RSA using the C++ interface of the GMP library

rsa.cpp

/*
CmakeLists.txt:

cmake_minimum_required(VERSION 3.6)
project(rsa)
set(CMAKE_CXX_STANDARD 14)
set(SOURCE_FILES main.cpp)
add_executable(rsa ${SOURCE_FILES})
target_link_libraries(rsa gmpxx gmp)
*/

#include <iostream>
#include <gmpxx.h>
#include <assert.h>
#include <map>

using std::cout;
using std::endl;
using std::pair;
using std::map;
using std::make_pair;
using std::string;

using keyset = map<string, pair<mpz_class, mpz_class>>;

// Calculation of the RSA keyset using GMP
// https://gmplib.org/
// Based on an earlier version in PHP
// https://gist.github.com/akosma/9058c43c76da2e6691637b1332058ddc
keyset rsa_keys(const mpz_t p, const mpz_t q, const mpz_t e) {
    mpz_t d, lambda, gcd;
    mpz_inits(d, lambda, gcd, NULL);

    mpz_class pc{p};
    mpz_class qc{q};
    mpz_class nc = pc * qc;
    mpz_class pc_1 = pc - 1;
    mpz_class qc_1 = qc - 1;

    mpz_lcm(lambda, pc_1.get_mpz_t(), qc_1.get_mpz_t());
    mpz_class lambdac{lambda};
    cout << "lambda = " << lambdac << endl;

    // e must be bigger than 1
    mpz_class ec{e};
    assert(ec > 1);

    // e must be smaller than lambda
    assert(ec < lambdac);

    // GCD(e, lambda) must be 1
    mpz_gcd(gcd, e, lambda);
    mpz_class gcdc{gcd};
    assert(gcdc == 1);

    mpz_invert(d, e, lambda);
    mpz_class dc{d};

    // e * d MOD lambda must be 1
    mpz_class calc = ec * dc % lambdac;
    assert(calc == 1);

    keyset result{{"public",  make_pair(ec, nc)},
                  {"private", make_pair(dc, nc)}};

    mpz_clears(d, gcd, lambda, NULL);

    return result;
}

// RSA encryption
mpz_class encrypt(const mpz_t message,
                  const mpz_t e,
                  const mpz_t n) {
    mpz_t encrypted;
    mpz_init(encrypted);
    mpz_powm(encrypted, message, e, n);
    mpz_class result{encrypted};
    mpz_clear(encrypted);
    return result;
}

// RSA decryption
mpz_class decrypt(const mpz_t encrypted,
                  const mpz_t d,
                  const mpz_t n) {
    mpz_t original;
    mpz_init(original);
    mpz_powm(original, encrypted, d, n);
    mpz_class result{original};
    mpz_clear(original);
    return result;
}

void display(mpz_class message, keyset k) {
    mpz_class e = k["public"].first;
    mpz_class d = k["private"].first;
    mpz_class n = k["public"].second;

    mpz_class encrypted = encrypt(message.get_mpz_t(), e.get_mpz_t(), n.get_mpz_t());
    mpz_class decrypted = decrypt(encrypted.get_mpz_t(), d.get_mpz_t(), n.get_mpz_t());

    // The decrypted message must be equal to the original
    assert(message == decrypted);

    cout << "Public key = (e: " << e << ", n: " << n << ")" << endl;
    cout << "Private key = (d: " << d << ", n: " << n << ")" << endl;
    cout << "Original message: " << message << endl;
    cout << "Encrypted message: " << encrypted << endl;
    cout << "Decrypted message: " << decrypted << endl;
    cout << endl;
}

template<typename T>
void display(T msg, T pi, T qi, T ei) {
    cout << "Initializing with p = " << pi << ", q = " << qi << ", e = " << ei << endl;

    mpz_t n, d;
    mpz_inits(n, d, NULL);

    mpz_class p{pi};
    mpz_class q{qi};
    mpz_class e{ei};
    mpz_class original{msg};

    auto k = rsa_keys(p.get_mpz_t(), q.get_mpz_t(), e.get_mpz_t());
    display(original, k);
    mpz_clears(n, d, NULL);
}

int main() {

    // Example taken from Wikipedia
    // https://en.wikipedia.org/wiki/RSA_(cryptosystem)#Key_generation
    display(65, 61, 53, 17);

    // Example from Twitter
    // https://twitter.com/kosamari/status/838738015010848769
    mpz_class msg{123};
    mpz_class n{323};
    mpz_class e{5};
    mpz_class d{29};
    keyset k{{"public",  make_pair(e, n)},
             {"private", make_pair(d, n)}};
    display(msg, k);

    // Very small prime numbers
    display(123, 13, 19, 17);

    // With some prime numbers from
    // http://www.bigprimes.net/
    display(67890, 541, 461, 107);
    display(123456, 1181, 929, 173);

    // The PHP version takes around 10 seconds on a MacBook Air
    display(123456, 1181, 929, 1987);

    // The PHP takes around 40 seconds in a MacBook Air
    display(123456, 1181, 929, 17);

    // Very big numbers; using Mersenne primes,
    // something impossible in the PHP version
    display("1111119999999999911111111",
            "162259276829213363391578010288127",
            "618970019642690137449562111",
            "170141183460469231731687303715884105727");

    return 0;
}

Hey did this compile for you?
If so, what compiler are you using?

Hey @selango2017 I have just tried this and it did work with me.
Be sure to have copied the CMakeList or, otherwise, compile with -lgmpxx -lgmp options.