bool prime_check(int i)
{
if(i==1)
return false;
if(i==2)
return true;
if(miller_rabin(i,2) && miller_rabin(i,3) && miller_rabin(i,5) && miller_rabin(i,7) && miller_rabin(i,11) && miller_rabin(i,13) && miller_rabin(i,17))
return true;
return false;
}
bool isPrime(const bigInt& a)
{
if (!checkSmall(a))
return false;
if (!miller_rabin(a, 2))
return false;
return lucas_selfridge(a);
}
int main()
{
ull n,i,check;
scanf("%llu",&n);
check = miller_rabin(n);
printf("%s\n",check?"PRIME":"COMPOSITE");
return 0;
}
bool prime_test(LL n) {
if (n < 2) return false;
if (n < 4) return true;
const int BASIC[12] = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37};
for (int i = 0; i < 12 && BASIC[i] < n; ++ i) {
if (!miller_rabin(n, BASIC[i])) return false;
}
return true;
}
int main()
{
mpz_t n;
mpz_init(n);
printf("Enter a number - ");
mpz_inp_str(n , NULL , 10);
miller_rabin(n);
}
unsigned long long prime(void){
unsigned long long p;
unsigned long long i = 1;
unsigned long long s = 1000;
while(i){
p = rand() % 65536;
i = !(miller_rabin(p, s));
}
return p;
}
int main()
{
ull n,i,check,test_cases;
scanf("%llu",&test_cases);
while(test_cases--)
{
scanf("%llu",&n);
printf("%s\n",miller_rabin(n)?"YES":"NO");
}
return 0;
}
void findFactor(bint n,int k) {
if(n==1)return;
if(miller_rabin(n, TIME)) {
factor[++fac_top] = n;
return;
}
bint p = n;
while(p >= n)
p = pollard_rho(p,k--);
findFactor(p,k);
findFactor(n/p,k);
}
int main()
{
int t;
int n;
type i;
int j;
type tmp;
int arr[16];
type var = 1;
scanf("%d", &t);
for(j =1; j <= t; j++) {
var = 1;
scanf("%d", &n);
for(i = 0; i < n; i++) {
scanf("%d", &arr[i]);
var = var * arr[i];
}
var++;
tmp = miller_rabin(var, 5);
if ( tmp == 0 ) {
for(i = 2; ; i++) {
if((var - (var/i) * i) == 0) {
var = var/i;
i--;
}
tmp = miller_rabin(var, 5);
if( tmp == 1) {
printf("Case #%d: %lld\n",j, var);
break;
}
}
} else {
printf("Case #%d: %lld\n",j, var);
}
}
return 0;
}
int main()
{
int *v;
v= (int *)malloc(sizeof(int)*1000001);
int j1, j2, j3, j4, j5, j6, s, n=0;
int s1, s2, s3, s4, s5;
for (j6=0; j6<10; j6++) {
for (j5=0; j5<10; j5++) {
s5 = j6 + j5;
for (j4=0; j4<10; j4++) {
s4 = s5 + j4;
for (j3=0; j3<10; j3++) {
s3 = s4 + j3;
for (j2=0; j2<10; j2++) {
s2 = s3 + j2;
for (j1=0; j1<10; j1++) {
v[s2 + j1 + n++] = 1;
}
}
}
}
}
}
v[1] = 1;
int t;
scanf("%d", &t);
while(t--) {
int m,n;
scanf("%d%d", &m, &n);
int count =0;
int num;
for(num = m; num <= n; num++) {
if(v[num] == 0) {
printf("%d\n", num);
if(num % 2 == 0) {
continue;
} else if(miller_rabin(num)) {
count ++;
printf("\t%d\n", num);
}
}
}
printf("%d\n",count);
}
return 0;
}
int main(int argc, char *argv[])
{
int n, cnt;
long long a;
while (scanf("%d", &n) != EOF) {
cnt=0;
while (n--) {
scanf("%lld",&a);
if (miller_rabin(a)) {
cnt++;
}
}
printf("%d\n",cnt);
}
return 0;
}
int problem263()
{
integer testnum = string_to_integer("5");
