diff options
Diffstat (limited to 'crypto/ecc.c')
| -rw-r--r-- | crypto/ecc.c | 417 |
1 files changed, 402 insertions, 15 deletions
diff --git a/crypto/ecc.c b/crypto/ecc.c index ed1237115066..dfe114bc0c4a 100644 --- a/crypto/ecc.c +++ b/crypto/ecc.c @@ -1,6 +1,6 @@ /* - * Copyright (c) 2013, Kenneth MacKay - * All rights reserved. + * 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 @@ -24,12 +24,15 @@ * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ +#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 <asm/unaligned.h> +#include <linux/ratelimit.h> #include "ecc.h" #include "ecc_curve_defs.h" @@ -112,7 +115,7 @@ static void vli_clear(u64 *vli, unsigned int ndigits) } /* Returns true if vli == 0, false otherwise. */ -static bool vli_is_zero(const u64 *vli, unsigned int ndigits) +bool vli_is_zero(const u64 *vli, unsigned int ndigits) { int i; @@ -123,6 +126,7 @@ static bool vli_is_zero(const u64 *vli, unsigned int ndigits) return true; } +EXPORT_SYMBOL(vli_is_zero); /* Returns nonzero if bit bit of vli is set. */ static u64 vli_test_bit(const u64 *vli, unsigned int bit) @@ -130,6 +134,11 @@ 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) { @@ -161,6 +170,27 @@ static unsigned int vli_num_bits(const u64 *vli, unsigned int ndigits) return ((num_digits - 1) * 64 + i); } +/* 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) { @@ -171,7 +201,7 @@ static void vli_set(u64 *dest, const u64 *src, unsigned int ndigits) } /* Returns sign of left - right. */ -static int vli_cmp(const u64 *left, const u64 *right, unsigned int ndigits) +int vli_cmp(const u64 *left, const u64 *right, unsigned int ndigits) { int i; @@ -184,6 +214,7 @@ static int vli_cmp(const u64 *left, const u64 *right, unsigned int ndigits) return 0; } +EXPORT_SYMBOL(vli_cmp); /* Computes result = in << c, returning carry. Can modify in place * (if result == in). 0 < shift < 64. @@ -239,8 +270,30 @@ static u64 vli_add(u64 *result, const u64 *left, const u64 *right, 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. */ -static u64 vli_sub(u64 *result, const u64 *left, const u64 *right, +u64 vli_sub(u64 *result, const u64 *left, const u64 *right, unsigned int ndigits) { u64 borrow = 0; @@ -258,9 +311,37 @@ static u64 vli_sub(u64 *result, const u64 *left, const u64 *right, 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) && defined(__SIZEOF_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; @@ -269,7 +350,6 @@ static uint128_t mul_64_64(u64 left, u64 right) u64 m1 = a0 * b1; u64 m2 = a1 * b0; u64 m3 = a1 * b1; - uint128_t result; m2 += (m0 >> 32); m2 += m1; @@ -280,7 +360,7 @@ static uint128_t mul_64_64(u64 left, u64 right) result.m_low = (m0 & 0xffffffffull) | (m2 << 32); result.m_high = m3 + (m2 >> 32); - +#endif return result; } @@ -330,6 +410,28 @@ static void vli_mult(u64 *result, const u64 *left, const u64 *right, 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 }; @@ -402,6 +504,170 @@ static void vli_mod_sub(u64 *result, const u64 *left, const u64 *right, 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 @@ -509,14 +775,33 @@ static void vli_mmod_fast_256(u64 *result, const u64 *product, } } -/* Computes result = product % curve_prime - * from http://www.nsa.gov/ia/_files/nist-routines.pdf -*/ +/* 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 u64 *curve_prime, unsigned int ndigits) { u64 tmp[2 * ECC_MAX_DIGITS]; + /* Currently, both NIST primes have -1 in lowest qword. */ + if (curve_prime[0] != -1ull) { + /* 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 3: vli_mmod_fast_192(result, product, curve_prime, tmp); @@ -525,13 +810,26 @@ static bool vli_mmod_fast(u64 *result, u64 *product, vli_mmod_fast_256(result, product, curve_prime, tmp); break; default: - pr_err("unsupports digits size!\n"); + 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 u64 *curve_prime, unsigned int ndigits) @@ -557,7 +855,7 @@ static void vli_mod_square_fast(u64 *result, const u64 *left, * See "From Euclid's GCD to Montgomery Multiplication to the Great Divide" * https://labs.oracle.com/techrep/2001/smli_tr-2001-95.pdf */ -static void vli_mod_inv(u64 *result, const u64 *input, const u64 *mod, +void vli_mod_inv(u64 *result, const u64 *input, const u64 *mod, unsigned int ndigits) { u64 a[ECC_MAX_DIGITS], b[ECC_MAX_DIGITS]; @@ -630,6 +928,7 @@ static void vli_mod_inv(u64 *result, const u64 *input, const u64 *mod, vli_set(result, u, ndigits); } +EXPORT_SYMBOL(vli_mod_inv); /* ------ Point operations ------ */ @@ -903,6 +1202,85 @@ static void ecc_point_mult(struct ecc_point *result, 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->p, ndigits); + vli_mod_inv(z, z, curve->p, ndigits); + apply_z(result->x, result->y, z, curve->p, ndigits); +} + +/* 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)) | ((!!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->p, ndigits); + idx = (!!vli_test_bit(u1, i)) | ((!!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->p, ndigits); + vli_mod_sub(tz, rx, tx, curve->p, ndigits); + xycz_add(tx, ty, rx, ry, curve->p, ndigits); + vli_mod_mult_fast(z, z, tz, curve->p, ndigits); + } + } + vli_mod_inv(z, z, curve->p, ndigits); + apply_z(rx, ry, z, curve->p, ndigits); +} +EXPORT_SYMBOL(ecc_point_mult_shamir); + static inline void ecc_swap_digits(const u64 *in, u64 *out, unsigned int ndigits) { @@ -948,6 +1326,7 @@ int ecc_is_key_valid(unsigned int curve_id, unsigned int ndigits, return __ecc_is_key_valid(curve, private_key, ndigits); } +EXPORT_SYMBOL(ecc_is_key_valid); /* * ECC private keys are generated using the method of extra random bits, @@ -1000,6 +1379,7 @@ int ecc_gen_privkey(unsigned int curve_id, unsigned int ndigits, u64 *privkey) 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) @@ -1036,13 +1416,17 @@ err_free_point: out: return ret; } +EXPORT_SYMBOL(ecc_make_pub_key); /* SP800-56A section 5.6.2.3.4 partial verification: ephemeral keys only */ -static int ecc_is_pubkey_valid_partial(const struct ecc_curve *curve, - struct ecc_point *pk) +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; @@ -1064,8 +1448,8 @@ static int ecc_is_pubkey_valid_partial(const struct ecc_curve *curve, return -EINVAL; return 0; - } +EXPORT_SYMBOL(ecc_is_pubkey_valid_partial); int crypto_ecdh_shared_secret(unsigned int curve_id, unsigned int ndigits, const u64 *private_key, const u64 *public_key, @@ -1121,3 +1505,6 @@ err_alloc_product: out: return ret; } +EXPORT_SYMBOL(crypto_ecdh_shared_secret); + +MODULE_LICENSE("Dual BSD/GPL"); |