void GenerateKeys(mp_int *d, mp_int *e, mp_int *n)
{
while (1)
{
mp_int p;
mp_init(&p);
mp_prime_random_ex(&p,8,2048, LTM_PRIME_2MSB_ON, &createRandom,NULL);
mp_print("P",&p);
mp_int q;
mp_init(&q);
mp_prime_random_ex(&q,8,2048, LTM_PRIME_2MSB_ON, &createRandom,NULL);
mp_print("Q",&q);
mp_int pp;
mp_init(&pp);
mp_sub_d(&p,1,&pp);
mp_int qq;
mp_init(&qq);
mp_sub_d(&q,1,&qq);
mp_int pq;
mp_init(&pq);
mp_mul(&pp,&qq,&pq);
mp_mul(&p,&q,n);
mp_set(d, 5);
mp_int temp;
mp_init(&temp);
mp_int g;
mp_init(&g);
mp_int t;
mp_init(&t);
mp_exteuclid(d,&pq,e, &temp,&g);
if (mp_cmp_d(&g,1) == 0)
return ;
// now we would have to add 1, but we prefer to get some new numbers
/* printf("Havve to add 1\n");
mp_add_d(d, 1, &t);
printf("Exchange 1\n");
mp_copy(&t,d);*/
}
}
int main(int argc, char *argv[])
{
mp_digit num;
mp_int a, b;
srand(time(NULL));
if(argc < 3) {
fprintf(stderr, "Usage: %s <a> <b>\n", argv[0]);
return 1;
}
printf("Test 7: Random & divisibility tests\n\n");
mp_init(&a);
mp_init(&b);
mp_read_radix(&a, argv[1], 10);
mp_read_radix(&b, argv[2], 10);
printf("a = "); mp_print(&a, stdout); fputc('\n', stdout);
printf("b = "); mp_print(&b, stdout); fputc('\n', stdout);
if(mpp_divis(&a, &b) == MP_YES)
printf("a is divisible by b\n");
else
printf("a is not divisible by b\n");
if(mpp_divis(&b, &a) == MP_YES)
printf("b is divisible by a\n");
else
printf("b is not divisible by a\n");
printf("\nb = mpp_random()\n");
mpp_random(&b);
printf("b = "); mp_print(&b, stdout); fputc('\n', stdout);
mpp_random(&b);
printf("b = "); mp_print(&b, stdout); fputc('\n', stdout);
mpp_random(&b);
printf("b = "); mp_print(&b, stdout); fputc('\n', stdout);
printf("\nTesting a for divisibility by first 170 primes\n");
num = 170;
if(mpp_divis_primes(&a, &num) == MP_YES)
printf("It is divisible by at least one of them\n");
else
printf("It is not divisible by any of them\n");
mp_clear(&b);
mp_clear(&a);
return 0;
}
int main(int argc, char *argv[])
{
mp_int a, b, c, x, y;
if(argc < 3) {
fprintf(stderr, "Usage: %s <a> <b>\n", argv[0]);
return 1;
}
printf("Test 5: Number theoretic functions\n\n");
mp_init(&a);
mp_init(&b);
mp_read_radix(&a, argv[1], 10);
mp_read_radix(&b, argv[2], 10);
printf("a = "); mp_print(&a, stdout); fputc('\n', stdout);
printf("b = "); mp_print(&b, stdout); fputc('\n', stdout);
mp_init(&c);
printf("\nc = (a, b)\n");
mp_gcd(&a, &b, &c);
printf("Euclid: c = "); mp_print(&c, stdout); fputc('\n', stdout);
/*
mp_bgcd(&a, &b, &c);
printf("Binary: c = "); mp_print(&c, stdout); fputc('\n', stdout);
*/
mp_init(&x);
mp_init(&y);
printf("\nc = (a, b) = ax + by\n");
mp_xgcd(&a, &b, &c, &x, &y);
