| u64 rx[2][ECC_MAX_DIGITS]; |
| u64 ry[2][ECC_MAX_DIGITS]; |
| u64 z[ECC_MAX_DIGITS]; |
| u64 sk[2][ECC_MAX_DIGITS]; |
| u64 *curve_prime = curve->p; |
| int i, nb; |
| int num_bits; |
| int carry; |
| |
| carry = vli_add(sk[0], scalar, curve->n, ndigits); |
| vli_add(sk[1], sk[0], curve->n, ndigits); |
| scalar = sk[!carry]; |
| if (curve->nbits == 521) /* NIST P521 */ |
| num_bits = curve->nbits + 2; |
| else |
| num_bits = sizeof(u64) * ndigits * 8 + 1; |
| |
| 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); |
| |
| 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); |
| xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve); |
| } |
| |
| nb = !vli_test_bit(scalar, 0); |
| xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve); |
| |
| /* 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); |
| /* xP * Yb * (X1 - X0) */ |
| vli_mod_mult_fast(z, z, point->x, curve); |
| |
| /* 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); |
| /* Xb * yP / (xP * Yb * (X1 - X0)) */ |
| vli_mod_mult_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); |
| |
| vli_set(result->x, rx[0], ndigits); |
| vli_set(result->y, ry[0], ndigits); |
| } |
| |
| /* Computes R = P + Q mod p */ |
| static void ecc_point_add(const struct ecc_point *result, |
| const struct ecc_point *p, const struct ecc_point *q, |
| const struct ecc_curve *curve) |
| { |
| u64 z[ECC_MAX_DIGITS]; |
| u64 px[ECC_MAX_DIGITS]; |
| u64 py[ECC_MAX_DIGITS]; |
| unsigned int ndigits = curve->g.ndigits; |
| |
| vli_set(result->x, q->x, ndigits); |
| vli_set(result->y, q->y, ndigits); |
| vli_mod_sub(z, result->x, p->x, curve->p, ndigits); |
| vli_set(px, p->x, ndigits); |
| vli_set(py, p->y, ndigits); |
| xycz_add(px, py, result->x, result->y, curve); |
| vli_mod_inv(z, z, curve->p, ndigits); |
| apply_z(result->x, result->y, z, curve); |
| } |
| |
| /* Computes R = u1P + u2Q mod p using Shamir's trick. |
| * Based on: Kenneth MacKay's micro-ecc (2014). |
| */ |
| void ecc_point_mult_shamir(const struct ecc_point *result, |
| const u64 *u1, const struct ecc_point *p, |
| const u64 *u2, const struct ecc_point *q, |
| const struct ecc_curve *curve) |
| { |
| u64 z[ECC_MAX_DIGITS]; |
| u64 sump[2][ECC_MAX_DIGITS]; |
| u64 *rx = result->x; |
| u64 *ry = result->y; |
| unsigned int ndigits = curve->g.ndigits; |
| unsigned int num_bits; |
| struct ecc_point sum = ECC_POINT_INIT(sump[0], sump[1], ndigits); |
| const struct ecc_point *points[4]; |
| const struct ecc_point *point; |
| unsigned int idx; |
| int i; |
| |
| ecc_point_add(&sum, p, q, curve); |
| points[0] = NULL; |
| points[1] = p; |
| points[2] = q; |
| points[3] = ∑ |
| |
| num_bits = max(vli_num_bits(u1, ndigits), vli_num_bits(u2, ndigits)); |
| i = num_bits - 1; |
| idx = !!vli_test_bit(u1, i); |
| idx |= (!!vli_test_bit(u2, i)) << 1; |
| point = points[idx]; |
| |
| vli_set(rx, point->x, ndigits); |
| vli_set(ry, point->y, ndigits); |
| vli_clear(z + 1, ndigits - 1); |
| z[0] = 1; |
| |
| for (--i; i >= 0; i--) { |
| ecc_point_double_jacobian(rx, ry, z, curve); |
| idx = !!vli_test_bit(u1, i); |
| idx |= (!!vli_test_bit(u2, i)) << 1; |
| point = points[idx]; |
| if (point) { |
| u64 tx[ECC_MAX_DIGITS]; |
| u64 ty[ECC_MAX_DIGITS]; |
| u64 tz[ECC_MAX_DIGITS]; |
| |
| vli_set(tx, point->x, ndigits); |
| vli_set(ty, point->y, ndigits); |
| apply_z(tx, ty, z, curve); |
| vli_mod_sub(tz, rx, tx, curve->p, ndigits); |
| xycz_add(tx, ty, rx, ry, curve); |
| vli_mod_mult_fast(z, z, tz, curve); |
| } |
| } |
| vli_mod_inv(z, z, curve->p, ndigits); |
