poj2447 RSA公钥加密破译

#include <stdio.h>

#include <stdlib.h>

#include <math.h>

#include <time.h>

#define MAXN 10

#define C 16381

long long min;

long long multi(long long a, long long b, long long n){

long long tmp = a % n, s = 0;

while(b){

if(b & 1) s = (s + tmp) % n;

tmp = (tmp + tmp) % n;

b >>= 1;

}

return s;

}

long long Pow(long long a, long long b, long long n){

long long tmp = a % n, s = 1;

while(b){

if(b & 1) s = multi(s, tmp, n);

tmp = multi(tmp, tmp, n);

b >>= 1;

}

return s;

}

int witness(long long a, long long n){

long long u = n - 1, t = 0, i, x, y;

while(!(u & 1)) u>>= 1, t ++;

x = Pow(a, u, n);

for(i = 1; i <= t; i ++){

y = multi(x, x, n);

if(y == 1 && x != 1&& x != n -1) return 1;

x = y;

}

if(x != 1) return 1;

return 0;

}

int test(long long n){

long long a;

int i;

if(n == 2) return 1;

if(n < 2 || !(n & 1)) return0;

srand((long long)time(0));

for(i = 0; i < MAXN; i ++){

a = ((long long) rand()) % (n - 2) + 2;

if(witness(a, n)) return 0;

}

return 1;

}

long long gcd(long long a, long long b){

return b ? gcd(b, a % b) : a;

}

long long pollard_rho(long long n, long long c){

long long x, y, d, i = 1, k = 2;

srand((long long)time(0));

x = ((long long) rand()) % (n - 1) + 1;

y = x;

while(1){

i ++;

x = (multi(x, x, n) + c) % n;

d = gcd(y - x + n, n);

if(d != 1 && d != n) returnd;

if(y == x) return n;

if(i == k) y = x, k <<= 1;

}

}

void find(long long n, long long c){

long long r;

if(n <= 1) return;

if(test(n)){

if(min > n) min = n;

return;

}

r = pollard_rho(n, c--);

find(r, c);

find(n / r, c);

}

int main(){

int t; 

long long i, s, n;

scanf("%d", &t);

while(t --){

scanf("%lld", &n);

if(test(n)){

printf("Prime\n");

continue;

}

min = n;

find(n, C);

printf("%lld\n", min);

}

return 0;

}