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Diffstat (limited to 'third_party/bearssl/src/rsa_i15_keygen.c')
| -rw-r--r-- | third_party/bearssl/src/rsa_i15_keygen.c | 583 |
1 files changed, 583 insertions, 0 deletions
diff --git a/third_party/bearssl/src/rsa_i15_keygen.c b/third_party/bearssl/src/rsa_i15_keygen.c new file mode 100644 index 0000000..e8da419 --- /dev/null +++ b/third_party/bearssl/src/rsa_i15_keygen.c @@ -0,0 +1,583 @@ +/* + * Copyright (c) 2018 Thomas Pornin <[email protected]> + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the + * "Software"), to deal in the Software without restriction, including + * without limitation the rights to use, copy, modify, merge, publish, + * distribute, sublicense, and/or sell copies of the Software, and to + * permit persons to whom the Software is furnished to do so, subject to + * the following conditions: + * + * The above copyright notice and this permission notice shall be + * included in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, + * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF + * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND + * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS + * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN + * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN + * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE + * SOFTWARE. + */ + +#include "inner.h" + +/* + * Make a random integer of the provided size. The size is encoded. + * The header word is untouched. + */ +static void +mkrand(const br_prng_class **rng, uint16_t *x, uint32_t esize) +{ + size_t u, len; + unsigned m; + + len = (esize + 15) >> 4; + (*rng)->generate(rng, x + 1, len * sizeof(uint16_t)); + for (u = 1; u < len; u ++) { + x[u] &= 0x7FFF; + } + m = esize & 15; + if (m == 0) { + x[len] &= 0x7FFF; + } else { + x[len] &= 0x7FFF >> (15 - m); + } +} + +/* + * This is the big-endian unsigned representation of the product of + * all small primes from 13 to 1481. + */ +static const unsigned char SMALL_PRIMES[] = { + 0x2E, 0xAB, 0x92, 0xD1, 0x8B, 0x12, 0x47, 0x31, 0x54, 0x0A, + 0x99, 0x5D, 0x25, 0x5E, 0xE2, 0x14, 0x96, 0x29, 0x1E, 0xB7, + 0x78, 0x70, 0xCC, 0x1F, 0xA5, 0xAB, 0x8D, 0x72, 0x11, 0x37, + 0xFB, 0xD8, 0x1E, 0x3F, 0x5B, 0x34, 0x30, 0x17, 0x8B, 0xE5, + 0x26, 0x28, 0x23, 0xA1, 0x8A, 0xA4, 0x29, 0xEA, 0xFD, 0x9E, + 0x39, 0x60, 0x8A, 0xF3, 0xB5, 0xA6, 0xEB, 0x3F, 0x02, 0xB6, + 0x16, 0xC3, 0x96, 0x9D, 0x38, 0xB0, 0x7D, 0x82, 0x87, 0x0C, + 0xF7, 0xBE, 0x24, 0xE5, 0x5F, 0x41, 0x04, 0x79, 0x76, 0x40, + 0xE7, 0x00, 0x22, 0x7E, 0xB5, 0x85, 0x7F, 0x8D, 0x01, 0x50, + 0xE9, 0xD3, 0x29, 0x42, 0x08, 0xB3, 0x51, 0x40, 0x7B, 0xD7, + 0x8D, 0xCC, 0x10, 0x01, 0x64, 0x59, 0x28, 0xB6, 0x53, 0xF3, + 0x50, 0x4E, 0xB1, 0xF2, 0x58, 0xCD, 0x6E, 0xF5, 0x56, 0x3E, + 0x66, 0x2F, 0xD7, 0x07, 0x7F, 0x52, 0x4C, 0x13, 0x24, 0xDC, + 0x8E, 0x8D, 0xCC, 0xED, 0x77, 0xC4, 0x21, 0xD2, 0xFD, 0x08, + 0xEA, 0xD7, 0xC0, 0x5C, 0x13, 0x82, 0x81, 0x31, 0x2F, 0x2B, + 0x08, 0xE4, 0x80, 0x04, 0x7A, 0x0C, 0x8A, 0x3C, 0xDC, 0x22, + 0xE4, 0x5A, 0x7A, 0xB0, 0x12, 0x5E, 0x4A, 0x76, 0x94, 0x77, + 0xC2, 0x0E, 0x92, 0xBA, 0x8A, 0xA0, 0x1F, 0x14, 0x51, 0x1E, + 0x66, 0x6C, 0x38, 0x03, 0x6C, 0xC7, 0x4A, 0x4B, 0x70, 0x80, + 0xAF, 0xCA, 0x84, 0x51, 0xD8, 0xD2, 0x26, 0x49, 0xF5, 0xA8, + 0x5E, 0x35, 0x4B, 0xAC, 0xCE, 0x29, 0x92, 0x33, 0xB7, 0xA2, + 0x69, 