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RSA算法描述：
1) 选择两个大素数 p、q， 计算 n = p*q;
2) 产生 e, d 使：
e*d = 1mod(p-1)(q-1)
e 与 (p-1)(q-1) 互质
[公钥] e、n
[私钥] d、n
3) 加密：
c = m^d mod n
4) 解密：
m = c^e mod n
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libtommath是一个大数算法库。以下的代码是用这个库中的函数实现的，相当简单。
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 | #include <tommath.h> typedef struct { int bits; /* bits in key */ mp_int n; /* modulus */ mp_int e; /* public exponent */ mp_int d; /* private exponent */ }rsa_key; int rsa_rng(unsigned char *dst, int len, void *dat) { int x; for (x = 0; x < len; x++) dst[x] = rand () & 0xFF; return len; } int rsa_preme_random( mp_int *a, int bits ) { int err = mp_prime_random_ex( a, 8, bits, LTM_PRIME_2MSB_ON|LTM_PRIME_SAFE, rsa_rng, NULL ); if (err != MP_OKAY) { return -1; } return 0; } int rsa_gen_key( rsa_key *key, int bits ) { mp_int p, q; mp_int sp, sq; mp_int n, m; mp_int e, d; mp_int t; //init mp_ints mp_init( &p ); mp_init( &q ); mp_init( &sp ); mp_init( &sq ); mp_init( &n ); mp_init( &m ); mp_init( &e ); mp_init( &d ); mp_init( &t ); //genarate p & q rsa_preme_random( &p, bits/2 ); rsa_preme_random( &q, bits/2 ); //make n & m mp_sub_d( &p, 1, &sp ); mp_sub_d( &q, 1, &sq ); mp_mul( &p, &q, &n ); mp_mul( &sp, &sq, &m ); //make e & d mp_set( &e, 127 ); retry_e: mp_gcd( &e, &m, &t ); if ( ( mp_cmp_d(&t, 1) ) > 0 ){ mp_add_d( &e, 2, &e ); goto retry_e; } mp_invmod( &e, &m, &d ); //copy n d e to key struct mp_init( &key->n ); mp_init( &key->d ); mp_init( &key->e ); key->bits = bits; mp_copy( &n, &key->n ); mp_copy( &d, &key->d ); mp_copy( &e, &key->e ); mp_clear( &p ); mp_clear( &q ); mp_clear( &sp );mp_clear( &sq ); mp_clear( &n ); mp_clear( &m ); mp_clear( &e ); mp_clear( &d ); mp_clear( &t ); return 0; } /*set rsa key by string */ int rsa_set_key( rsa_key *key, char *sn, char *se, char *sd, int bits, int radix ) { key->bits = bits; mp_init( &key->n ); mp_init( &key->d ); mp_init( &key->e ); if ( sn ) mp_read_radix( &key->n, sn, radix ); if ( se ) mp_read_radix( &key->e, se, radix ); if ( sd ) mp_read_radix( &key->d, sd, radix ); return 0; } /*encrypt by private key */ int rsa_encrypt(mp_int *c, mp_int *m, rsa_key *key) { mp_exptmod( c, &key->d, &key->n, m ); return 0; } /*decrypt by public key */ int rsa_decrypt(mp_int *m, mp_int *c, rsa_key *key) { mp_exptmod( m, &key->e, &key->n, c ); return 0; } int rsa_test() { mp_int c, m; rsa_key key; char sn[] = "BB7F51983FD8707FD6227C23DEF5D5377A5A737CEF3C5252E578EFE136DF87B50473F9341F1640C8D258034E14C16993FCE6C6B8C3CEEB65FC8FBCD8EB77B3B05AC7C4D09E0FA1BA2EFE87D3184DB6718AE41A7CAD89B8DCE0FE80CEB523D5D647F9DB58A31D2E71AC677E67FA6E75820736C9893761EE4ACD11F31DBDC349EF" ; char se[] = "010001" ; char sm[] = "AA7B0BF4AAE8B7C2ECC485ACFA57770E50BB9207233E4278654717E470691981C187F81FFC3B90895063EF98C0D86B5297B655399309E6699FEE2270B0F3431B5ABAD7E516261926C35BF6BBFEFB49366EBE96DC510E9CBD915337E8188D517D15DCF90298C40233EEEAFD5A9459F5D3410E6B89B44DF6E818FA3594EF935534" ; char sc[1024]; mp_init( &c ); mp_init( &m ); rsa_set_key( &key, sn, se, NULL, 128, 16 ); mp_read_radix( &m, sm, 16 ); rsa_decrypt( &m, &c, &key ); mp_toradix( &c, sc, 16 ); printf ( "%s\n" , sc); return 0; } |
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