C++实现的Miller-Rabin素性测试程序

来源：互联网发布：安徽继远软件知乎编辑：程序博客网时间：2024/06/03 20:51

Miller-Rabin素性测试算法是概率算法，不是确定算法。然而测试的计算速度快，比较有效，被广泛使用。

另外一个值得介绍的算法是AKS算法，是三位印度人发明的，AKS是他们的姓氏首字母。ASK算法是确定算法，其时间复杂度相当于多项式的，属于可计算的算法。

代码来自Sanfoundry的C++ Program to Implement Miller Rabin Primality Test。

源程序如下：

/*  * C++ Program to Implement Miller Rabin Primality Test */#include <iostream>#include <cstring>#include <cstdlib>#define ll long longusing namespace std;  /*  * calculates (a * b) % c taking into account that a * b might overflow  */ll mulmod(ll a, ll b, ll mod){    ll x = 0,y = a % mod;    while (b > 0)    {        if (b % 2 == 1)        {                x = (x + y) % mod;        }        y = (y * 2) % mod;        b /= 2;    }    return x % mod;}/*  * modular exponentiation */ll modulo(ll base, ll exponent, ll mod){    ll x = 1;    ll y = base;    while (exponent > 0)    {        if (exponent % 2 == 1)            x = (x * y) % mod;        y = (y * y) % mod;        exponent = exponent / 2;    }    return x % mod;}   /* * Miller-Rabin primality test, iteration signifies the accuracy */bool Miller(ll p,int iteration){    if (p < 2)    {        return false;    }    if (p != 2 && p % 2==0)    {        return false;    }    ll s = p - 1;    while (s % 2 == 0)    {        s /= 2;    }    for (int i = 0; i < iteration; i++)    {        ll a = rand() % (p - 1) + 1, temp = s;        ll mod = modulo(a, temp, p);        while (temp != p - 1 && mod != 1 && mod != p - 1)        {            mod = mulmod(mod, mod, p);            temp *= 2;        }        if (mod != p - 1 && temp % 2 == 0)        {            return false;        }    }    return true;}//Mainint main(){    int iteration = 5;    ll num;    cout<<"Enter integer to test primality: ";    cin>>num;    if (Miller(num, iteration))        cout<<num<<" is prime"<<endl;    else        cout<<num<<" is not prime"<<endl;    return 0;}

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