Prime-Based Encryption Algorithm

A Feistel cipher that uses reptend primes (primes with repeating decimal expansions) for data transformation. Built with Python, it includes tools to visualize and analyze the cipher's behavior. Uses SHA-256 for key generation and a 3-stage nonlinear function.

Features

1. Reptend Prime-Based Feistel Network:

   • Uses cyclic patterns from reptend primes for data transformation
   • SHA-256 based key generation
   • Three-stage nonlinear function: cubic → reptend pattern → cubic
   • Substitution box built from prime's decimal expansion

2. