平方-乘算法与Miller-Rabin素性测试算法

平方-乘算法

代码实现

a=19244;h=17;n=221
a=input("a^h(mod n)\na");h=input("h");n=input("n")
h=int(h);a=int(a);n=int(n)
H=bin(h)
z=a
#print(a,'----',H[2])
for i in range(3,H.__len__()):
    if(H[i]=='1'):
        a=(a*a)%n
        a=(a*z)%n
    if(H[i]=='0'):
        a=(a*a)%n
print(a)

测试用例

Miller-Rabin素性测试算法

代码实现

#include <iostream>
#include <cmath>
using namespace std;
int modpow(int base, int exp, int mod) {
    int cnt = 1;
    base %= mod;
    while (exp > 0) {
        if (exp % 2 == 1) {
            cnt = (cnt * base) % mod;
        }
        exp >>= 1;
        base = (base * base) % mod;
    }

    return cnt;
}
bool MR(int n, int a) {
    if (n <= 1 || n == 4) {
        return false;
    }
    if (n <= 3) {
        return true;
    }

    int d = n - 1;
    while (d % 2 == 0) {
        d /= 2;
    }
    int x = modpow(a, d, n);
    if (x == 1 || x == n - 1) {
        return true;
    }
    while (d != n - 1) {
        x = (x * x) % n;
        d *= 2;
        if (x == 1) {
            return false;
        }
        if (x == n - 1) {
            return true;
        }
    }
    return false;
}
int main() {
    int n, a;
    n=2017,a=19;
    cout<<"待测正整数为"<<n<<" 基数为"<<a<<endl;
    //cin >> n >> a;
    if (MR(n, a)) {
        cout << n << " 是素数" << endl;
    } else {
        cout << n << " 不是素数" << endl;
    }

    return 0;
}