printf("c = "); mp_print(&c, stdout); fputc('\n', stdout);
printf("x = "); mp_print(&x, stdout); fputc('\n', stdout);
printf("y = "); mp_print(&y, stdout); fputc('\n', stdout);
printf("\nc = a^-1 (mod b)\n");
if(mp_invmod(&a, &b, &c) == MP_UNDEF) {
printf("a has no inverse mod b\n");
} else {
printf("c = "); mp_print(&c, stdout); fputc('\n', stdout);
}
mp_clear(&y);
mp_clear(&x);
mp_clear(&c);
mp_clear(&b);
mp_clear(&a);
return 0;
}
int main(int argc, char *argv[])
{
int ix;
mp_digit num;
mp_int a;
srand(time(NULL));
if(argc < 2) {
fprintf(stderr, "Usage: %s <a>\n", argv[0]);
return 1;
}
printf("Test 8: Probabilistic primality testing\n\n");
mp_init(&a);
mp_read_radix(&a, argv[1], 10);
printf("a = ");
mp_print(&a, stdout);
fputc('\n', stdout);
printf("\nChecking for divisibility by small primes ... \n");
num = 170;
if(mpp_divis_primes(&a, &num) == MP_YES) {
printf("it is not prime\n");
goto CLEANUP;
}
printf("Passed that test (not divisible by any small primes).\n");
for(ix = 0; ix < 10; ix++) {
printf("\nPerforming Rabin-Miller test, iteration %d\n", ix + 1);
if(mpp_pprime(&a, 5) == MP_NO) {
printf("it is not prime\n");
goto CLEANUP;
}
}
printf("All tests passed; a is probably prime\n");
CLEANUP:
mp_clear(&a);
return 0;
}
int main(int argc, char *argv[])
{
int ix;
mp_int mp;
#ifdef MAC_CW_SIOUX
argc = ccommand(&argv);
#endif
mp_init(&mp);
for(ix = 1; ix < argc; ix++) {
mp_read_radix(&mp, argv[ix], 10);
mp_print(&mp, stdout);
fputc('\n', stdout);
}
mp_clear(&mp);
return 0;
}
int main(int argc, char *argv[])
{
int ix, num, prec = PRECISION;
mp_int a, b, c, d;
instant_t start, finish;
time_t seed;
unsigned int d1, d2;
seed = time(NULL);
if(argc < 2) {
fprintf(stderr, "Usage: %s <num-tests>\n", argv[0]);
return 1;
}
if((num = atoi(argv[1])) < 0)
num = -num;
printf("Test 5a: Euclid vs. Binary, a GCD speed test\n\n"
"Number of tests: %d\n"
"Precision: %d digits\n\n", num, prec);
mp_init_size(&a, prec);
mp_init_size(&b, prec);
mp_init(&c);
mp_init(&d);
printf("Verifying accuracy ... \n");
srand((unsigned int)seed);
for(ix = 0; ix < num; ix++) {
mpp_random_size(&a, prec);
mpp_random_size(&b, prec);
mp_gcd(&a, &b, &c);
mp_bgcd(&a, &b, &d);
if(mp_cmp(&c, &d) != 0) {
printf("Error! Results not accurate:\n");
printf("a = "); mp_print(&a, stdout); fputc('\n', stdout);
printf("b = "); mp_print(&b, stdout); fputc('\n', stdout);
printf("c = "); mp_print(&c, stdout); fputc('\n', stdout);
printf("d = "); mp_print(&d, stdout); fputc('\n', stdout);
mp_clear(&a); mp_clear(&b); mp_clear(&c); mp_clear(&d);
return 1;
}
}
mp_clear(&d);
printf("Accuracy confirmed for the %d test samples\n", num);
printf("Testing Euclid ... \n");
srand((unsigned int)seed);
