What is dual key encryption?

Dual key encryption, also known as public/private key cryptography, uses two linked keys: a public key for encryption and a private key for decryption.

Is RSA an example of dual key encryption?

Yes. RSA is a widely used asymmetric encryption algorithm that relies on a public and private key pair.

Why is asymmetric encryption slower than symmetric encryption?

Asymmetric encryption uses complex mathematical operations, making it slower, but it provides stronger security for key exchange and authentication.

How does RSA encryption work in C++?

RSA encryption in C++ uses prime numbers and modular arithmetic to generate public and private keys. Messages are encrypted with the public key and decrypted with the private key.

What mathematical concepts are needed for RSA encryption?

RSA encryption requires knowledge of prime number factorization, the Greatest Common Divisor (GCD), Lowest Common Multiple (LCM), and calculating the modular multiplicative inverse.

Why are prime numbers important in RSA encryption?

Prime numbers are used to generate the modulus in RSA. The difficulty of factoring large semi-primes ensures the security of the encryption.

Which C++ library can help with RSA encryption?

Libraries like BigInteger are commonly used to handle the large numbers required for RSA encryption in C++.

Dual Key (RSA) Encryption in C++: A Mathematical Guide

Dual Key Encryption in C++

Dual key encryption, also known as public/private key cryptography, is a core concept in modern data security. It is widely used in secure communications, digital certificates, and encrypted web applications. In this tutorial, you will learn how public and private key encryption works in C++, why it is classified as asymmetric encryption, and how dual keys are used to securely encrypt and decrypt data.

This explanation is designed for tertiary-level students and beginners who want a clear, practical understanding of cryptography concepts without unnecessary complexity.

What Is Dual Key (Public/Private Key) Encryption? | Explanation for C++ Kids

Dual key encryption is an encryption method that uses two mathematically related keys:

A public key, which is shared openly and used to encrypt data
A private key, which is kept secret and used to decrypt data

This approach is formally known as public key cryptography or asymmetric encryption. Unlike symmetric encryption, where the same key is used for both encryption and decryption, dual key encryption ensures that encrypted data can only be decrypted by the intended recipient.

Why Asymmetric Encryption Is Important | Explanation for C++ Kids

Asymmetric encryption solves a major problem in secure communication: key sharing. Since the public key can be distributed freely, there is no need to transmit a secret key over an insecure channel.

Key advantages include:

Improved security for data transmission
Safe communication over public networks
Strong authentication mechanisms
Foundation for HTTPS, SSL/TLS, and digital signatures

Because of these benefits, public/private key encryption is commonly used in web applications, secure messaging systems, and online banking platforms.

How Dual Key Encryption Works (Step by Step) | Explanation for C++ Kids

The dual key encryption process follows a logical sequence:

A key pair is generated (public key and private key)
The sender encrypts data using the public key
The encrypted message is transmitted
The recipient decrypts the message using the private key

Only the matching private key can decrypt the data, even though the public key is visible to everyone. This is what makes asymmetric cryptography secure.

C++ Example: Public and Private Key Encryption

In C++, asymmetric encryption can be implemented using cryptographic libraries or the Web Crypto API. The general workflow remains the same regardless of the specific implementation.

A typical C++ public/private key encryption process includes:

Generating an RSA key pair
Encrypting data with the public key
Decrypting encrypted data with the private key

This approach allows C++ applications to securely handle sensitive information such as passwords, tokens, and confidential messages.

The Mathematics of Public Key Encryption | Math Explanation for C++ Kids

At its core, dual key encryption relies on the mathematical difficulty of factoring large numbers. Our C++ RSA encryption tutorial focuses on the relationship between prime numbers and modular arithmetic. To generate a secure pair of keys, we follow a rigorous mathematical process:

Prime Selection: Choosing two large prime numbers ( and ) to create a semi-prime modulus.
LCM Calculation: Determining the Lowest Common Multiple of $(p-1)$ and $(q-1)$.
Key Generation: Selecting a Public Key that is coprime to the LCM.
The Inverse: Calculating the Private Key as the modular multiplicative inverse of the Public Key.
Encrypt data: $[Unicode(data)]^{public\_key} % semi_prime = encoded_data;$
Decrypt data: $[encoded\_data]^{private\_key} % semi_prime = original data;$

Implementing RSA Logic in C++

While many modern applications use the built-in WebCrypto API, writing a manual RSA implementation is the best way to grasp how ciphertext and plaintext interact.

Using C++'s BigInteger capability, we can handle the large-scale integer calculations required for secure encryption. Below, we explore the C++ code required to transform a standard Unicode string into an encrypted hexadecimal array, ensuring that only the holder of the private key can reverse the process.

Create a new C++ class file;
Call it DualKeyEncryption.
Type out the adjoining C++ code for encrypting and decrypting a chunk of data using a Public Key - Private Key pair.

By The Way: The encryption algorithm described in the above steps is called R.S.A. algorithm; and coming up with an algorithm that can factor very large semi primes into their prime factors in linear time is called the R.S.A. problem.

Also noteworthy is the fact that there are other ways of implementing an open-lock-only encryption algorithm; like the Logarithm Encryption, e.t.c.

Important: We obligatorily wrote a BigInteger class for use with this section.
It is freely available on Github or you can download it as a zip file here.

