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 Perl?

RSA encryption in Perl 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 Perl library can help with RSA encryption?

Libraries like bigint are commonly used to handle the large numbers required for RSA encryption in Perl.

Dual Key (RSA) Encryption in Perl: A Mathematical Guide

Dual Key Encryption in Perl

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 Perl, 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 Perl 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 Perl 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 Perl 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.

Perl Example: Public and Private Key Encryption

In Perl, 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 Perl 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 Perl applications to securely handle sensitive information such as passwords, tokens, and confidential messages.

The Mathematics of Public Key Encryption | Math Explanation for Perl Kids

At its core, dual key encryption relies on the mathematical difficulty of factoring large numbers. Our Perl 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 Perl

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 Perl's bigint capability, we can handle the large-scale integer calculations required for secure encryption. Below, we explore the Perl 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 Perl module file;
Call it DualKeyEncryption.pm.
Type out the adjoining Perl 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: bigint is inbuilt in Perl.
You only need to use the bigint library.

The Perl code module for finding LCM is from the Primary Category.
Just make a copy of it into the current folder (project).

Why Use RSA in Perl?

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

Dual Key Encryption vs Symmetric Encryption | Explanation for Perl 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 Perl 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 Perl provides a strong foundation for learning advanced security and cryptography topics.

Key Takeaways from the Perl 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
Perl supports public key encryption through cryptographic APIs and libraries
This method is essential for secure communication on the web

Summary: Perl Dual Key Encryption Algorithm

By understanding RSA encryption in Perl, 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.

Perl Code for Dual Key Encryption - Module File

package DUALKEYENCRYPTION;

BEGIN {
    require Exporter;

    # for the sake of standard
    our $VERSION = 2017.10;

    # Inherit from exporter to export functions and variables
    our @ISA = qw(Exporter);

    # Functions and variables to be exported by default
    our @EXPORT_OK = qw(encodeWord decodeWord);
}

use warnings;
use strict;
use bigint;

my $semi_prime;

# simulate an object construct
sub new {
    my $self = shift;
    $semi_prime = shift;

    my $this = {};
    bless $this, $self;

    return $this;
}

##
# STEP VI:
##
sub encodeWord {
    shift;
    my $msg = shift;
    my $key = shift;
    my @encryption = ();
    my $x;
    for (0 .. $#{$msg}) {
        # get unicode of this character as x
        $x = ord($msg->[$_]);
        # use RSA to encrypt & save in base 16
        push (@encryption, substr (($x**$key % $semi_prime)->as_hex(), 2)); # remove hex designator('0x')
    }

    return \@encryption;
}

##
# STEP VII:
##
sub decodeWord {
    shift;
    my $code = shift;
    my $key = shift;
    my $decryption = "";
    my $c;
    for (0 .. $#{$code}) {
        # use RSA to decrypt
        $c = hex($code->[$_])**$key % $semi_prime;
        $decryption .= chr($c);
    }

    return $decryption;
}

1;

Perl Code for Dual Key Encryption - Main Class

#!/usr/bin/perl;

use strict;
use warnings;
use bigint;

use DUALKEYENCRYPTION;

##
# STEP I:
##
my $p1 = 101; # 1st prime
my $p2 = 401; # 2nd prime
##
# STEP II:
##
my $semi_prime = $p1 * $p2;

##
# STEP III:
##
use LCM;
my $lcm = LCM->new([$p1 - 1, $p2 - 1]);
$lcm = $lcm->getLCM();

##
# STEP IV:
##
# pick a random prime (public_key) that lies
# between 1 And LCM but Not a factor of LCM
my $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
my $i = 1;
while (($lcm * $i + 1) % $public_key != 0) {
$i += 1;
}

##
# STEP V:
##
my $private_key = ($i * $lcm + 1) / $public_key;

my @message = split(//, "merry xmas");
my $go_secure = DUALKEYENCRYPTION->new($semi_prime);

my $encrypted = $go_secure->encodeWord(\@message, $public_key);
print("\nMessage is '", join("", @message), "';\nEncrypted version is ", join(", ", @{$encrypted}));

my $decrypted = $go_secure->decodeWord($encrypted, $private_key);
print("\n\nDecrypted version is '", $decrypted, "'.");

print "\n\n";

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