start = now();
for(ix = 0; ix < num; ix++) {
mpp_random_size(&a, prec);
mpp_random_size(&b, prec);
mp_gcd(&a, &b, &c);
}
finish = now();
d1 = (finish.sec - start.sec) * 1000000;
d1 -= start.usec; d1 += finish.usec;
printf("Testing binary ... \n");
srand((unsigned int)seed);
start = now();
for(ix = 0; ix < num; ix++) {
mpp_random_size(&a, prec);
mpp_random_size(&b, prec);
mp_bgcd(&a, &b, &c);
}
finish = now();
d2 = (finish.sec - start.sec) * 1000000;
d2 -= start.usec; d2 += finish.usec;
printf("Euclidean algorithm time: %u usec\n", d1);
printf("Binary algorithm time: %u usec\n", d2);
printf("Improvement: %.2f%%\n",
(1.0 - ((double)d2 / (double)d1)) * 100.0);
mp_clear(&c);
mp_clear(&b);
mp_clear(&a);
return 0;
}
int main(int argc, char *argv[])
{
mp_int a, b, c;
int pco;
mp_err res;
printf("Test 9: Logical functions\n\n");
if(argc < 3) {
fprintf(stderr, "Usage: %s <a> <b>\n", argv[0]);
return 1;
}
mp_init(&a); mp_init(&b); mp_init(&c);
mp_read_radix(&a, argv[1], 16);
mp_read_radix(&b, argv[2], 16);
printf("a = "); mp_print(&a, stdout); fputc('\n', stdout);
printf("b = "); mp_print(&b, stdout); fputc('\n', stdout);
mpl_not(&a, &c);
printf("~a = "); mp_print(&c, stdout); fputc('\n', stdout);
mpl_and(&a, &b, &c);
printf("a & b = "); mp_print(&c, stdout); fputc('\n', stdout);
mpl_or(&a, &b, &c);
printf("a | b = "); mp_print(&c, stdout); fputc('\n', stdout);
mpl_xor(&a, &b, &c);
printf("a ^ b = "); mp_print(&c, stdout); fputc('\n', stdout);
mpl_rsh(&a, &c, 1);
printf("a >> 1 = "); mp_print(&c, stdout); fputc('\n', stdout);
mpl_rsh(&a, &c, 5);
printf("a >> 5 = "); mp_print(&c, stdout); fputc('\n', stdout);
mpl_rsh(&a, &c, 16);
printf("a >> 16 = "); mp_print(&c, stdout); fputc('\n', stdout);
mpl_lsh(&a, &c, 1);
printf("a << 1 = "); mp_print(&c, stdout); fputc('\n', stdout);
mpl_lsh(&a, &c, 5);
printf("a << 5 = "); mp_print(&c, stdout); fputc('\n', stdout);
mpl_lsh(&a, &c, 16);
printf("a << 16 = "); mp_print(&c, stdout); fputc('\n', stdout);
mpl_num_set(&a, &pco);
printf("population(a) = %d\n", pco);
mpl_num_set(&b, &pco);
printf("population(b) = %d\n", pco);
res = mpl_parity(&a);
if(res == MP_EVEN)
printf("a has even parity\n");
else
printf("a has odd parity\n");
mp_clear(&c);
mp_clear(&b);
mp_clear(&a);
return 0;
}
int main (int argc, char **argv){
mp_int num1,den1,num2,den2;
mp_rat q1,q2,q3,q4;
//mp_rat *bernoulli;
int i;
clock_t start,stop;
if (argc < 5) {
fprintf(stderr, "usage: %s integer integer integer integer \n", argv[0]);
exit(EXIT_FAILURE);
}
mp_init_multi(&num1,&den1,&num2,&den2,NULL);
mp_get_str(argv[1], &num1, 10);
mp_get_str(argv[2], &den1, 10);
mp_get_str(argv[3], &num2, 10);
