int bdModExp(T y, T x, T e, T m)
{
/* Compute y = x^e mod m
x,e < m */
size_t n;
int status;
assert(y && x && e && m);
/* Make sure all variables are the same size */
n = max(e->ndigits, m->ndigits);
n = max(x->ndigits, n);
bd_resize(y, n);
bd_resize(x, n);
bd_resize(e, n);
bd_resize(m, n);
/* Finally, do the business */
status = mpModExp(y->digits, x->digits, e->digits, m->digits, n);
y->ndigits = mpSizeof(y->digits, n);
return status;
}
int main(void)
{
DIGIT_T n[MOD_SIZE], e[MOD_SIZE], d[MOD_SIZE];
DIGIT_T s[MOD_SIZE], m[MOD_SIZE], m1[MOD_SIZE], s1[MOD_SIZE];
size_t nbytes;
char decimal[MOD_SIZE*4];
/* Data in big-endian byte format:-
*/
unsigned char nn[] = {
0x0A, 0x66, 0x79, 0x1D, 0xC6, 0x98, 0x81, 0x68,
0xDE, 0x7A, 0xB7, 0x74, 0x19, 0xBB, 0x7F, 0xB0,
0xC0, 0x01, 0xC6, 0x27, 0x10, 0x27, 0x00, 0x75,
0x14, 0x29, 0x42, 0xE1, 0x9A, 0x8D, 0x8C, 0x51,
0xD0, 0x53, 0xB3, 0xE3, 0x78, 0x2A, 0x1D, 0xE5,
0xDC, 0x5A, 0xF4, 0xEB, 0xE9, 0x94, 0x68, 0x17,
0x01, 0x14, 0xA1, 0xDF, 0xE6, 0x7C, 0xDC, 0x9A,
0x9A, 0xF5, 0x5D, 0x65, 0x56, 0x20, 0xBB, 0xAB,
};
unsigned char ee[] = { 0x01, 0x00, 0x01 };
unsigned char dd[] = {
0x01, 0x23, 0xC5, 0xB6, 0x1B, 0xA3, 0x6E, 0xDB,
0x1D, 0x36, 0x79, 0x90, 0x41, 0x99, 0xA8, 0x9E,
0xA8, 0x0C, 0x09, 0xB9, 0x12, 0x2E, 0x14, 0x00,
0xC0, 0x9A, 0xDC, 0xF7, 0x78, 0x46, 0x76, 0xD0,
0x1D, 0x23, 0x35, 0x6A, 0x7D, 0x44, 0xD6, 0xBD,
0x8B, 0xD5, 0x0E, 0x94, 0xBF, 0xC7, 0x23, 0xFA,
0x87, 0xD8, 0x86, 0x2B, 0x75, 0x17, 0x76, 0x91,
0xC1, 0x1D, 0x75, 0x76, 0x92, 0xDF, 0x88, 0x81,
};
unsigned char mm[] = {
0x00, 0x01, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x30, 0x20,
0x30, 0x0C, 0x06, 0x08, 0x2A, 0x86, 0x48, 0x86,
0xF7, 0x0D, 0x02, 0x02, 0x05, 0x00, 0x04, 0x10,
0xDC, 0xA9, 0xEC, 0xF1, 0xC1, 0x5C, 0x1B, 0xD2,
0x66, 0xAF, 0xF9, 0xC8, 0x79, 0x93, 0x65, 0xCD,
};
unsigned char ss[] = {
0x06, 0xDB, 0x36, 0xCB, 0x18, 0xD3, 0x47, 0x5B,
0x9C, 0x01, 0xDB, 0x3C, 0x78, 0x95, 0x28, 0x08,
0x02, 0x79, 0xBB, 0xAE, 0xFF, 0x2B, 0x7D, 0x55,
0x8E, 0xD6, 0x61, 0x59, 0x87, 0xC8, 0x51, 0x86,
0x3F, 0x8A, 0x6C, 0x2C, 0xFF, 0xBC, 0x89, 0xC3,
0xF7, 0x5A, 0x18, 0xD9, 0x6B, 0x12, 0x7C, 0x71,
0x7D, 0x54, 0xD0, 0xD8, 0x04, 0x8D, 0xA8, 0xA0,
0x54, 0x46, 0x26, 0xD1, 0x7A, 0x2A, 0x8F, 0xBE,
};
printf("Test BIGDIGITS using 508-bit RSA key from 'Some Examples of the PKCS Standards'\n");
/* Convert bytes to BIGDIGITS */
mpConvFromOctets(n, MOD_SIZE, nn, sizeof(nn));
mpConvFromOctets(e, MOD_SIZE, ee, sizeof(ee));
mpConvFromOctets(d, MOD_SIZE, dd, sizeof(dd));
mpConvFromOctets(m, MOD_SIZE, mm, sizeof(mm));
mpConvFromOctets(s1, MOD_SIZE, ss, sizeof(ss));
printf("n ="); mpPrintNL(n, MOD_SIZE);
printf("e ="); mpPrintNL(e, MOD_SIZE);
printf("d ="); mpPrintNL(d, MOD_SIZE);
printf("m ="); mpPrintNL(m, MOD_SIZE);
/* Sign, i.e. Encrypt with private key, s = m^d mod n */
mpModExp(s, m, d, n, MOD_SIZE);
printf("s ="); mpPrintNL(s, MOD_SIZE);
/* Did we get the same answer as expected? */
if (!mpEqual(s1, s, MOD_SIZE))
printf("<= ERROR - no match\n");
else
printf("<= OK\n");
assert(mpEqual(s1, s, MOD_SIZE));
/* Verify, i.e. Decrypt with public key m' = s^e mod n */
mpModExp(m1, s, e, n, MOD_SIZE);
printf("m'="); mpPrintNL(m1, MOD_SIZE);
/* Check that we got back where we started */
if (!mpEqual(m1, m, MOD_SIZE))
printf("<= ERROR - no match\n");
else
printf("<= OK\n");
assert(mpEqual(m1, m, MOD_SIZE));
/* Now convert back to octets (bytes) */
memset(mm, 0, sizeof(mm));
nbytes = mpConvToOctets(m, MOD_SIZE, mm, sizeof(mm));
printf("%d non-zero bytes converted from m:\n", nbytes);
pr_bytes(mm, sizeof(mm));
memset(ee, 0, sizeof(ee));
nbytes = mpConvToOctets(e, MOD_SIZE, ee, sizeof(ee));
printf("%d non-zero bytes converted from e:\n", nbytes);
pr_bytes(ee, sizeof(ee));
/* Do a conversion to decimal */
nbytes = mpConvToDecimal(e, MOD_SIZE, decimal, sizeof(decimal));
printf("%d non-zero decimal digits converted from e:\n", nbytes);
printf("%s\n", decimal);
assert(strcmp(decimal, "65537") == 0);
printf("OK, successfully completed tests.\n");
return 0;
}