| apply_z(rx, ry, z, curve); |
| } |
| EXPORT_SYMBOL(ecc_point_mult_shamir); |
| |
| /* |
| * This function performs checks equivalent to Appendix A.4.2 of FIPS 186-5. |
| * Whereas A.4.2 results in an integer in the interval [1, n-1], this function |
| * ensures that the integer is in the range of [2, n-3]. We are slightly |
| * stricter because of the currently used scalar multiplication algorithm. |
| */ |
| static int __ecc_is_key_valid(const struct ecc_curve *curve, |
| const u64 *private_key, unsigned int ndigits) |
| { |
| u64 one[ECC_MAX_DIGITS] = { 1, }; |
| u64 res[ECC_MAX_DIGITS]; |
| |
| if (!private_key) |
| return -EINVAL; |
| |
| if (curve->g.ndigits != ndigits) |
| return -EINVAL; |
| |
| /* Make sure the private key is in the range [2, n-3]. */ |
| if (vli_cmp(one, private_key, ndigits) != -1) |
| return -EINVAL; |
| vli_sub(res, curve->n, one, ndigits); |
| vli_sub(res, res, one, ndigits); |
| if (vli_cmp(res, private_key, ndigits) != 1) |
| return -EINVAL; |
| |
| return 0; |
| } |
| |
| int ecc_is_key_valid(unsigned int curve_id, unsigned int ndigits, |
| const u64 *private_key, unsigned int private_key_len) |
| { |
| int nbytes; |
| const struct ecc_curve *curve = ecc_get_curve(curve_id); |
| |
| nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT; |
| |
| if (private_key_len != nbytes) |
| return -EINVAL; |
| |
| return __ecc_is_key_valid(curve, private_key, ndigits); |
| } |
| EXPORT_SYMBOL(ecc_is_key_valid); |
| |
| /* |
| * ECC private keys are generated using the method of rejection sampling, |
| * equivalent to that described in FIPS 186-5, Appendix A.2.2. |
| * |
| * This method generates a private key uniformly distributed in the range |
| * [2, n-3]. |
| */ |
| int ecc_gen_privkey(unsigned int curve_id, unsigned int ndigits, |
| u64 *private_key) |
| { |
| const struct ecc_curve *curve = ecc_get_curve(curve_id); |
| unsigned int nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT; |
| unsigned int nbits = vli_num_bits(curve->n, ndigits); |
| int err; |
| |
| /* |
| * Step 1 & 2: check that N is included in Table 1 of FIPS 186-5, |
| * section 6.1.1. |
| */ |
| if (nbits < 224) |
| return -EINVAL; |
| |
| /* |
| * FIPS 186-5 recommends that the private key should be obtained from a |
| * RBG with a security strength equal to or greater than the security |
| * strength associated with N. |
| * |
| * The maximum security strength identified by NIST SP800-57pt1r4 for |
| * ECC is 256 (N >= 512). |
| * |
| * This condition is met by the default RNG because it selects a favored |
| * DRBG with a security strength of 256. |
| */ |
| if (crypto_get_default_rng()) |
| return -EFAULT; |
| |
| /* Step 3: obtain N returned_bits from the DRBG. */ |
| err = crypto_rng_get_bytes(crypto_default_rng, |
| (u8 *)private_key, nbytes); |
| crypto_put_default_rng(); |
| if (err) |
| return err; |
| |
| /* Step 4: make sure the private key is in the valid range. */ |
| if (__ecc_is_key_valid(curve, private_key, ndigits)) |
| return -EINVAL; |
| |
| return 0; |
| } |
| EXPORT_SYMBOL(ecc_gen_privkey); |
| |
| int ecc_make_pub_key(unsigned int curve_id, unsigned int ndigits, |
| const u64 *private_key, u64 *public_key) |
| { |
| int ret = 0; |
| struct ecc_point *pk; |
| const struct ecc_curve *curve = ecc_get_curve(curve_id); |
| |
| if (!private_key) { |
| ret = -EINVAL; |
| goto out; |
| } |
| |
| pk = ecc_alloc_point(ndigits); |
| if (!pk) { |
| ret = -ENOMEM; |
| goto out; |
| } |
| |
| ecc_point_mult(pk, &curve->g, private_key, NULL, curve, ndigits); |
