test_big_int02.hpp

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/*
 * Author: Sven Gothel <sgothel@jausoft.com>
 * Copyright (c) 2024 Gothel Software e.K.
 *
 * Permission is hereby granted, free of charge, to any person obtaining
 * a copy of this software and associated documentation files (the
 * "Software"), to deal in the Software without restriction, including
 * without limitation the rights to use, copy, modify, merge, publish,
 * distribute, sublicense, and/or sell copies of the Software, and to
 * permit persons to whom the Software is furnished to do so, subject to
 * the following conditions:
 *
 * The above copyright notice and this permission notice shall be
 * included in all copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
 * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
 * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
 * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
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 */
#include <iostream>
 
#include <jau/test/catch2_ext.hpp>
 
#include <jau/int_types.hpp>
#include <jau/mp/big_int.hpp>
 
using namespace jau;
using namespace jau::mp;
using namespace jau::int_literals;
 
static BigInt phi(const BigInt& P, const BigInt& Q) {
    const BigInt one(BigInt::one());
    return (P-one)*(Q-one);
}
/**
 * Returns e with `1 < e < Φ(n)`
 *
 * e must be co-prime to phi and smaller than phi
 */
static BigInt eval_e(BigInt e, const BigInt& phi) {
    const BigInt one(BigInt::one());
    while (e < phi && gcd(e, phi) != one ) {
        ++e;
    }
    return e;
}
 
TEST_CASE( "MP Big Encryption Test 00", "[big_int_t][arithmetic][math]" ) {
    std::cout << "big_int mp_word_bits " << std::to_string( mp_word_bits ) << std::endl;
    // textbook RSA (insecure)
    {
        BigInt pub_P(53), pub_Q(59), pub_n(pub_P*pub_Q);
        BigInt sec_phi = phi(pub_P, pub_Q);
        BigInt pub_e = eval_e(BigInt(2), sec_phi);
        std::cout << "Public Key:: P " << pub_P << ", Q " << pub_Q << ", n " << pub_n << ", e " << pub_e << std::endl;
 
        // Private key (d stands for decrypt)
        // choosing d such that it satisfies
        // d*e = 1 + k * totient
        BigInt sec_k = 2; // an arbitrary constant
        BigInt sec_d = ( sec_k * sec_phi + 1 ) / pub_e;
        std::cout << "Private Key:: phi " << sec_phi << ", k " << sec_k << ", d " << sec_d << std::endl;
 
        // big_int_t clear("0x112233445566778899aabbccddeeff0102030405060708090a0b0c0d0e0f");
        BigInt clear(1122);
        std::cout << "clear:: " << clear.to_hex_string(true) << std::endl;
 
        BigInt cipher = clear.mod_pow(pub_e, pub_n);
        std::cout << "encrypted:: " << cipher.to_hex_string(true) << std::endl;
 
        BigInt decrypted = cipher.mod_pow(sec_d, pub_n);
        std::cout << "decrypted:: " << decrypted.to_hex_string(true) << std::endl;
 
        REQUIRE( clear == decrypted );
    }
}