| 1 | /* |
| 2 | * seedsearch — find a seed whose first P-256 candidate is out of range. |
| 3 | * |
| 4 | * PROTOCOL.md requires rejection sampling mod n when deriving a P-256 scalar |
| 5 | * from a seed, and discussion #6 requires a vector that actually exercises |
| 6 | * the rejection branch: "pin a seed that requires a rejection, or the branch |
| 7 | * goes untested". A rejection happens with probability about 2^-32, so no |
| 8 | * seed anybody picks by hand will ever hit it. This searches for one. |
| 9 | * |
| 10 | * The search space is deliberately reproducible rather than random: |
| 11 | * |
| 12 | * seed_k = "contra/v1/vector-search!" || u64be(k) (32 bytes) |
| 13 | * |
| 14 | * so the witness is a single number: the vector file pins k, and anyone can |
| 15 | * rebuild the seed from it without trusting this program. It also makes the |
| 16 | * seed visibly generated rather than plausibly a real key. (Threads race, so |
| 17 | * the k reported is a witness, not necessarily the smallest one.) |
| 18 | * |
| 19 | * A hit is a k where OS2IP(candidate_0) is 0 or >= n, with |
| 20 | * |
| 21 | * candidate_0 = HKDF-SHA-256(IKM = seed_k, salt = "", |
| 22 | * info = "contra/v1/ec-p256" || 0x00) |
| 23 | * |
| 24 | * This tool is a helper, not an authority. Whatever it finds is re-derived |
| 25 | * and re-checked by gen.c against OpenSSL before it reaches the vector file. |
| 26 | * |
| 27 | * Build: make seedsearch Run: ./seedsearch [threads] |
| 28 | */ |
| 29 | #define OPENSSL_SUPPRESS_DEPRECATED 1 |
| 30 | |
| 31 | #include <inttypes.h> |
| 32 | #include <pthread.h> |
| 33 | #include <stdint.h> |
| 34 | #include <stdio.h> |
| 35 | #include <stdlib.h> |
| 36 | #include <string.h> |
| 37 | |
| 38 | #include <openssl/sha.h> |
| 39 | |
| 40 | #define SEED_PREFIX "contra/v1/vector-search!" /* 24 bytes, no NUL */ |
| 41 | #define SEED_PREFIX_LEN 24 |
| 42 | #define EC_LABEL "contra/v1/ec-p256" |
| 43 | #define EC_LABEL_LEN 17 |
| 44 | |
| 45 | /* P-256 group order n, big-endian. */ |
| 46 | static const unsigned char P256_N[32] = { |
| 47 | 0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, |
| 48 | 0xff, 0xff, 0xff, 0xff, 0xff, 0xbc, 0xe6, 0xfa, 0xad, 0xa7, 0x17, |
| 49 | 0x9e, 0x84, 0xf3, 0xb9, 0xca, 0xc2, 0xfc, 0x63, 0x25, 0x51}; |
| 50 | |
| 51 | /* HMAC-SHA-256 over a key of at most 64 bytes. Enough for this search. */ |
| 52 | static void hmac_sha256(const unsigned char *key, size_t keylen, |
| 53 | const unsigned char *msg, size_t msglen, |
| 54 | unsigned char out[32]) { |
| 55 | unsigned char ipad[64], opad[64], inner[32]; |
| 56 | SHA256_CTX c; |
| 57 | size_t i; |
| 58 | |
| 59 | memset(ipad, 0x36, sizeof ipad); |
| 60 | memset(opad, 0x5c, sizeof opad); |
| 61 | for (i = 0; i < keylen; i++) { |
| 62 | ipad[i] ^= key[i]; |
| 63 | opad[i] ^= key[i]; |
| 64 | } |
| 65 | |
| 66 | SHA256_Init(&c); |
| 67 | SHA256_Update(&c, ipad, sizeof ipad); |
| 68 | SHA256_Update(&c, msg, msglen); |
| 69 | SHA256_Final(inner, &c); |
| 70 | |
| 71 | SHA256_Init(&c); |
| 72 | SHA256_Update(&c, opad, sizeof opad); |
| 73 | SHA256_Update(&c, inner, sizeof inner); |
| 74 | SHA256_Final(out, &c); |
| 75 | } |
| 76 | |