mp_get_str(argv[4], &den2, 10);
printf("Numerator 1: ");mp_print(&num1);puts("");
printf("Denominator 1: ");mp_print(&den1);puts("");
printf("Numerator 2: ");mp_print(&num2);puts("");
printf("Denominator 2: ");mp_print(&den2);puts("");
mpq_init_multi(&q1,&q2,&q3,&q4,NULL);puts("000");
mpq_set(&q1,&num1,&den1);puts("111");
printf("Rational1: ");mpq_print(&q1);puts("");
mpq_set(&q2,&num2,&den2);puts("222");
printf("Rational2: ");mpq_print(&q2);puts("");
mpq_add(&q1,&q2,&q3);;
printf("R1 + R2 = ");mpq_print(&q3);puts("");
mpq_sub(&q1,&q2,&q3);
printf("R1 - R2 = ");mpq_print(&q3);puts("");
mpq_mul(&q1,&q2,&q3);
printf("R1 * R2 = ");mpq_print(&q3);puts("");
mpq_div(&q1,&q2,&q3);
printf("R1 / R2 = ");mpq_print(&q3);puts("");
//mpq_pow_d(&q1,123,&q3);
printf("R1 ^ 123 = ");mpq_print(&q3);puts("");
printf("cmp(R1, R2) = %d\n",mpq_cmp(&q1,&q2));
printf("cmp(R2, R1) = %d\n",mpq_cmp(&q2,&q1));
printf("cmp(R1, R1) = %d\n",mpq_cmp(&q1,&q1));
mp_set_int(&num2,123);
//mp_expt(&num1,&num2,&num1);
printf("num1 ^123 = ");mp_fwrite(&num1,10,stdout);puts("");
mpq_set_epsilon(50);
//mpq_set_int(&q1,128,2);
//mpq_set_int(&q1,529,1849);
//mpq_set_int(&q1,3481,11664);
//mpq_set_int(&q1,1764,1849);
mpq_set_int(&q1,44521,46656);
mpq_sqrt(&q1,&q1);
printf("sqrt(R1) = ");mpq_print(&q1);puts("");
//SeidelBernoulli(20);
//bernoulli = malloc(sizeof(mp_rat) * 102);
start = clock();
//bern_rat_init(10);
//bhbern(50);
stop = clock();
puts("bernoulli");
for(i=0;i<=(50);i++){
//mpq_print(&bern_array[i]);printf(" %d\n",i);
}
mpq_bernoulli(10,&q1);
printf("B_10 = ");mpq_print(&q1);puts("");
mpq_bernoulli(4,&q1);
printf("B_4 = ");mpq_print(&q1);puts("");
mpq_bernoulli(0,&q1);
printf("B_0 = ");mpq_print(&q1);puts("");
mpq_bernoulli(1,&q1);
printf("B_1 = ");mpq_print(&q1);puts("");
mpq_bernoulli(2,&q1);
printf("B_3 = ");mpq_print(&q1);puts("");
mpq_bernoulli(100,&q1);
printf("B_100 = ");mpq_print(&q1);puts("");
mpq_bernoulli(98,&q1);
printf("B_98 = ");mpq_print(&q1);puts("");
printf("Time: %6.6f\n",( (double)stop - (double)start )/((double)CLOCKS_PER_SEC) );
mpq_bernoulli_free();
exit(EXIT_SUCCESS);
}
int main(int argc, char *argv[])
{
int ix;
mp_int a, b, c, m;
mp_digit r;
if(argc < 4) {
fprintf(stderr, "Usage: %s <a> <b> <m>\n", argv[0]);
return 1;
}
printf("Test 4: Modular arithmetic\n\n");
mp_init(&a);
mp_init(&b);
mp_init(&m);
mp_read_radix(&a, argv[1], 10);
mp_read_radix(&b, argv[2], 10);
mp_read_radix(&m, argv[3], 10);
printf("a = "); mp_print(&a, stdout); fputc('\n', stdout);
printf("b = "); mp_print(&b, stdout); fputc('\n', stdout);
printf("m = "); mp_print(&m, stdout); fputc('\n', stdout);
mp_init(&c);
printf("\nc = a (mod m)\n");
