lab10

#include <iostream>

#include <cmath>

using namespace std;


int gcd(int a, int b) {

    if (b == 0)

        return a;

    return gcd(b, a % b);

}


long long modExp(long long base, long long exp, long long mod) {

    long long result = 1;

    while (exp > 0) {

        if (exp % 2 == 1)

            result = (result * base) % mod;

        base = (base * base) % mod;

        exp /= 2;

    }

    return result;

}


long long modInverse(long long e, long long phi) {

    long long m0 = phi, t, q;

    long long x0 = 0, x1 = 1;

    if (phi == 1)

        return 0;

    while (e > 1) {

        q = e / phi;

        t = phi;

        phi = e % phi;

        e = t;

        t = x0;

        x0 = x1 - q * x0;

        x1 = t;

    }

    if (x1 < 0)

        x1 += m0;

    return x1;

}


void generateKeys(long long &n, long long &e, long long &d) {

    long long p = 61, q = 53;

    n = p * q;

    long long phi = (p - 1) * (q - 1);

    e = 17;

    d = modInverse(e, phi);

}


long long encrypt(long long message, long long e, long long n) {

    return modExp(message, e, n);

}


long long decrypt(long long ciphertext, long long d, long long n) {

    return modExp(ciphertext, d, n);

}


int main() {

    long long n, e, d;

    generateKeys(n, e, d);


    cout << "Public Key (e, n): (" << e << ", " << n << ")" << endl;

    cout << "Private Key (d, n): (" << d << ", " << n << ")" << endl;


    long long message;

    cout << "Enter a message (as a number less than " << n << "): ";

    cin >> message;


    long long ciphertext = encrypt(message, e, n);

    cout << "Encrypted Message: " << ciphertext << endl;


    long long userCiphertext, userD, userN;

    cout << "\nEnter the encrypted message: ";

    cin >> userCiphertext;

    cout << "Enter the private key (d): ";

    cin >> userD;

    cout << "Enter the modulus (n): ";

    cin >> userN;


    long long decryptedMessage = decrypt(userCiphertext, userD, userN);

    cout << "Decrypted Message: " << decryptedMessage << endl;


    return 0;

}


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