integer testnum_helper = string_to_integer("5");
integer two = string_to_integer("2");
integer total_src = string_to_integer("0");
integer total_tar = string_to_integer("0");
integer target_dif = string_to_integer("6");
integer dif = string_to_integer("0");
int found = 0;
integer lastprime = string_to_integer("5");
//int sexy_count = 0;
printf("text here\n");
while (found < 4) {
//printf("gets 1\n");
if (miller_rabin(testnum) == PRIME) {
subtract_integer(testnum, lastprime, dif);
if (compare_integers(dif, target_dif) == 0) {
printf("difference between %s and %s is six\n",
integer_to_string(testnum), integer_to_string(lastprime));
found++;
}else {
found = 1;
}
copy_integer(testnum, lastprime);
add_integer(total_src, testnum, total_tar);
copy_integer(total_tar, total_src);
printf("Total is %s\n", integer_to_string(total_tar));
}
add_integer(testnum_helper, two, testnum);
copy_integer(testnum, testnum_helper);
printf("Tested %s\n", integer_to_string(testnum));
}
return 0;
}
int main()
{
// VARIABLES DECLARATION
//Clées Générées
mpz_t clee_privee; mpz_init(clee_privee);
mpz_t clee_publique; mpz_init(clee_publique);
mpz_t clee_modulo; mpz_init(clee_modulo);
// Auto GMP + test prima
mpz_t __n; mpz_init(__n);
mpz_t __max; mpz_init(__max);
mpz_t __two; mpz_init_set_ui(__two, 2);
mpz_t __p; mpz_init(__p);
mpz_t __q; mpz_init(__q);
gmp_randstate_t __rand_state;
gmp_randinit_default(__rand_state);
gmp_randseed_ui (__rand_state, time(NULL));
// Manu GMP
mpz_t _p, _q; mpz_init (_p); mpz_init (_q);
mpz_t _n; mpz_init (_n);
mpz_t _phi; mpz_init(_phi);
mpz_t _e,_d; mpz_init(_e); mpz_init(_d);
mpz_t _temp1; mpz_init(_temp1);
mpz_t _temp2; mpz_init(_temp2);
//manu Small
int p,q;
int n;
int phi;
int e,d;
// In / Out
char s_temp[1000]="";
char s_in[1000] = "ref.txt";
char s_out[1000] = "out.txt";
FILE * f_in ;
FILE * f_out;
// Some vars
int longeur_nombres=100;
int clees_generees=0;
int i,j;
char c = ' ';
int menu;
int continuer =1;
int base_cryptage=10;
char separator='\n';
while (continuer ==1 )
{
if (clees_generees==1) {printf("\n\n\n\nLes clees ont ete generees");}
else {printf("\n\n\nLes clees n'ont pas encore ete generees");}
//Menu
printf("\n\t-> 1: generer des cles RSA manuellement (petits nombres ; sans GMP).");
printf("\n\t-> 2: generer des cles RSA manuellement (grands nombres ; avec GMP).");
printf("\n\t-> 3: generer des cles RSA automatiquement (avec GMP ).");
printf("\n\t-> 8: Entrer manuellement les clees.");
printf("\n\t-> 9: Charger les clees a partir d'un fichier.");
if (clees_generees==1)
{
printf("\n\n4: Cripter un fichier.");
printf("\n5: Decripter un fichier.");
printf("\n10: Enregistrer les clees dans un fichier");
}
printf("\n\n6: Test de primalite ( Miller Rabin ).");
printf("\n\n0: Quitter.");
printf("\n\nChoix : ");
scanf("%d",&menu);
switch (menu)
{
case 0: // quiter
continuer=0;
break;
case 1: // setup RSA