0x7D, 0x0C, 0xE0, 0x9C, 0xDB, 0x04, 0xD6, 0xB4, 0xBC, + 0x39, 0xD7, 0x7F, 0x9E, 0x9D, 0x78, 0x38, 0x7F, 0x51, 0x54, + 0x50, 0x8B, 0x9E, 0x9C, 0x03, 0x6C, 0xF5, 0x9D, 0x2C, 0x74, + 0x57, 0xF0, 0x27, 0x2A, 0xC3, 0x47, 0xCA, 0xB9, 0xD7, 0x5C, + 0xFF, 0xC2, 0xAC, 0x65, 0x4E, 0xBD +}; + +/* + * We need temporary values for at least 7 integers of the same size + * as a factor (including header word); more space helps with performance + * (in modular exponentiations), but we much prefer to remain under + * 2 kilobytes in total, to save stack space. The macro TEMPS below + * exceeds 1024 (which is a count in 16-bit words) when BR_MAX_RSA_SIZE + * is greater than 4350 (default value is 4096, so the 2-kB limit is + * maintained unless BR_MAX_RSA_SIZE was modified). + */ +#define MAX(x, y) ((x) > (y) ? (x) : (y)) +#define TEMPS MAX(1024, 7 * ((((BR_MAX_RSA_SIZE + 1) >> 1) + 29) / 15)) + +/* + * Perform trial division on a candidate prime. This computes + * y = SMALL_PRIMES mod x, then tries to compute y/y mod x. The + * br_i15_moddiv() function will report an error if y is not invertible + * modulo x. Returned value is 1 on success (none of the small primes + * divides x), 0 on error (a non-trivial GCD is obtained). + * + * This function assumes that x is odd. + */ +static uint32_t +trial_divisions(const uint16_t *x, uint16_t *t) +{ + uint16_t *y; + uint16_t x0i; + + y = t; + t += 1 + ((x[0] + 15) >> 4); + x0i = br_i15_ninv15(x[1]); + br_i15_decode_reduce(y, SMALL_PRIMES, sizeof SMALL_PRIMES, x); + return br_i15_moddiv(y, y, x, x0i, t); +} + +/* + * Perform n rounds of Miller-Rabin on the candidate prime x. This + * function assumes that x = 3 mod 4. + * + * Returned value is 1 on success (all rounds completed successfully), + * 0 otherwise. + */ +static uint32_t +miller_rabin(const br_prng_class **rng, const uint16_t *x, int n, + uint16_t *t, size_t tlen) +{ + /* + * Since x = 3 mod 4, the Miller-Rabin test is simple: + * - get a random base a (such that 1 < a < x-1) + * - compute z = a^((x-1)/2) mod x + * - if z != 1 and z != x-1, the number x is composite + * + * We generate bases 'a' randomly with a size which is + * one bit less than x, which ensures that a < x-1. It + * is not useful to verify that a > 1 because the probability + * that we get a value a equal to 0 or 1 is much smaller + * than the probability of our Miller-Rabin tests not to + * detect a composite, which is already quite smaller than the + * probability of the hardware misbehaving and return a + * composite integer because of some glitch (e.g. bad RAM + * or ill-timed cosmic ray). + */ + unsigned char *xm1d2; + size_t xlen, xm1d2_len, xm1d2_len_u16, u; + uint32_t asize; + unsigned cc; + uint16_t x0i; + + /* + * Compute (x-1)/2 (encoded). + */ + xm1d2 = (unsigned char *)t; + xm1d2_len = ((x[0] - (x[0] >> 4)) + 7) >> 3; + br_i15_encode(xm1d2, xm1d2_len, x); + cc = 0; + for (u = 0; u < xm1d2_len; u ++) { + unsigned w; + + w = xm1d2[u]; + xm1d2[u] = (unsigned char)((w >> 1) | cc); + cc = w << 7; + } + + /* + * We used some words of the provided buffer for (x-1)/2. + */ + xm1d2_len_u16 = (xm1d2_len + 1) >> 1; + t += xm1d2_len_u16; + tlen -= xm1d2_len_u16; + + xlen = (x[0] + 15) >> 4; + asize = x[0] - 1 - EQ0(x[0] & 15); + x0i = br_i15_ninv15(x[1]); + while (n -- > 0) { + uint16_t *a; + uint32_t eq1, eqm1; + + /* + * Generate a random