mp_mod(&a, &m, &c);
printf("c = "); mp_print(&c, stdout); fputc('\n', stdout);
printf("\nc = b (mod m)\n");
mp_mod(&b, &m, &c);
printf("c = "); mp_print(&c, stdout); fputc('\n', stdout);
printf("\nc = b (mod 1853)\n");
mp_mod_d(&b, 1853, &r);
printf("c = %04X\n", r);
printf("\nc = (a + b) mod m\n");
mp_addmod(&a, &b, &m, &c);
printf("c = "); mp_print(&c, stdout); fputc('\n', stdout);
printf("\nc = (a - b) mod m\n");
mp_submod(&a, &b, &m, &c);
printf("c = "); mp_print(&c, stdout); fputc('\n', stdout);
printf("\nc = (a * b) mod m\n");
mp_mulmod(&a, &b, &m, &c);
printf("c = "); mp_print(&c, stdout); fputc('\n', stdout);
printf("\nc = (a ** b) mod m\n");
mp_exptmod(&a, &b, &m, &c);
printf("c = "); mp_print(&c, stdout); fputc('\n', stdout);
printf("\nIn-place modular squaring test:\n");
for(ix = 0; ix < 5; ix++) {
printf("a = (a * a) mod m a = ");
mp_sqrmod(&a, &m, &a);
mp_print(&a, stdout);
fputc('\n', stdout);
}
mp_clear(&c);
mp_clear(&m);
mp_clear(&b);
mp_clear(&a);
return 0;
}
int main(int argc, char *argv[])
{
int ix;
mp_int a, b, c, d;
mp_digit r;
mp_err res;
if(argc < 3) {
fprintf(stderr, "Usage: %s <a> <b>\n", argv[0]);
return 1;
}
printf("Test 3: Multiplication and division\n\n");
srand(time(NULL));
mp_init(&a);
mp_init(&b);
mp_read_radix(&a, argv[1], 10);
mp_read_radix(&b, argv[2], 10);
printf("a = "); mp_print(&a, stdout); fputc('\n', stdout);
printf("b = "); mp_print(&b, stdout); fputc('\n', stdout);
mp_init(&c);
printf("\nc = a * b\n");
mp_mul(&a, &b, &c);
printf("c = "); mp_print(&c, stdout); fputc('\n', stdout);
printf("\nc = b * 32523\n");
mp_mul_d(&b, 32523, &c);
printf("c = "); mp_print(&c, stdout); fputc('\n', stdout);
mp_init(&d);
printf("\nc = a / b, d = a mod b\n");
mp_div(&a, &b, &c, &d);
printf("c = "); mp_print(&c, stdout); fputc('\n', stdout);
printf("d = "); mp_print(&d, stdout); fputc('\n', stdout);
ix = rand() % 256;
printf("\nc = a / %d, r = a mod %d\n", ix, ix);
mp_div_d(&a, (mp_digit)ix, &c, &r);
printf("c = "); mp_print(&c, stdout); fputc('\n', stdout);
printf("r = %04X\n", r);
#if EXPT
printf("\nc = a ** b\n");
mp_expt(&a, &b, &c);
printf("c = "); mp_print(&c, stdout); fputc('\n', stdout);
#endif
ix = rand() % 256;
printf("\nc = 2^%d\n", ix);
mp_2expt(&c, ix);
printf("c = "); mp_print(&c, stdout); fputc('\n', stdout);
#if SQRT
printf("\nc = sqrt(a)\n");
if((res = mp_sqrt(&a, &c)) != MP_OKAY) {
printf("mp_sqrt: %s\n", mp_strerror(res));
} else {
printf("c = "); mp_print(&c, stdout); fputc('\n', stdout);
mp_sqr(&c, &c);
printf("c^2 = "); mp_print(&c, stdout); fputc('\n', stdout);
}
#endif
mp_clear(&d);
mp_clear(&c);
mp_clear(&b);
mp_clear(&a);
return 0;
}