printf("\nEntrez deux nombres premiers p et q, : \n"); // On entre deux nbres premiers p, q
do { printf("\tp = "); scanf("%d",&p); } while( premier(p)!= 1 );
do { printf("\tp = %d, q = ",p); scanf("%d",&q); } while( q==p || premier(q)!= 1 );
n = p*q; // on calcul la première partie de la clé publique
phi=(p-1)*(q-1); // on calcule l'indicatrice d'euler de n
printf("\tphi(%d) = %d\n",n,phi);
printf("\nEntrez un nombre e, tel que Pgcd(%d,e) = 0 :\n",phi);
do { printf("\te = "); scanf("%d",&e);printf("\n"); d= inverseModulo(e,phi); } while( d==0 );
printf("\n\td = %d , car (%d * %d = 1 mod %d )\n",d,d,e,phi);
while (d<0) {d+=n;}
printf("\n\tCle Publique : { %d, %d }",e,n);
printf("\n\tCle Privee : { %d, %d }\n\n",d,n);
mpz_set_ui(clee_privee,d);
mpz_set_ui(clee_publique,e);
mpz_set_ui(clee_modulo,n);
clees_generees=1;
break;
case 2: // setup RSA
printf("\nEntrez deux nombres premiers p et q, : \n"); // On entre deux nbres premiers p, q
do { printf("\tp = "); gmp_scanf("%Zd",_p); } while( mpz_premier(_p)!= 1 );
do { gmp_printf("\tp = %Zd, q = ",_p); gmp_scanf("%Zd",_q); } while( mpz_cmp(_q,_p)==0 || mpz_premier(_q)!= 1 );
mpz_mul(_n,_p,_q); // on calcul la première partie de la clé publique
mpz_sub_ui(_temp1,_p,1);
mpz_sub_ui(_temp2,_q,1);
mpz_mul(_phi,_temp1,_temp2); // on calcule l'indicatrice d'euler de n
gmp_printf("\tphi(%Zd) = %Zd\n",_n,_phi);
gmp_printf("\nEntrez un nombre e, tel que Pgcd(%Zd,e) = 0 :\n",_phi);
do { printf("\te = "); gmp_scanf("%Zd",_e);printf("\n"); mpz_inverseModulo(&_d,_e,_phi); } while( mpz_cmp_ui(_d,0)==0 );
gmp_printf("%Zd",_e);
gmp_printf("%Zd",_phi);
gmp_printf("\n\td = %Zd , car (%Zd * %Zd = 1 mod %Zd )\n",_d,_d,_e,_phi);
gmp_printf("\n\tCle Publique : { %Zd, %Zd }",_e,_n);
gmp_printf("\n\tCle Privee : { %Zd, %Zd }\n\n",_d,_n);
mpz_set(clee_privee,_d);
mpz_set(clee_publique,_e);
mpz_set(clee_modulo,_n);
clees_generees=1;
break;
case 8:
printf("\n\n\t * ENTREZ LES CLEES *\n");
printf("\n\tClee publique = "); gmp_scanf("%Zd",clee_publique);
printf("\tClee privee = "); gmp_scanf("%Zd",clee_privee);
printf("\tClee Modulo = "); gmp_scanf("%Zd",clee_modulo);
printf("\n\n");
clees_generees=1;
break;
case 9: // Charger les clees a partir d'un fichier
{
j=0;
do
{
printf("\n\n\t\t * CHARGER *\n( clee publique / privee / modulo)\n ");
printf("\n\t1 : Input : %s",s_in);
printf("\n\t2 : separateur input : ");
if (separator == '\n'){printf("retour a la ligne");}
if (separator == '\t'){printf("tabulation");}
if (separator == ' '){printf("espace");}
printf("\n\n\t0 : Charger !!! :");
scanf("%d",&menu);
if (menu == 1) {printf("\n\tnouveau fichier : "); scanf("%s",s_in);}
if (menu == 2)
{
printf("\n\tnouveau caractere de separation :");
printf("\n\t\t1 : retour a la ligne");
printf("\n\t\t2 : tabulation ");
printf("\n\t\t3 : espace ");
printf("\n\n\t\t0 : annuler ");
scanf("%d",&menu);
if (menu==1) { separator='\n';}