| |
| /* SP800-56A rev 3 5.6.2.1.3 key check */ |
| if (ecc_is_pubkey_valid_full(curve, pk)) { |
| ret = -EAGAIN; |
| goto err_free_point; |
| } |
| |
| ecc_swap_digits(pk->x, public_key, ndigits); |
| ecc_swap_digits(pk->y, &public_key[ndigits], ndigits); |
| |
| err_free_point: |
| ecc_free_point(pk); |
| out: |
| return ret; |
| } |
| EXPORT_SYMBOL(ecc_make_pub_key); |
| |
| /* SP800-56A section 5.6.2.3.4 partial verification: ephemeral keys only */ |
| int ecc_is_pubkey_valid_partial(const struct ecc_curve *curve, |
| struct ecc_point *pk) |
| { |
| u64 yy[ECC_MAX_DIGITS], xxx[ECC_MAX_DIGITS], w[ECC_MAX_DIGITS]; |
| |
| if (WARN_ON(pk->ndigits != curve->g.ndigits)) |
| return -EINVAL; |
| |
| /* Check 1: Verify key is not the zero point. */ |
| if (ecc_point_is_zero(pk)) |
| return -EINVAL; |
| |
| /* Check 2: Verify key is in the range [1, p-1]. */ |
| if (vli_cmp(curve->p, pk->x, pk->ndigits) != 1) |
| return -EINVAL; |
| if (vli_cmp(curve->p, pk->y, pk->ndigits) != 1) |
| return -EINVAL; |
| |
| /* Check 3: Verify that y^2 == (x^3 + a·x + b) mod p */ |
| vli_mod_square_fast(yy, pk->y, curve); /* y^2 */ |
| vli_mod_square_fast(xxx, pk->x, curve); /* x^2 */ |
| vli_mod_mult_fast(xxx, xxx, pk->x, curve); /* x^3 */ |
| vli_mod_mult_fast(w, curve->a, pk->x, curve); /* a·x */ |
| vli_mod_add(w, w, curve->b, curve->p, pk->ndigits); /* a·x + b */ |
| vli_mod_add(w, w, xxx, curve->p, pk->ndigits); /* x^3 + a·x + b */ |
| if (vli_cmp(yy, w, pk->ndigits) != 0) /* Equation */ |
| return -EINVAL; |
| |
| return 0; |
| } |
| EXPORT_SYMBOL(ecc_is_pubkey_valid_partial); |
| |
| /* SP800-56A section 5.6.2.3.3 full verification */ |
| int ecc_is_pubkey_valid_full(const struct ecc_curve *curve, |
| struct ecc_point *pk) |
| { |
| struct ecc_point *nQ; |
| |
| /* Checks 1 through 3 */ |
| int ret = ecc_is_pubkey_valid_partial(curve, pk); |
| |
| if (ret) |
| return ret; |
| |
| /* Check 4: Verify that nQ is the zero point. */ |
| nQ = ecc_alloc_point(pk->ndigits); |
| if (!nQ) |
| return -ENOMEM; |
| |
| ecc_point_mult(nQ, pk, curve->n, NULL, curve, pk->ndigits); |
| if (!ecc_point_is_zero(nQ)) |
| ret = -EINVAL; |
| |
| ecc_free_point(nQ); |
| |
| return ret; |
| } |
| EXPORT_SYMBOL(ecc_is_pubkey_valid_full); |
| |
| int crypto_ecdh_shared_secret(unsigned int curve_id, unsigned int ndigits, |
| const u64 *private_key, const u64 *public_key, |
| u64 *secret) |
| { |
| int ret = 0; |
| struct ecc_point *product, *pk; |
| u64 rand_z[ECC_MAX_DIGITS]; |
| unsigned int nbytes; |
| const struct ecc_curve *curve = ecc_get_curve(curve_id); |
| |
| if (!private_key || !public_key || ndigits > ARRAY_SIZE(rand_z)) { |
| 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; |
| } |
| |
| ecc_swap_digits(public_key, pk->x, ndigits); |
| ecc_swap_digits(&public_key[ndigits], pk->y, ndigits); |
| ret = ecc_is_pubkey_valid_partial(curve, pk); |
| if (ret) |
| goto err_alloc_product; |
| |
| product = ecc_alloc_point(ndigits); |
| if (!product) { |
| ret = -ENOMEM; |
| goto err_alloc_product; |
| } |
| |
| ecc_point_mult(product, pk, private_key, rand_z, curve, ndigits); |
| |
| if (ecc_point_is_zero(product)) { |
| ret = -EFAULT; |
| goto err_validity; |
| } |
| |
| ecc_swap_digits(product->x, secret, ndigits); |
| |
| err_validity: |
| memzero_explicit(rand_z, sizeof(rand_z)); |
| ecc_free_point(product); |
| err_alloc_product: |
| ecc_free_point(pk); |
| out: |
| return ret; |
| } |
| EXPORT_SYMBOL(crypto_ecdh_shared_secret); |
| |
| MODULE_LICENSE("Dual BSD/GPL"); |