RSA.rar_quantum computing_quantum key_rsa_大因数分解_大整数分解

/* LibTomCrypt, modular cryptographic library -- Tom St Denis * * LibTomCrypt is a library that provides various cryptographic * algorithms in a highly modular and flexible manner. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://libtomcrypt.org */ /* RSA Code by Tom St Denis */ #include "mycrypt.h" #ifdef MRSA int rsa_make_key(prng_state *prng, int wprng, int size, long e, rsa_key *key) { mp_int p, q, tmp1, tmp2, tmp3; int err; _ARGCHK(key != NULL); if ((size < (MIN_RSA_SIZE/8)) || (size > (MAX_RSA_SIZE/8))) { return CRYPT_INVALID_KEYSIZE; } if ((e < 3) || ((e & 1) == 0)) { return CRYPT_INVALID_ARG; } if ((err = prng_is_valid(wprng)) != CRYPT_OK) { return err; } if ((err = mp_init_multi(&p, &q, &tmp1, &tmp2, &tmp3, NULL)) != MP_OKAY) { return mpi_to_ltc_error(err); } /* make primes p and q (optimization provided by Wayne Scott) */ if ((err = mp_set_int(&tmp3, e)) != MP_OKAY) { goto error; } /* tmp3 = e */ /* make prime "p" */ do { if ((err = rand_prime(&p, size*4, prng, wprng)) != CRYPT_OK) { goto done; } if ((err = mp_sub_d(&p, 1, &tmp1)) != MP_OKAY) { goto error; } /* tmp1 = p-1 */ if ((err = mp_gcd(&tmp1, &tmp3, &tmp2)) != MP_OKAY) { goto error; } /* tmp2 = gcd(p-1, e) */ } while (mp_cmp_d(&tmp2, 1) != 0); /* while e divides p-1 */ /* make prime "q" */ do { if ((err = rand_prime(&q, size*4, prng, wprng)) != CRYPT_OK) { goto done; } if ((err = mp_sub_d(&q, 1, &tmp1)) != MP_OKAY) { goto error; } /* tmp1 = q-1 */ if ((err = mp_gcd(&tmp1, &tmp3, &tmp2)) != MP_OKAY) { goto error; } /* tmp2 = gcd(q-1, e) */ } while (mp_cmp_d(&tmp2, 1) != 0); /* while e divides q-1 */ /* tmp1 = lcm(p-1, q-1) */ if ((err = mp_sub_d(&p, 1, &tmp2)) != MP_OKAY) { goto error; } /* tmp2 = p-1 */ /* tmp1 = q-1 (previous do/while loop) */ if ((err = mp_lcm(&tmp1, &tmp2, &tmp1)) != MP_OKAY) { goto error; } /* tmp1 = lcm(p-1, q-1) */ /* make key */ if ((err = mp_init_multi(&key->e, &key->d, &key->N, &key->dQ, &key->dP, &key->qP, &key->pQ, &key->p, &key->q, NULL)) != MP_OKAY) { goto error; } if ((err = mp_set_int(&key->e, e)) != MP_OKAY) { goto error2; } /* key->e = e */ if ((err = mp_invmod(&key->e, &tmp1, &key->d)) != MP_OKAY) { goto error2; } /* key->d = 1/e mod lcm(p-1,q-1) */ if ((err = mp_mul(&p, &q, &key->N)) != MP_OKAY) { goto error2; } /* key->N = pq */ /* optimize for CRT now */ /* find d mod q-1 and d mod p-1 */ if ((err = mp_sub_d(&p, 1, &tmp1)) != MP_OKAY) { goto error2; } /* tmp1 = q-1 */ if ((err = mp_sub_d(&q, 1, &tmp2)) != MP_OKAY) { goto error2; } /* tmp2 = p-1 */ if ((err = mp_mod(&key->d, &tmp1, &key->dP)) != MP_OKAY) { goto error2; } /* dP = d mod p-1 */ if ((err = mp_mod(&key->d, &tmp2, &key->dQ)) != MP_OKAY) { goto error2; } /* dQ = d mod q-1 */ if ((err = mp_invmod(&q, &p, &key->qP)) != MP_OKAY) { goto error2; } /* qP = 1/q mod p */ if ((err = mp_mulmod(&key->qP, &q, &key->N, &key->qP)) != MP_OKAY) { goto error2; } /* qP = q * (1/q mod p) mod N */ if ((err = mp_invmod(&p, &q, &key->pQ)) != MP_OKAY) { goto error2; } /* pQ = 1/p mod q */ if ((err = mp_mulmod(&key->pQ, &p, &key->N, &key->pQ)) != MP_OKAY) { goto error2; } /* pQ = p * (1/p mod q) mod N */ if ((err = mp_copy(&p, &key->p)) != MP_OKAY) { goto error2; } if ((err = mp_copy(&q, &key->q)) != MP_OKAY) { goto error2; } /* shrink ram required */ if ((err = mp_shrink(&key->e)) != MP_OKAY) { goto error2; } if ((err = mp_shrink(&key->d)) != MP_OKAY) { goto error2; } if ((err = mp_shrink(&key->N)) != MP_OKAY) { goto error2; } if ((err = mp_shrink(&key->dQ)) != MP_OKAY) { goto error2; } if ((err = mp_shrink(&key->dP)) != MP_OKAY) { goto error2; } if ((err = mp_shrink(&key->qP)) != MP_OKAY) { goto error2; } if ((err = mp_shrink(&key->pQ)) != MP_OKAY) { goto error2; } if ((err = mp_shrink(&key->p)) != MP_OKAY) { goto error2; } if ((err = mp_shrink(&key->q)) != MP_OKAY) { goto error2; } err = CRYPT_OK; key->type = PK_PRIVATE_OPTIMIZED; goto done; error2: mp_clear_multi(&key->d, &key->e, &key->N, &key->dQ, &key->dP, &key->qP, &key->pQ, &key->p, &key->q, NULL); error: err = mpi_to_ltc_error(err); done: mp_clear_multi(&tmp3, &tmp2, &tmp1, &p, &q, NULL); return err; } #endif