int test_sub(testspec_t *t, FILE *ofp)
{
mp_int in[3], out[1];
int v;
mp_result res, expect;
if(!parse_int_values(t, in, out, &expect))
return imath_errno = MP_BADARG, 0;
if(strcmp(t->code, "subv") == 0) {
if((res = mp_int_to_int(in[1], &v)) != MP_OK)
return imath_errno = res, 0;
if((res = mp_int_sub_value(in[0], v, in[2])) != expect)
return imath_errno = res, 0;
} else {
if((res = mp_int_sub(in[0], in[1], in[2])) != expect)
return imath_errno = res, 0;
}
if(expect == MP_OK && mp_int_compare(in[2], out[0]) != 0) {
mp_int_to_string(in[2], 10, g_output, OUTPUT_LIMIT);
return imath_errno = OTHER_ERROR, 0;
}
return 1;
}
/*
Compute mul * atan(1/x) to prec digits of precision, and store the
result in sum.
Computes atan(1/x) using the formula:
1 1 1 1
atan(1/x) = --- - ---- + ---- - ---- + ...
x 3x^3 5x^5 7x^7
*/
mp_result arctan(mp_small radix, mp_small mul, mp_small x, mp_small prec,
mp_int sum) {
mpz_t t, v;
mp_result res;
mp_small rem, sign = 1, coeff = 1;
mp_int_init(&t);
mp_int_init(&v);
++prec;
/* Compute mul * radix^prec * x
The initial multiplication by x saves a special case in the loop for
the first term of the series.
*/
if ((res = mp_int_expt_value(radix, prec, &t)) != MP_OK ||
(res = mp_int_mul_value(&t, mul, &t)) != MP_OK ||
(res = mp_int_mul_value(&t, x, &t)) != MP_OK)
goto CLEANUP;
x *= x; /* assumes x <= sqrt(MP_SMALL_MAX) */
mp_int_zero(sum);
do {
if ((res = mp_int_div_value(&t, x, &t, &rem)) != MP_OK) goto CLEANUP;
if ((res = mp_int_div_value(&t, coeff, &v, &rem)) != MP_OK) goto CLEANUP;
/* Add or subtract the result depending on the current sign (1 = add) */
if (sign > 0)
res = mp_int_add(sum, &v, sum);
else
res = mp_int_sub(sum, &v, sum);
if (res != MP_OK) goto CLEANUP;
sign = -sign;
coeff += 2;
} while (mp_int_compare_zero(&t) != 0);
res = mp_int_div_value(sum, radix, sum, NULL);
CLEANUP:
mp_int_clear(&v);
mp_int_clear(&t);
return res;
}
int main(int argc, char *argv[]) {
mp_result res;
mpz_t sum1, sum2;
int ndigits, out = 0;
clock_t start, end;
if (argc < 2) {
fprintf(stderr, "Usage: %s <num-digits> [<radix>]\n", argv[0]);
return 1;
}
if ((ndigits = abs(atoi(argv[1]))) == 0) {
fprintf(stderr, "%s: you must request at least 1 digit\n", argv[0]);
return 1;
} else if ((mp_word)ndigits > MP_DIGIT_MAX) {
fprintf(stderr, "%s: you may request at most %u digits\n", argv[0],
(unsigned int)MP_DIGIT_MAX);
return 1;
}
if (argc > 2) {
int radix = atoi(argv[2]);
if (radix < MP_MIN_RADIX || radix > MP_MAX_RADIX) {
fprintf(stderr, "%s: you may only specify a radix between %d and %d\n",
argv[0], MP_MIN_RADIX, MP_MAX_RADIX);
return 1;
}
g_radix = radix;
}
mp_int_init(&sum1);
mp_int_init(&sum2);
start = clock();
/* sum1 = 16 * arctan(1/5) */
if ((res = arctan(g_radix, 16, 5, ndigits, &sum1)) != MP_OK) {
fprintf(stderr, "%s: error computing arctan: %d\n", argv[0], res);
out = 1;
goto CLEANUP;
}
/* sum2 = 4 * arctan(1/239) */
if ((res = arctan(g_radix, 4, 239, ndigits, &sum2)) != MP_OK) {
fprintf(stderr, "%s: error computing arctan: %d\n", argv[0], res);
out = 1;
goto CLEANUP;
}
/* pi = sum1 - sum2 */
if ((res = mp_int_sub(&sum1, &sum2, &sum1)) != MP_OK) {
fprintf(stderr, "%s: error computing pi: %d\n", argv[0], res);
out = 1;
goto CLEANUP;
}
end = clock();
mp_int_to_string(&sum1, g_radix, g_buf, sizeof(g_buf));
printf("%c.%s\n", g_buf[0], g_buf + 1);