if (menu==2) { separator='\t';}
if (menu==3) { separator=' ';}
}
}while (menu!=0);
f_in = fopen(s_in,"r");
c = '0';
while(c != EOF)
{
i=0;
c = '0';
while(c != EOF && c!= separator)
{
c = fgetc(f_in);
if (c != EOF && c!= separator)
{
s_temp[i]=c;
i++;
}
}
if (c!=EOF)
{
s_temp[i]='\0';
if (j==0) {mpz_set_str(clee_publique,s_temp,10); }
if (j==1) {mpz_set_str(clee_privee ,s_temp,10); }
if (j==2) {mpz_set_str(clee_modulo ,s_temp,10); }
j++;
}
}
fclose(f_in);
printf("\nappuyez sur une touche pour continuer");
clees_generees=1;
getchar(); getchar();
j=0;
}
break;
case 3: // auto crypte rabin
mpz_mul_2exp(__max, __two, longeur_nombres );
printf("\nGeneration de 2 nombres premiers p et q, : \n");
do
{
mpz_urandomm(__p, __rand_state, __max);
// a remplacer par une boucle propre sur les 100 plus petits premiers par exemple
if (mpz_even_p(__p)) continue;
if (mpz_fdiv_ui(__p, 3) == 0) continue;
if (mpz_fdiv_ui(__p, 5) == 0) continue;
if (mpz_fdiv_ui(__p, 7) == 0) continue;
} while (miller_rabin(__p, __rand_state, 100) == 0);
do
{
mpz_urandomm(__q, __rand_state, __max);
// a remplacer par une boucle propre sur les 100 plus petits premiers par exemple
if (mpz_even_p(__q)) continue;
if (mpz_fdiv_ui(__q, 3) == 0) continue;
if (mpz_fdiv_ui(__q, 5) == 0) continue;
if (mpz_fdiv_ui(__q, 7) == 0) continue;
} while (miller_rabin(__q, __rand_state, 100) == 0);
do
{
mpz_urandomm(_e, __rand_state, __max);
// a remplacer par une boucle propre sur les 100 plus petits premiers par exemple
if (mpz_even_p(_e)) continue;
if (mpz_fdiv_ui(_e, 3) == 0) continue;
if (mpz_fdiv_ui(_e, 5) == 0) continue;
if (mpz_fdiv_ui(_e, 7) == 0) continue;
} while (miller_rabin(_e, __rand_state, 100) == 0);
gmp_printf("\n\tp = %Zd,\n\n\tq = %Zd",__p,__q);
mpz_mul(_n,__p,__q); // on calcul la première partie de la clé publique
mpz_sub_ui(_temp1,__p,1);
mpz_sub_ui(_temp2,__q,1);
mpz_mul(_phi,_temp1,_temp2); // on calcule l'indicatrice d'euler de n
gmp_printf("\n\n\tphi(%Zd) \n\t= %Zd\n",_n,_phi);
mpz_inverseModulo(&_d,_e,_phi);
gmp_printf("\n\tCle Publique : \n\t{ %Zd,\n\t%Zd }",_e,_n);
gmp_printf("\n\n\tCle Privee : \n\t{ %Zd,\n\t%Zd }\n\n",_d,_n);
mpz_set(clee_privee,_d);
mpz_set(clee_publique,_e);
mpz_set(clee_modulo,_n);
clees_generees=1;
break;
case 4: // crypte
if (clees_generees==1)
{
do
{
printf("\n\n\t * CRYPTAGE *\n");
printf("\n\t1 : Input : %s",s_in);
printf("\n\t2 : Output : %s",s_out);
printf("\n\t3 : Base : %d",base_cryptage);
printf("\n\t4 : separateur : ");
if (separator == '\n'){printf("retour a la ligne");}
if (separator == '\t'){printf("tabulation");}
if (separator == ' '){printf("espace");}
printf("\n\n\t0 : CRYPTER !!! :");
scanf("%d",&menu);
if (menu == 1) {printf("\n\tnouveau fichier : "); scanf("%s",s_in);}
if (menu == 2) {printf("\n\tnouveau fichier : "); scanf("%s",s_out);}
if (menu == 3) {printf("\n\tnouvelle base ( entre 2 et 36) : "); scanf("%d",&base_cryptage);
