int
mpz_millerrabin (mpz_srcptr n, int reps)
{
int r;
mpz_t nm1, nm3, x, y, q;
unsigned long int k;
gmp_randstate_t rstate;
int is_prime;
TMP_DECL;
TMP_MARK;
MPZ_TMP_INIT (nm1, SIZ (n) + 1);
mpz_sub_ui (nm1, n, 1L);
MPZ_TMP_INIT (x, SIZ (n) + 1);
MPZ_TMP_INIT (y, 2 * SIZ (n)); /* mpz_powm_ui needs excessive memory!!! */
/* Perform a Fermat test. */
mpz_set_ui (x, 210L);
mpz_powm (y, x, nm1, n);
if (mpz_cmp_ui (y, 1L) != 0)
{
TMP_FREE;
return 0;
}
MPZ_TMP_INIT (q, SIZ (n));
/* Find q and k, where q is odd and n = 1 + 2**k * q. */
k = mpz_scan1 (nm1, 0L);
mpz_tdiv_q_2exp (q, nm1, k);
/* n-3 */
MPZ_TMP_INIT (nm3, SIZ (n) + 1);
mpz_sub_ui (nm3, n, 3L);
ASSERT (mpz_cmp_ui (nm3, 1L) >= 0);
gmp_randinit_default (rstate);
is_prime = 1;
for (r = 0; r < reps && is_prime; r++)
{
/* 2 to n-2 inclusive, don't want 1, 0 or -1 */
mpz_urandomm (x, rstate, nm3);
mpz_add_ui (x, x, 2L);
is_prime = millerrabin (n, nm1, x, y, q, k);
}
gmp_randclear (rstate);
TMP_FREE;
return is_prime;
}
int main() {
unsigned long long n,i=1;
for(n=2;n<SMALL;n++) if(isprime((int)n)) printf("%llu %d\n",i++,intsqrt(n));
if(n%2==0) n++;
for(;n<(1ULL<<32);n+=2) {
if(millerrabin((unsigned int)n)) printf("%llu %d\n",i++,intsqrt(n));
}
for(;n<(1ULL<<63);n+=2) {
if(ullmillerrabin(n)) printf("%llu %d\n",i++,intsqrt(n));
}
return 0;
}
/* it seems the routine breaks down if n>=2^63 */
int ullmillerrabin(unsigned long long n) {
if(n<4294967296ULL) return millerrabin(n);
if(!(n&1)) return 0;
if(n<4759123141ULL)
return ullwitness(n,2) && ullwitness(n,7) && ullwitness(n,61);
if(n<2152302898747ULL)
return ullwitness(n,2) && ullwitness(n,3) && ullwitness(n,5) &&
ullwitness(n,7) && ullwitness(n,11);
if(n<3474749660383ULL)
return ullwitness(n,2) && ullwitness(n,3) && ullwitness(n,5) &&
ullwitness(n,7) && ullwitness(n,11) && ullwitness(n,13);
if(n<341550071728321ULL)
return ullwitness(n,2) && ullwitness(n,3) && ullwitness(n,5) &&
ullwitness(n,7) && ullwitness(n,11) && ullwitness(n,13) &&
ullwitness(n,17);
return ullwitness(n,2) && ullwitness(n,325) && ullwitness(n,9375) &&
ullwitness(n,28178) && ullwitness(n,450775) && ullwitness(n,9780504) &&
ullwitness(n,1795265022);
}
// Generate a numbits-bit probable prime using the Random-Search algorithm
void rndsearch(int numbits, int maxitr, FILE* primesfile, FILE* rndfile) {
bool found_prime = false;
int count = 1;
int num_bytes = ceil(numbits/8.0);
BIGNUM* num_orig = BN_new();
char* num_trimmed = (char*)calloc(1, num_bytes);
// Iterate through potential numbers in RandomFile
while(!found_prime) {
printf("RANDOM-SEARCH: iteration %d\n", count);
// Generate random odd numbit-long integer
RndOddNum(numbits, num_orig, rndfile);
num_trimmed = BN_bn2dec(num_orig);
// Test with trial division
printf(" n = %s\n", num_trimmed);
printf(" ");
if(trialdiv(num_trimmed, primesfile)) {
// Passed trial division, check Miller-Rabin
if(millerrabin(num_trimmed, maxitr, primesfile, " ")) {
found_prime = true;
}
}
count++;
}
BN_free(num_orig);
free(num_trimmed);
// PSEUDO-CODE
// - Generate a random numbit-bit number
// - Read ceil(numbit/8) bytes from the random file
// - Set bits 0 and numbit-1 to 1
// - Set bits numbit to ceil(numbit/8)*8 to 0
// - Run the Trial Division test
// - If it passes, run the Miller-Rabin test
// - If it passes that too, return that prime number
// - If it fails either test, return to the beginning and try a new number
}
/*
* rndsearch function to generate numbits-bit probable prime
* @param: k numbits, maxitr, FILE pointer to primesfile, FILE pointer to rndfile
* @output: Print out rndsearch process and generate a probable prime
*/
void rndsearch(int k, int maxitr, FILE *fp, FILE *fp_rndfile)
{
int byte = 0;
int x_byte = ceil_func((double)k/8, (int)k/8);
char *temp = malloc(x_byte); //read in x_byte from rndfile
int itr_count = 1;
while((byte = fread(temp, 1, x_byte, fp_rndfile)) > 0)
{
BIGNUM *bn_n = RndOddNum(k, temp, x_byte);
if(bn_n == NULL)
{
free(temp);
return; //ERROR has happened in RndOddNum() function call
}
else
{
//Print itr
fprintf(stdout, "RANDOM-SEARCH: iteration %d\n", itr_count);
itr_count += 1;
fprintf(stdout, " n = %s\n", BN_bn2dec(bn_n));