fprintf(stderr, "Computation took %.2f sec.\n",
(double)(end - start) / CLOCKS_PER_SEC);
CLEANUP:
mp_int_clear(&sum1);
mp_int_clear(&sum2);
return out;
}
int main(int argc, char *argv[])
{
int opt, modbits;
FILE *ofp = stdout;
char *expt = NULL;
rsa_key the_key;
mp_result res;
/* Process command-line arguments */
while((opt = getopt(argc, argv, "e:")) != EOF) {
switch(opt) {
case 'e':
expt = optarg;
break;
default:
fprintf(stderr, "Usage: rsakey [-e <expt>] <modbits> [<outfile>]\n");
return 1;
}
}
if(optind >= argc) {
fprintf(stderr, "Error: You must specify the number of modulus bits.\n");
fprintf(stderr, "Usage: rsakey [-e <expt>] <modbits> [<outfile>]\n");
return 1;
}
modbits = (int) strtol(argv[optind++], NULL, 0);
if(modbits < CHAR_BIT) {
fprintf(stderr, "Error: Invalid value for number of modulus bits.\n");
return 1;
}
if(modbits % 2 == 1)
++modbits;
/* Check if output file is specified */
if(optind < argc) {
if((ofp = fopen(argv[optind], "wt")) == NULL) {
fprintf(stderr, "Error: Unable to open output file for writing.\n"
" - Filename: %s\n"
" - Error: %s\n", argv[optind], strerror(errno));
return 1;
}
}
if((res = rsa_key_init(&the_key)) != MP_OK) {
fprintf(stderr, "Error initializing RSA key structure:\n"
" - %s (%d)\n", mp_error_string(res), res);
return 1;
}
/* If specified, try to load the key exponent */
if(expt != NULL) {
if((res = mp_int_read_string(&(the_key.e), 10, expt)) != MP_OK) {
fprintf(stderr, "Error: Invalid value for encryption exponent.\n"
" - %s (%d)\n", mp_error_string(res), res);
goto EXIT;
}
}
if((res = mp_int_randomize(&(the_key.p), (modbits / 2))) != MP_OK) {
fprintf(stderr, "Error: Unable to randomize first prime.\n"
" - %s (%d)\n", mp_error_string(res), res);
goto EXIT;
}
fprintf(stderr, "p: ");
find_prime(&(the_key.p), stderr);
if((res = mp_int_randomize(&(the_key.q), (modbits / 2))) != MP_OK) {
fprintf(stderr, "Error: Unable to randomize second prime.\n"
" - %s (%d)\n", mp_error_string(res), res);
goto EXIT;
}
fprintf(stderr, "\nq: ");
find_prime(&(the_key.q), stderr);
fputc('\n', stderr);
/* Temporarily, the key's "n" field will be (p - 1) * (q - 1) for
purposes of computing the decryption exponent.
*/
mp_int_mul(&(the_key.p), &(the_key.q), &(the_key.n));
mp_int_sub(&(the_key.n), &(the_key.p), &(the_key.n));
mp_int_sub(&(the_key.n), &(the_key.q), &(the_key.n));
mp_int_add_value(&(the_key.n), 1, &(the_key.n));
if(expt == NULL &&
(res = mp_int_randomize(&(the_key.e), (modbits / 2))) != MP_OK) {
fprintf(stderr, "Error: Unable to randomize encryption exponent.\n"
" - %s (%d)\n", mp_error_string(res), res);
goto EXIT;
}
while((res = mp_int_invmod(&(the_key.e), &(the_key.n),
&(the_key.d))) != MP_OK) {
if(expt != NULL) {
fprintf(stderr, "Error: Unable to compute decryption exponent.\n"
" - %s (%d)\n", mp_error_string(res), res);
goto EXIT;
}
if((res = mp_int_randomize(&(the_key.e), (modbits / 2))) != MP_OK) {
fprintf(stderr, "Error: Unable to re-randomize encryption exponent.\n"
" - %s (%d)\n", mp_error_string(res), res);
goto EXIT;
}
}
/* Recompute the real modulus, now that exponents are done. */
mp_int_mul(&(the_key.p), &(the_key.q), &(the_key.n));
/* Write completed key to the specified output file */
rsa_key_write(&the_key, ofp);
EXIT:
fclose(ofp);
rsa_key_clear(&the_key);
return 0;
}