if (base_cryptage<2 || base_cryptage>36) {base_cryptage=10;}}
if (menu == 4)
{
printf("\n\tnouveau caractere de separation :");
printf("\n\t\t1 : retour a la ligne");
printf("\n\t\t2 : tabulation ");
printf("\n\t\t3 : espace ");
printf("\n\n\t\t0 : annuler ");
scanf("%d",&menu);
if (menu==1) { separator='\n';}
if (menu==2) { separator='\t';}
if (menu==3) { separator=' ';}
}
}while (menu!=0);
f_in = fopen(s_in,"r");
f_out = fopen(s_out,"w+");
c = ' ';
while(c != EOF)
{
c = fgetc(f_in);
if (c!=EOF)
{
mpz_set_ui(_temp1,(unsigned int)c);
mpz_powm(_temp1,_temp1,clee_publique,clee_modulo);
mpz_out_str (f_out, base_cryptage, _temp1 );
fputc(separator,f_out);
}
}
fclose(f_in);
fclose(f_out);
printf("\nappuyez sur une touche pour continuer");
getchar(); getchar();
}
else
{
printf("\nVous devez d'abord generer un set de Clees");
printf("\nappuyez sur une touche pour continuer");
getchar(); getchar();
}
break;
case 5: // Décrypte
if (clees_generees==1)
{
do
{
printf("\n\n\t * DECRYPTAGE *\n");
printf("\n\t1 : Input : %s",s_in);
printf("\n\t2 : Output : %s",s_out);
printf("\n\t3 : Base : %d",base_cryptage);
printf("\n\t4 : separateur input : ");
if (separator == '\n'){printf("retour a la ligne");}
if (separator == '\t'){printf("tabulation");}
if (separator == ' '){printf("espace");}
printf("\n\n\t0 : DECRYPTER !!! :");
scanf("%d",&menu);
if (menu == 1) {printf("\n\tnouveau fichier : "); scanf("%s",s_in);}
if (menu == 2) {printf("\n\tnouveau fichier : "); scanf("%s",s_out);}
if (menu == 3) {printf("\n\tnouvelle base ( entre 2 et 36) : "); scanf("%d",&base_cryptage);
if (base_cryptage<2 || base_cryptage>36) {base_cryptage=10;}}
if (menu == 4)
{
printf("\n\tnouveau caractere de separation :");
printf("\n\t\t1 : retour a la ligne");
printf("\n\t\t2 : tabulation ");
printf("\n\t\t3 : espace ");
printf("\n\n\t\t0 : annuler ");
scanf("%d",&menu);
if (menu==1) { separator='\n';}
if (menu==2) { separator='\t';}
if (menu==3) { separator=' ';}
}
}while (menu!=0);
f_in = fopen(s_in,"r");
f_out = fopen(s_out,"w+");
c = '0';
while(c != EOF)
{
i=0;
c = '0';
while(c != EOF && c!= separator)
{
c = fgetc(f_in);
if (c != EOF && c!= separator)
{
s_temp[i]=c;
i++;
}
}
if (c!=EOF)
{
s_temp[i]='\0';
mpz_set_str(_temp1,s_temp,base_cryptage);
mpz_powm(_temp1,_temp1,clee_privee,clee_modulo);
fputc((char)(mpz_get_ui(_temp1)),f_out);
}
}
fclose(f_in);
fclose(f_out);
printf("\nappuyez sur une touche pour continuer");
getchar(); getchar();
}
else
{
printf("\nVous devez d'abord generer un set de Clees");
printf("\nappuyez sur une touche pour continuer");
getchar(); getchar();
}
break;
case 10: // enregistre les clees
if (clees_generees==1)
{
do
{
printf("\n\n\t * SAUVER *\n");
printf("\n\t1 : Output : %s",s_out);
printf("\n\t2 : separateur : ");
if (separator == '\n'){printf("retour a la ligne");}
if (separator == '\t'){printf("tabulation");}
