KHAN Encryption Algorithm

Author: Ayaz Khan
Date: 05/27/2024

Overview

The Keyed Hashing and Asymmetric Nonce (KHAN) encryption algorithm is a novel encryption system based on cyclic primes and unique movement patterns. This algorithm ensures that each character in the plaintext is mapped to a unique movement in the cyclic sequence, providing robust security through its unique mathematical foundations.

Features

• Unique Movement Patterns: Each character in the plaintext is mapped to a unique movement in the cyclic sequence.
• Cyclic Primes: Utilizes cyclic prime numbers and their sequences to generate encryption keys.
• Superposition Movements: Handles equal clockwise and anticlockwise movements efficiently.
• Overall Net Movement of Zero: Ensures that the net overall movement for each pattern sequence results in zero.
• Security: Designed to be resistant to common brute-force and frequency analysis attacks.

Mathematical Description

Let ( p ) be a cyclic prime number, and let ( S ) be the first ( p-1 ) digits of its cyclic sequence.

For any ( n ) and ( k ) such that ( 1 \leq k \leq n ), let:

[ S_k = \text{substring of } S \text{ starting at } k \text{ and length } \lfloor \log_{10}(p) \rfloor ]

Movements

• Clockwise Movement: [ \text{clockwise}k = (S_k - S{k+1}) \mod (p-1) ]
• Anticlockwise Movement: [ \text{anticlockwise}k = (S{k+1} - S_k) \mod (p-1) ]
• Minimal Movement: [ \text{movement}_k = \min(\text{clockwise}_k, \text{anticlockwise}_k) ]

Superposition Movements

A superposition movement occurs when the minimal movement is equal in both directions. The magnitude of the superposition movement is:

[ \text{superposition} = \frac{p-1}{2} ]

Net Overall Movement

The algorithm ensures that the overall net movement for each pattern sequence results in zero, thereby maintaining the integrity and consistency of the encryption:

[ \sum_{k=1}^{n} \text{movement}_k = 0 ]

Usage

Installation

First, install the necessary dependencies using pip:

pip install pycryptodome

Example Comparison Code

import time
import random
import string
from Crypto.PublicKey import RSA
from Crypto.Cipher import PKCS1_OAEP
from Crypto.Cipher import AES
from Crypto.Util.Padding import pad, unpad

# Define the KHAN encryption and decryption functions here (refer to your provided code)

# Function to generate random plaintext of a given length
def generate_plaintext(length):
    return ''.join(random.choice(string.ascii_letters + string.digits) for _ in range(length))

# Function to measure encryption and decryption time for Khan encryption
def measure_khan_encryption(khan_encrypt, khan_decrypt, plaintext):
    start_time = time.time()
    ciphertext, char_to_movement, movement_to_char, z_value, superposition_sequence = khan_encrypt(plaintext)
    encryption_time = time.time() - start_time

    start_time = time.time()
    decrypted_text = khan_decrypt(ciphertext, char_to_movement, movement_to_char, z_value, superposition_sequence)
    decryption_time = time.time() - start_time

    return encryption_time, decryption_time, decrypted_text

# Function to measure encryption and decryption time for RSA
def measure_rsa_encryption(plaintext):
    key = RSA.generate(2048)
    cipher_rsa = PKCS1_OAEP.new(key)
    
    start_time = time.time()
    ciphertext = cipher_rsa.encrypt(plaintext.encode())
    encryption_time = time.time() - start_time

    start_time = time.time()
    decrypted_text = cipher_rsa.decrypt(ciphertext).decode()
    decryption_time = time.time() - start_time

    return encryption_time, decryption_time, decrypted_text

# Function to measure encryption and decryption time for AES
def measure_aes_encryption(plaintext):
    key = ''.join(random.choice(string.ascii_letters + string.digits) for _ in range(16)).encode()
    cipher_aes = AES.new(key, AES.MODE_CBC)
    iv = cipher_aes.iv

    start_time = time.time()
    ciphertext = cipher_aes.encrypt(pad(plaintext.encode(), AES.block_size))
    encryption_time = time.time() - start_time

    start_time = time.time()
    cipher_aes = AES.new(key, AES.MODE_CBC, iv)
    decrypted_text = unpad(cipher_aes.decrypt(ciphertext), AES.block_size).decode()
    decryption_time = time.time() -......
# Placeholder functions for Khan encryption and decryption

```python
def khan_encrypt(plaintext):
    # Implement your Khan encryption algorithm here
    return plaintext, {}, {}, 0, []  # Placeholder

def khan_decrypt(ciphertext, char_to_movement, movement_to_char, z_value, superposition_sequence):
    # Implement your Khan decryption algorithm here
    return ciphertext  # Placeholder