base. We don't need the base to be + * really uniform modulo x, so we just get a random + * number which is one bit shorter than x. + */ + a = t; + a[0] = x[0]; + a[xlen] = 0; + mkrand(rng, a, asize); + + /* + * Compute a^((x-1)/2) mod x. We assume here that the + * function will not fail (the temporary array is large + * enough). + */ + br_i15_modpow_opt(a, xm1d2, xm1d2_len, + x, x0i, t + 1 + xlen, tlen - 1 - xlen); + + /* + * We must obtain either 1 or x-1. Note that x is odd, + * hence x-1 differs from x only in its low word (no + * carry). + */ + eq1 = a[1] ^ 1; + eqm1 = a[1] ^ (x[1] - 1); + for (u = 2; u <= xlen; u ++) { + eq1 |= a[u]; + eqm1 |= a[u] ^ x[u]; + } + + if ((EQ0(eq1) | EQ0(eqm1)) == 0) { + return 0; + } + } + return 1; +} + +/* + * Create a random prime of the provided size. 'size' is the _encoded_ + * bit length. The two top bits and the two bottom bits are set to 1. + */ +static void +mkprime(const br_prng_class **rng, uint16_t *x, uint32_t esize, + uint32_t pubexp, uint16_t *t, size_t tlen) +{ + size_t len; + + x[0] = esize; + len = (esize + 15) >> 4; + for (;;) { + size_t u; + uint32_t m3, m5, m7, m11; + int rounds; + + /* + * Generate random bits. We force the two top bits and the + * two bottom bits to 1. + */ + mkrand(rng, x, esize); + if ((esize & 15) == 0) { + x[len] |= 0x6000; + } else if ((esize & 15) == 1) { + x[len] |= 0x0001; + x[len - 1] |= 0x4000; + } else { + x[len] |= 0x0003 << ((esize & 15) - 2); + } + x[1] |= 0x0003; + + /* + * Trial division with low primes (3, 5, 7 and 11). We + * use the following properties: + * + * 2^2 = 1 mod 3 + * 2^4 = 1 mod 5 + * 2^3 = 1 mod 7 + * 2^10 = 1 mod 11 + */ + m3 = 0; + m5 = 0; + m7 = 0; + m11 = 0; + for (u = 0; u < len; u ++) { + uint32_t w; + + w = x[1 + u]; + m3 += w << (u & 1); + m3 = (m3 & 0xFF) + (m3 >> 8); + m5 += w << ((4 - u) & 3); + m5 = (m5 & 0xFF) + (m5 >> 8); + m7 += w; + m7 = (m7 & 0x1FF) + (m7 >> 9); + m11 += w << (5 & -(u & 1)); + m11 = (m11 & 0x3FF) + (m11 >> 10); + } + + /* + * Maximum values of m* at this point: + * m3: 511 + * m5: 2310 + * m7: 510 + * m11: 2047 + * We use the same properties to make further reductions. + */ + + m3 = (m3 & 0x0F) + (m3 >> 4); /* max: 46 */ + m3 = (m3 & 0x0F) + (m3 >> 4); /* max: 16 */ + m3 = ((m3 * 43) >> 5) & 3; + + m5 = (m5 & 0xFF) + (m5 >> 8); /* max: 263 */ + m5 = (m5 & 0x0F) + (m5 >> 4); /* max: 30 */ + m5 = (m5 & 0x0F) + (m5 >> 4); /* max: 15 */ + m5 -= 10 & -GT(m5, 9); + m5 -= 5 & -GT(m5, 4); + + m7 = (m7 & 0x3F) + (m7 >> 6); /* max: 69 */ + m7 = (m7 & 7) + (m7 >> 3); /* max: 14 */ + m7 = ((m7 * 147) >> 7) & 7; + + /* + * 2^5 = 32 = -1 mod 11. + */ + m11 = (m11 & 0x1F) + 66 - (m11 >> 5); /* max: 97 */ + m11 -= 88 & -GT(m11, 87); + m11 -= 44 & -GT(m11, 43); + m11 -= 22 & -GT(m11, 21); + m11 -= 11 & -GT(m11, 10); + + /* + * If any of these modulo is 0, then the candidate is + * not prime. Also, if pubexp is 3, 5, 7 or 11, and the + * corresponding modulus is 1, then the candidate must + * be rejected, because we need e to be invertible + * modulo p-1. We can use simple comparisons here + * because they won't leak information on a candidate + * that we keep, only on one that we reject (and is thus + * not secret). + */ + if (m3 == 0 || m5 == 0 || m7 == 0 || m11 == 0) { + continue; + } + if ((pubexp == 3 && m3 == 1) + || (pubexp == 5 && m5 == 1) + || (pubexp == 7 && m7 == 1) + || (pubexp == 11 && m11 == 1)) + { + continue; + } + + /* + * More trial divisions. + */ + if (!trial_divisions(x, t)) { + continue; + } + + /* + * Miller-Rabin algorithm. Since we selected a random + * integer, not a maliciously crafted integer, we can use + * relatively few rounds to lower the risk of a false + * positive (i.e. declaring prime a non-prime) under + * 2^(-80). It is not useful to lower the probability much + * below that, since that would be substantially below + * the probability of the hardware misbehaving. Sufficient + * numbers of rounds are extracted from the Handbook of + * Applied Cryptography, note 4.49 (page 149). + * + * Since we work on the encoded size (esize), we need to + * compare with encoded thresholds. + */ + if (esize < 320) { + rounds = 12; + } else if (esize < 480) { + rounds = 9; + } else if (esize < 693) { + rounds = 6; + } else if (esize < 906) { + rounds = 4; + } else if (esize < 1386) { + rounds = 3; + } else { + rounds = 2; + } + + if (miller_rabin(rng, x, rounds, t, tlen)) { + return; + } + } +} + +/* + * Let p be a prime (p > 2^33, p = 3 mod 4). Let m = (p-1)/2, provided + * as parameter (with announced bit length equal to that of p). This + * function computes d = 1/e mod p-1 (for an odd integer e). Returned + * value is 1 on success, 0 on error (an error is reported if e is not + * invertible modulo p-1). + * + * The temporary buffer (t) must have room for at least 4 integers of + * the size of p. + */ +static uint32_t +invert_pubexp(uint16_t *d, const uint16_t *m, uint32_t e, uint16_t *t) +{ + uint16_t *f; + uint32_t r; + + f = t; + t += 1 + ((m[0] + 15) >> 4); + + /* + * Compute d = 1/e mod m. Since p = 3 mod 4, m is odd. + */ + br_i15_zero(d, m[0]); + d[1] = 1; + br_i15_zero(f, m[0]); + f[1] = e & 0x7FFF; + f[2] = (e >> 15) & 0x7FFF; + f[3] = e >> 30; + r = br_i15_moddiv(d, f, m, br_i15_ninv15(m[1]), t); + + /* + * We really want d = 1/e mod p-1, with p = 2m. By the CRT, + * the result is either the d we got, or d + m. + * + * Let's write e*d = 1 + k*m, for some integer k. Integers e + * and m are odd. If d is odd, then e*d is odd, which implies + * that k must be even; in that case, e*d = 1 + (k/2)*2m, and + * thus d is already fine. Conversely, if d is even, then k + * is odd, and we must add m to d in order to get the correct + * result. + */ + br_i15_add(d, m, (uint32_t)(1 - (d[1] & 1))); + + return r; +} + +/* + * Swap two buffers in RAM. They must be disjoint. + */ +static void +bufswap(void *b1, void *b2, size_t len) +{ + size_t u; + unsigned char *buf1, *buf2; + + buf1 = b1; + buf2 = b2; + for (u = 0; u < len; u ++) { + unsigned w; + + w = buf1[u]; + buf1[u] = buf2[u]; + buf2[u] = w; + } +} + +/* see bearssl_rsa.h */ +uint32_t +br_rsa_i15_keygen(const br_prng_class **rng, + br_rsa_private_key *sk, void *kbuf_priv, + br_rsa_public_key *pk, void *kbuf_pub, + unsigned size, uint32_t pubexp) +{ + uint32_t esize_p, esize_q; + size_t plen, qlen, tlen; + uint16_t *p, *q, *t; + uint16_t tmp[TEMPS]; + uint32_t r; + + if (size < BR_MIN_RSA_SIZE || size > BR_MAX_RSA_SIZE) { + return 0; + } + if (pubexp == 0) { + pubexp = 3; + } else if (pubexp == 1 || (pubexp & 1) == 0) { + return 0; + } + + esize_p = (size + 1) >> 1; + esize_q = size - esize_p; + sk->n_bitlen = size; + sk->p = kbuf_priv; + sk->plen = (esize_p + 7) >> 3; + sk->q = sk->p + sk->plen; + sk->qlen = (esize_q + 7) >> 3; + sk->dp = sk->q + sk->qlen; + sk->dplen = sk->plen; + sk->dq = sk->dp + sk->dplen; + sk->dqlen = sk->qlen; + sk->iq = sk->dq + sk->dqlen; + sk->iqlen = sk->plen; + + if (pk != NULL) { + pk->n = kbuf_pub; + pk->nlen = (size + 7) >> 3; + pk->e = pk->n + pk->nlen; + pk->elen = 4; + br_enc32be(pk->e, pubexp); + while (*pk->e == 0) { + pk->e ++; + pk->elen --; + } + } + + /* + * We now switch to encoded sizes. + * + * floor((x * 17477) / (2^18)) is equal to floor(x/15) for all + * integers x from 0 to 23833. + */ + esize_p += MUL15(esize_p, 17477) >> 18; + esize_q += MUL15(esize_q, 17477) >> 18; + plen = (esize_p + 15) >> 4; + qlen = (esize_q + 15) >> 4; + p = tmp; + q = p + 1 + plen; + t = q + 1 + qlen; + tlen = ((sizeof tmp) / sizeof(uint16_t)) - (2 + plen + qlen); + + /* + * When looking for primes p and q, we temporarily divide + * candidates by 2, in order to compute the inverse of the + * public exponent. + */ + + for (;;) { + mkprime(rng, p, esize_p, pubexp, t, tlen); + br_i15_rshift(p, 1); + if (invert_pubexp(t, p, pubexp, t + 1 + plen)) { + br_i15_add(p, p, 1); + p[1] |= 1; + br_i15_encode(sk->p, sk->plen, p); + br_i15_encode(sk->dp, sk->dplen, t); + break; + } + } + + for (;;) { + mkprime(rng, q, esize_q, pubexp, t, tlen); + br_i15_rshift(q, 1); + if (invert_pubexp(t, q, pubexp, t + 1 + qlen)) { + br_i15_add(q, q, 1); + q[1] |= 1; + br_i15_encode(sk->q, sk->qlen, q); + br_i15_encode(sk->dq, sk->dqlen, t); + break; + } + } + + /* + * If p and q have the same size, then it is possible that q > p + * (when the target modulus size is odd, we generate p with a + * greater bit length than q). If q > p, we want to swap p and q + * (and also dp and dq) for two reasons: + * - The final step below (inversion of q modulo p) is easier if + * p > q. + * - While BearSSL's RSA code is perfectly happy with RSA keys such + * that p < q, some other implementations have restrictions and + * require p > q. + * + * Note that we can do a simple non-constant-time swap here, + * because the only information we leak here is that we insist on + * returning p and q such that p > q, which is not a secret. + */ + if (esize_p == esize_q && br_i15_sub(p, q, 0) == 1) { + bufswap(p, q, (1 + plen) * sizeof *p); + bufswap(sk->p, sk->q, sk->plen); + bufswap(sk->dp, sk->dq, sk->dplen); + } + + /* + * We have produced p, q, dp and dq. We can now compute iq = 1/d mod p. + * + * We ensured that p >= q, so this is just a matter of updating the + * header word for q (and possibly adding an extra word). + * + * Theoretically, the call below may fail, in case we were + * extraordinarily unlucky, and p = q. Another failure case is if + * Miller-Rabin failed us _twice_, and p and q are non-prime and + * have a factor is common. We report the error mostly because it + * is cheap and we can, but in practice this never happens (or, at + * least, it happens way less often than hardware glitches). + */ + q[0] = p[0]; + if (plen > qlen) { + q[plen] = 0; + t ++; + tlen --; + } + br_i15_zero(t, p[0]); + t[1] = 1; + r = br_i15_moddiv(t, q, p, br_i15_ninv15(p[1]), t + 1 + plen); + br_i15_encode(sk->iq, sk->iqlen, t); + + /* + * Compute the public modulus too, if required. + */ + if (pk != NULL) { + br_i15_zero(t, p[0]); + br_i15_mulacc(t, p, q); + br_i15_encode(pk->n, pk->nlen, t); + } + + return r; +} |