//Use trial division function to check if n passes trial division test
int trialdiv_returnCode = trialdiv(bn_n, fp, 2);
//reset fp pointer to beginning of primesfile for next time use
rewind(fp);
if(trialdiv_returnCode == -1)
{
//error has happened in trialdiv function. Terminate this function
free(temp);
BN_free(bn_n); //free from RndOddNum() function call
return;
}
else if(trialdiv_returnCode == 0)
{
BN_free(bn_n);
continue; //bn_n does not pass trial division test. Continue to generate next number
}
int millerrabin_returnCode = millerrabin(bn_n, maxitr, fp, 2);
//reset fp pointer to beginning of primesfile for next time use
rewind(fp);
if(millerrabin_returnCode == -1)
{
//error has happened in millerrabin function. Terminate this function
free(temp);
BN_free(bn_n); //free from RndOddNum() function call
return;
}
else if(millerrabin_returnCode == 1)
{
free(temp);
BN_free(bn_n); //free from RndOddNum() function call
return; //Prove n to be a prime number. End function
}
else
{
//continue generate the next probable prime
BN_free(bn_n);
}
}
}
//Free in case we have never generated a bn_n that passes both tests
free(temp);
fprintf(stderr, "Run out of bytes in rndfile and we have not successfully generated a prime number\n");
}
int main(int argc, char *argv[]) {
int i;
char *trialNum = NULL;
char *rndFile = NULL;
char *inFile = NULL;
int maxVal;
int maxIterations;
int numBits;
if (argc <= 2) {
usage();
return 0;
}
// Variable parsing for tablecheck
if (strncmp(argv[1], "primes", 6) == 0) {
if (argc != 3) {
usage();
return 0;
}
for (i = 1; i < argc; i++) {
if (argc == 3) {
if (strncmp(argv[i], "-n=", 3) == 0) {
maxVal = atoi(argv[i] + 3);
}
if (!argv[i]) {
usage();
return 0;
}
}
else {
usage();
return 0;
}
}
if (maxVal < 1) {
usage();
return 0;
}
else {
// Call tablecheck function
primes(maxVal);
}
}
else if (strncmp(argv[1], "trialdiv", 8) == 0) {
if (argc != 4) {
usage();
return 0;
}
for (i = 1; i < argc; i++) {
if (argc == 4) {
if (strncmp(argv[i], "-n=", 3) == 0) {
trialNum = argv[i] + 3;
}
if (strncmp(argv[i], "-p=", 3) == 0) {
inFile = argv[i] + 3;
}
if (!argv[i]) {
usage();
return 0;
}
}
else {
usage();
return 0;
}
}
if (trialNum == NULL || inFile == NULL) {
usage();
return 0;
}
else {
// Call keyExpand function
trialdiv(trialNum, inFile);
}
}
else if (strncmp(argv[1], "millerrabin", 11) == 0) {
if (argc != 5) {
usage();
return 0;
}
for (i = 1; i < argc; i++) {
if (argc == 5) {
if (strncmp(argv[i], "-n=", 3) == 0) {
trialNum = argv[i] + 3;
}
if (strncmp(argv[i], "-t=", 3) == 0) {
maxIterations = atoi(argv[i] + 3);
}
if (strncmp(argv[i], "-p=", 3) == 0) {
inFile = argv[i] + 3;
}
if (!argv[i]) {
usage();
return 0;
}
}
else {
usage();
return 0;
}
}
if (trialNum == NULL || maxIterations < 1 || inFile == NULL) {
usage();
return 0;
}
else {
// Call keyExpand function
millerrabin(trialNum, maxIterations, inFile, 0);
}
}
else if (strncmp(argv[1], "rndsearch", 9) == 0) {
if (argc != 6) {
usage();
return 0;
}
for (i = 1; i < argc; i++) {
if (argc == 6) {
if (strncmp(argv[i], "-k=", 3) == 0) {
numBits = atoi(argv[i] + 3);
}
if (strncmp(argv[i], "-t=", 3) == 0) {
maxIterations = atoi(argv[i] + 3);
}
if (strncmp(argv[i], "-p=", 3) == 0) {
inFile = argv[i] + 3;
}
if (strncmp(argv[i], "-r=", 3) == 0) {
rndFile = argv[i] + 3;
}
if (!argv[i]) {
usage();
return 0;
}
}
else {
usage();
return 0;
}
}
if (numBits < 1 || maxIterations < 1 || inFile == NULL || rndFile == NULL) {
usage();
return 0;
}
else {
// Call rndsearch function
rndsearch(numBits, maxIterations, inFile, rndFile);
}
}
else if (strncmp(argv[1], "maurer", 6) == 0) {
if (argc != 5) {
usage();
return 0;
}
for (i = 1; i < argc; i++) {
if (argc == 5) {
if (strncmp(argv[i], "-k=", 3) == 0) {
numBits = atoi(argv[i] + 3);
}
if (strncmp(argv[i], "-p=", 3) == 0) {
inFile = argv[i] + 3;
}
if (strncmp(argv[i], "-r=", 3) == 0) {
rndFile = argv[i] + 3;
}
if (!argv[i]) {
usage();
return 0;
}
}
else {
usage();
return 0;
}
}
if (numBits < 1 || inFile == NULL || rndFile == NULL) {
usage();
return 0;
}
else {
// Call rndsearch function
maurer(numBits, inFile, rndFile);
}
}
// If these conditions are not met, then print usage and quit.
else {
usage();
return 0;
}
return 0;
}