The C++ algorithm class for finding LCM has been explained in the Primary Category.
Create a new C++ class file called LCM in your current project and copy the L.C.M. code into it.

Why Use RSA in C++?

Educational Value: Great for learning cryptography concepts.
Practical Applications: Secure login systems, encrypted messaging, and digital signatures.
Flexibility: C++ runs everywhere — windows, linux, and android.

Dual Key Encryption vs Symmetric Encryption | Explanation for C++ Kids

It is important to distinguish between symmetric encryption and dual key encryption:

Symmetric vs Asymmetric Encryption Differences
Feature	Symmetric Encryption	Dual Key Encryption
*Number of keys*	One shared key	Two separate keys
*Security*	Lower for key exchange	Higher for communication
*Speed*	Faster	Slower
*Common use*	Data storage	Secure communication

In practice, many systems use both methods together, combining the speed of symmetric encryption with the security of asymmetric encryption.

Common Uses of Public/Private Key Cryptography | Explanation for C++ Kids

Public and private key encryption is used in many real-world applications, including:

Secure web communication (HTTPS)
Digital certificates and authentication
Secure email systems
Encrypted file sharing
Secure API communication

Understanding dual key encryption in C++ provides a strong foundation for learning advanced security and cryptography topics.

Key Takeaways from the C++ Dual Key Encryption Algorithm

Dual key encryption uses a public key for encryption and a private key for decryption
It is also known as public/private key cryptography or asymmetric encryption
C++ supports public key encryption through cryptographic APIs and libraries
This method is essential for secure communication on the web

Summary: C++ Dual Key Encryption Algorithm

By understanding RSA encryption in C++, you gain insight into how modern cryptography protects sensitive information. Whether you're a student exploring modular arithmetic or a developer implementing public/private key cryptography, this tutorial provides the foundation you need.

C++ Code for Dual Key Encryption - Header File

#pragma once

#include "BigInteger.h"
#include <string>
#include <vector>

using namespace std;

class DualKeyEncryption
{
public:
    DualKeyEncryption(int);
    virtual ~DualKeyEncryption();

    vector<string> encodeWord(vector<char>, int);
    string decodeWord(vector<string>, int);

private:
    string semi_prime;
};

C++ Code for Dual Key Encryption - Class File

#include "stdafx.h"
#include "DualKeyEncryption.h"

DualKeyEncryption::DualKeyEncryption(int semi_p)
{
    semi_prime = to_string(semi_p);
}

/*
* STEP VI:
*/
vector<string> DualKeyEncryption::encodeWord(vector<char> msg, int key) {
    vector<string> encryption = {};
    string x;
    for (size_t i = 0; i < msg.size(); i++) {
        // get unicode of this character as x
        x = to_string((int)msg[i]);
        // use RSA to encrypt & save in base 16
        encryption.push_back(BigInteger::decToHex(BigInteger::powerModulus(x, key, semi_prime)));
    }

    return encryption;
}

/*
* STEP VII:
*/
string DualKeyEncryption::decodeWord(vector<string> code, int key) {
    string decryption = "";
    string char_string;
    int c;
    for (size_t i = 0; i < code.size(); i++) {
        char_string = "";
        // use RSA to decrypt
        c = stoi(BigInteger::powerModulus(BigInteger::hexToDec(code[i]), key, semi_prime));
        char_string += (char)c;
        decryption += char_string;
    }

    return decryption;
}

DualKeyEncryption::~DualKeyEncryption()
{
}

C++ Code for Dual Key Encryption - Main Class

#include "stdafx.h"
#include "LCM.h"
#include "DualKeyEncryption.h"

#include <iostream>

using namespace std;

int main() {
    /*
    * STEP I:
    */
    unsigned p1 = 101; // 1st prime
    unsigned p2 = 401; // 2nd prime
    /*
    * STEP II:
    */
    int semi_prime = p1 * p2;

    /*
    * STEP III:
    */
    // get L.C.M. of p1-1 and p2-1
    LCM l_c_m({ p1 - 1, p2 - 1 });
    int lcm = l_c_m.getLCM();

    /*
    * STEP IV:
    */
    // pick a random prime (public_key) that lies
    // between 1 and LCM but not a factor of LCM
    int public_key = 313;

    // find 'public_key' complement - private_key - such that
    // (public_key * private_key) % LCM = 1
    //this involves some measure of trial and error
    int i = 1;
    while ((lcm * i + 1) % public_key != 0) {
        i++;
    }
    /*
    * STEP V:
    */
    int private_key = (i * lcm + 1) / public_key;

    vector<char> message = { 'm', 'e', 'r', 'r', 'y', ' ', 'x', 'm', 'a', 's' };

    DualKeyEncryption go_secure(semi_prime);
    vector<string> encrypted = go_secure.encodeWord(message, public_key);
    string disp = "", msg = "";
    for (size_t i = 0; i < encrypted.size(); i++) {
        disp += encrypted[i] + "; ";
        msg += message[i];
    }
    cout << "Message is '" << msg << "';\nEncrypted version is " << disp << endl;

    string decrypted = go_secure.decodeWord(encrypted, private_key);
    cout << "\n\nDecrypted version is '" << decrypted << "'.";

    return 0;
}

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