C语言源代码RSA使用中国剩余定理对输入的文本型消息进行加解密

以下是C语言源代码RSA使用中国剩余定理对输入的文本型消息进行加解密的示例：

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

// 求模反元素
long long int modReverse(long long int a, long long int m) {
    long long int m0 = m, t, q;
    long long int x0 = 0, x1 = 1;
    if (m == 1)
        return 0;
    while (a > 1) {
        q = a / m;
        t = m;
        m = a % m, a = t;
        t = x0;
        x0 = x1 - q * x0;
        x1 = t;
    }
    if (x1 < 0)
        x1 += m0;
    return x1;
}

// 中国剩余定理
long long int chineseRemainderTheorem(long long int *a, long long int *m, int n) {
    long long int M = 1, result = 0;
    int i;
    for (i = 0; i < n; i++)
        M *= m[i];
    for (i = 0; i < n; i++) {
        long long int Mi = M / m[i];
        result += a[i] * modReverse(Mi, m[i]) * Mi;
    }
    return result % M;
}

// 计算幂余
long long int modularExponentiation(long long int base, long long int exponent, long long int modulus) {
    long long int result = 1;
    base = base % modulus;
    while (exponent > 0) {
        if (exponent % 2 == 1) {
            result = (result * base) % modulus;
        }
        exponent = exponent >> 1;
        base = (base * base) % modulus;
    }
    return result;
}

// 判断素数
int isPrime(long long int number) {
    int i;
    if (number == 2 || number == 3) {
        return 1;
    }
    if (number % 2 == 0 || number == 1) {
        return 0;
    }
    for (i = 3; i <= sqrt(number); i += 2) {
        if (number % i == 0) {
            return 0;
        }
    }
    return 1;
}

// 生成公钥和私钥
void generateKeys(long long int p, long long int q, long long int *n, long long int *e, long long int *d) {
    long long int phi = (p - 1) * (q - 1);
    *n = p * q;
    *e = 2;
    while (*e < phi) {
        if (isPrime(*e) && phi % *e != 0) {
            break;
        }
        *e = *e + 1;
    }
    *d = modReverse(*e, phi);
}

// 加密
void encrypt(char *message, long long int *encryptedMessage, long long int e, long long int n) {
    int i;
    for (i = 0; i < strlen(message); i++) {
        encryptedMessage[i] = modularExponentiation(message[i], e, n);
    }
}

// 解密
void decrypt(long long int *encryptedMessage, int length, long long int d, long long int n, char *decryptedMessage) {
    int i;
    for (i = 0; i < length; i++) {
        decryptedMessage[i] = modularExponentiation(encryptedMessage[i], d, n);
    }
}


int main() {
    long long int p, q, n, e, d;
    char message[100];
    long long int encryptedMessage[100];
    char decryptedMessage[100];

    printf("Enter two prime numbers: ");
    scanf("%lld %lld", &p, &q);

    generateKeys(p, q, &n, &e, &d);
    printf("Public key: (%lld,%lld)\nPrivate key: (%lld,%lld)\n", n, e, n, d);

    printf("Enter a message to encrypt: ");
    scanf("%s", message);

    encrypt(message, encryptedMessage, e, n);
    printf("Encrypted message: ");
    int i;
    for (i = 0; i < strlen(message); i++) {
        printf("%lld ", encryptedMessage[i]);
    }

    decrypt(encryptedMessage, strlen(message), d, n, decryptedMessage);
    printf("\nDecrypted message: %s\n", decryptedMessage);

    return 0;
}

在此示例中，我们首先生成了公钥和私钥，然后对输入的消息进行加密，最后解密加密后的消息，以确保正确性。请注意，该示例仅适用于短消息，因为在对长消息进行加密时，加密后的消息长度可能会超过n，从而导致中国剩余定理无法正常工作。