if (separator == ' '){printf("espace");}
printf("\n\n\t0 : CRYPTER !!! :");
scanf("%d",&menu);
if (menu == 1) {printf("\n\tnouveau fichier : "); scanf("%s",s_out);}
if (menu == 2)
{
printf("\n\tnouveau caractere de separation :");
printf("\n\t\t1 : retour a la ligne");
printf("\n\t\t2 : tabulation ");
printf("\n\t\t3 : espace ");
printf("\n\n\t\t0 : annuler ");
scanf("%d",&menu);
if (menu==1) { separator='\n';}
if (menu==2) { separator='\t';}
if (menu==3) { separator=' ';}
}
}while (menu!=0);
f_out = fopen(s_out,"w+");
mpz_out_str (f_out, 10, clee_publique );
fputc(separator,f_out);
mpz_out_str (f_out, 10, clee_privee );
putc(separator,f_out);
mpz_out_str (f_out, 10, clee_modulo );
fputc(separator,f_out);
fclose(f_out);
printf("\nappuyez sur une touche pour continuer");
getchar(); getchar();
}
else
{
printf("\nVous devez d'abord generer un set de Clees");
printf("\nappuyez sur une touche pour continuer");
getchar(); getchar();
}
break;
case 6: // Test de primalité
printf("Entrez un nombre, et nous vous dirrons s'il est premier ou pas :\n\t n = ");
gmp_scanf("%Zd",__n);
if (miller_rabin(__n, __rand_state, 100) == 1)
{ printf("\n PROBABLEMENT, ce nombre est probablement premier ."); }
else { printf("\n NON, ce nombre n'est pas premier !"); }
break;
default : printf(" -> Choix non reconnu !"); break;
}
}
return 0;
}
/**
* 取下一个可能的素数
* 参见java语言BigInteger.nextProbablePrime()实现
*/
NUT_API BigInteger next_prime(const BigInteger& n)
{
if (n <= 1)
return BigInteger(2);
const size_t SMALL_PRIME_THRESHOLD = 95;
const size_t DEFAULT_PRIME_CERTAINTY = 2;
const BigInteger SMALL_PRIME_PRODUCT(((uint64_t) 3) * 5 * 7 * 11 * 13 * 17 * 19 *
23 * 29 * 31 * 37 * 41);
BigInteger result(n);
++result;
// Fastpath for small numbers
if (result.bit_length() < SMALL_PRIME_THRESHOLD)
{
// Ensure an odd number
if (result.bit_at(0) == 0)
++result;
while(true)
{
// Do cheap "pre-test" if applicable
if (result.bit_length() > 6)
{
const int64_t r = (int64_t) (result % SMALL_PRIME_PRODUCT).to_integer();
if ((0 == r % 3) || (0 == r % 5) || (0 == r % 7) || (0 == r % 11) ||
(0 == r % 13) || (0 == r % 17) || (0 == r % 19) || (0 == r % 23) ||
(0 == r % 29) || (0 == r % 31) || (0 == r % 37) || (0 == r % 41))
{
result += 2;
continue; // Candidate is composite; try another
}
}
// All candidates of bit_length 2 and 3 are prime by this point
if (result.bit_length() < 4)
return result;
// The expensive test
if (miller_rabin(result, DEFAULT_PRIME_CERTAINTY))
return result;
result += 2;
}
}
// Start at previous even number
if (result.bit_at(0) == 1)
--result;
// Looking for the next large prime
size_t search_len = (result.bit_length() / 20) * 64;
while (true)
{
BitSieve search_sieve(result, (int) search_len);
const BigInteger candidate = search_sieve.retrieve(result, DEFAULT_PRIME_CERTAINTY);
if (!candidate.is_zero())
return candidate;
result += 2 * search_len;
}
}
