Miller-Rabin素性检验算法C语言

Miller-Rabin 素性检验算法是一种基于随机化的素性检验算法。下面是一个用 C 语言实现的 Miller-Rabin 素性检验算法的示例代码：

#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include <math.h>

int modular_exponentiation(int base, int exponent, int modulus)
{
    int result = 1;
    while (exponent > 0)
    {
        if (exponent % 2 == 1)
        {
            result = (result * base) % modulus;
        }
        base = (base * base) % modulus;
        exponent = exponent / 2;
    }
    return result;
}

int miller_rabin(int n, int k)
{
    if (n <= 1 || n == 4)
    {
        return 0;
    }
    if (n <= 3)
    {
        return 1;
    }
    int d = n - 1;
    while (d % 2 == 0)
    {
        d = d / 2;
    }
    for (int i = 0; i < k; i++)
    {
        int a = 2 + rand() % (n - 3);
        int x = modular_exponentiation(a, d, n);
        if (x == 1 || x == n - 1)
        {
            continue;
        }
        int j;
        for (j = 0; j < (int)log2(n - 1); j++)
        {
            x = (x * x) % n;
            if (x == 1)
            {
                return 0;
            }
            if (x == n - 1)
            {
                break;
            }
        }
        if (j == (int)log2(n - 1))
        {
            return 0;
        }
    }
    return 1;
}

int main()
{
    srand(time(NULL));
    int n, k;
    printf("Enter a number to check if it is prime: ");
    scanf("%d", &n);
    printf("Enter the number of iterations for the test: ");
    scanf("%d", &k);
    if (miller_rabin(n, k))
    {
        printf("%d is probably prime.\n", n);
    }
    else
    {
        printf("%d is composite.\n", n);
    }
    return 0;
}

这个程序中，`modular_exponentiation` 函数用于计算模幂，`miller_rabin` 函数用于执行 Miller-Rabin 素性检验。在 `main` 函数中，用户输入要检验的数和测试的迭代次数，然后调用 `miller_rabin` 函数进行素性检验。最终输出结果。