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(I'm so sorry!) Linux kernel mirror (for testing) git.kernel.org/pub/scm/linux/kernel/git/torvalds/linux.git
kernel os linux
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* 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 <linux/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_POW2(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], 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);
struct ecc_point *ecc_alloc_point(unsigned int ndigits){ struct ecc_point *p; size_t ndigits_sz;
if (!ndigits) return NULL;
p = kmalloc_obj(*p); if (!p) return NULL;
ndigits_sz = ndigits * sizeof(u64); p->x = kmalloc(ndigits_sz, GFP_KERNEL); if (!p->x) goto err_alloc_x;
p->y = kmalloc(ndigits_sz, GFP_KERNEL); if (!p->y) goto err_alloc_y;
p->ndigits = ndigits;
return p;
err_alloc_y: kfree(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; }}
#ifdef __has_builtin#if __has_builtin(__builtin_addcll)#define USE_BUILTIN_ADDC#endif#endif
/* Computes result = left + right + carry_in and updates carry_out */static inline void add_carry(u64 left, u64 right, u64 *result, u64 carry_in, u64 *carry_out){#ifdef USE_BUILTIN_ADDC *result = __builtin_addcll(left, right, carry_in, carry_out);#else u64 sum1, sum2; u64 c1 = __builtin_uaddll_overflow(left, right, &sum1); u64 c2 = __builtin_uaddll_overflow(sum1, carry_in, &sum2); *result = sum2; *carry_out = c1 | c2;#endif}
#ifdef __has_builtin#if __has_builtin(__builtin_subcll)#define USE_BUILTIN_SUBC#endif#endif
/* Computes result = left - right - borrow_in and updates borrow_out */static inline void sub_borrow(u64 left, u64 right, u64 *result, u64 borrow_in, u64 *borrow_out){#ifdef USE_BUILTIN_SUBC *result = __builtin_subcll(left, right, borrow_in, borrow_out);#else u64 diff1, diff2; u64 b1 = __builtin_usubll_overflow(left, right, &diff1); u64 b2 = __builtin_usubll_overflow(diff1, borrow_in, &diff2); *result = diff2; *borrow_out = b1 | b2;#endif}
/* 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++) add_carry(left[i], right[i], &result[i], carry, &carry);
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; int i;
if (ndigits == 0) return right;
carry = __builtin_uaddll_overflow(left[0], right, &result[0]);
for (i = 1; i < ndigits; i++) carry = __builtin_uaddll_overflow(left[i], carry, &result[i]);
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++) sub_borrow(left[i], right[i], &result[i], borrow, &borrow);
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; int i;
if (ndigits == 0) return right;
borrow = __builtin_usubll_overflow(left[0], right, &result[0]);
for (i = 1; i < ndigits; i++) borrow = __builtin_usubll_overflow(left[i], borrow, &result[i]);
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;}
/* Calculate addition with overflow checking. Returns true on wrap-around, * false otherwise. */static bool check_add_128_128_overflow(uint128_t *result, uint128_t a, uint128_t b){ bool carry;
result->m_low = a.m_low + b.m_low; carry = (result->m_low < a.m_low);
result->m_high = a.m_high + b.m_high + carry;
/* Using constant-time bitwise arithmetic to prevent timing * side-channels. */ carry = (result->m_high < a.m_high) | ((result->m_high == a.m_high) & carry);
return carry;}
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]); r2 += check_add_128_128_overflow(&r01, r01, product); }
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); check_add_128_128_overflow(&r01, 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; }
r2 += check_add_128_128_overflow(&r01, r01, product); }
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); if (vli_is_zero(z, ndigits)) { if (vli_cmp(p->y, q->y, ndigits)) { /* P + (-P) is the point at infinity. */ vli_clear(result->x, ndigits); vli_clear(result->y, ndigits); return; } /* The co-Z addition formula does not handle P == Q. */ z[0] = 1; ecc_point_double_jacobian(result->x, result->y, z, curve); goto out; } vli_set(px, p->x, ndigits); vli_set(py, p->y, ndigits); xycz_add(px, py, result->x, result->y, curve);out: 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] = !ecc_point_is_zero(point);
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 && !ecc_point_is_zero(point)) { u64 tx[ECC_MAX_DIGITS]; u64 ty[ECC_MAX_DIGITS]; u64 tz[ECC_MAX_DIGITS];
if (vli_is_zero(z, ndigits)) { /* Adding to infinity starts a new accumulator. */ vli_set(rx, point->x, ndigits); vli_set(ry, point->y, ndigits); z[0] = 1; continue; } 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); if (vli_is_zero(tz, ndigits)) { if (!vli_cmp(ry, ty, ndigits)) ecc_point_double_jacobian(rx, ry, z, curve); else /* Adding opposite points yields infinity. */ vli_clear(z, ndigits); continue; } 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 stdrng because it selects a favored DRBG * with a security strength of 256. */ /* Step 3: obtain N returned_bits from the DRBG. */ err = crypto_stdrng_get_bytes(private_key, nbytes); 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_DESCRIPTION("core elliptic curve module");MODULE_LICENSE("Dual BSD/GPL");