| 77 | /* True when the candidate is not a usable P-256 scalar: zero, or >= n. */ |
| 78 | static int out_of_range(const unsigned char c[32]) { |
| 79 | int i, nonzero = 0; |
| 80 | |
| 81 | for (i = 0; i < 32; i++) |
| 82 | if (c[i]) { |
| 83 | nonzero = 1; |
| 84 | break; |
| 85 | } |
| 86 | if (!nonzero) return 1; |
| 87 | |
| 88 | for (i = 0; i < 32; i++) { |
| 89 | if (c[i] < P256_N[i]) return 0; |
| 90 | if (c[i] > P256_N[i]) return 1; |
| 91 | } |
| 92 | return 1; /* exactly n */ |
| 93 | } |
| 94 | |
| 95 | static volatile int g_found = 0; |
| 96 | static uint64_t g_found_k = 0; |
| 97 | static pthread_mutex_t g_mu = PTHREAD_MUTEX_INITIALIZER; |
| 98 | |
| 99 | struct span { |
| 100 | uint64_t start, stride, limit; |
| 101 | }; |
| 102 | |
| 103 | static void *worker(void *arg) { |
| 104 | struct span *s = arg; |
| 105 | unsigned char seed[32], prk[32], info[EC_LABEL_LEN + 2], cand[32]; |
| 106 | unsigned char zero_salt[32]; |
| 107 | uint64_t k; |
| 108 | |
| 109 | memset(zero_salt, 0, sizeof zero_salt); |
| 110 | memcpy(seed, SEED_PREFIX, SEED_PREFIX_LEN); |
| 111 | memcpy(info, EC_LABEL, EC_LABEL_LEN); |
| 112 | info[EC_LABEL_LEN] = 0x00; /* counter i = 0 */ |
| 113 | info[EC_LABEL_LEN + 1] = 0x01; /* HKDF-Expand block counter T(1) */ |
| 114 | |
| 115 | for (k = s->start; k < s->limit && !g_found; k += s->stride) { |
| 116 | int i; |
| 117 | for (i = 0; i < 8; i++) seed[24 + i] = (unsigned char)(k >> (56 - 8 * i)); |
| 118 | |
| 119 | /* HKDF-Extract with a zero-length salt: RFC 5869 substitutes |
| 120 | * HashLen zero bytes as the HMAC key. */ |
| 121 | hmac_sha256(zero_salt, sizeof zero_salt, seed, sizeof seed, prk); |
| 122 | /* HKDF-Expand, first and only 32-byte block. */ |
| 123 | hmac_sha256(prk, sizeof prk, info, sizeof info, cand); |
| 124 | |
| 125 | /* Cheap filter first: a candidate >= n must open 0xFFFFFFFF. */ |
| 126 | if (cand[0] != 0xff || cand[1] != 0xff || cand[2] != 0xff || |
| 127 | cand[3] != 0xff) |
| 128 | continue; |
| 129 | |
| 130 | if (out_of_range(cand)) { |
| 131 | pthread_mutex_lock(&g_mu); |
| 132 | if (!g_found || k < g_found_k) g_found_k = k; |
| 133 | g_found = 1; |
| 134 | pthread_mutex_unlock(&g_mu); |
| 135 | return NULL; |
| 136 | } |
| 137 | } |
| 138 | return NULL; |
| 139 | } |
| 140 | |
| 141 | int main(int argc, char **argv) { |
| 142 | long nthreads = (argc > 1) ? strtol(argv[1], NULL, 10) : 8; |
| 143 | pthread_t *th; |
| 144 | struct span *spans; |
| 145 | long i; |
| 146 | |
| 147 | if (nthreads < 1) nthreads = 1; |
| 148 | th = calloc((size_t)nthreads, sizeof *th); |
| 149 | spans = calloc((size_t)nthreads, sizeof *spans); |
| 150 | if (!th || !spans) return 1; |
| 151 | |
| 152 | for (i = 0; i < nthreads; i++) { |
| 153 | spans[i].start = (uint64_t)i; |
| 154 | spans[i].stride = (uint64_t)nthreads; |
| 155 | spans[i].limit = UINT64_C(1) << 40; |
| 156 | pthread_create(&th[i], NULL, worker, &spans[i]); |
| 157 | } |
| 158 | for (i = 0; i < nthreads; i++) pthread_join(th[i], NULL); |
| 159 | |
| 160 | if (!g_found) { |
| 161 | fprintf(stderr, "seedsearch: no rejecting seed found\n"); |
| 162 | return 1; |
| 163 | } |
| 164 | printf("%" PRIu64 "\n", g_found_k); |
| 165 | return 0; |
| 166 | } |
| 167 | |
amadan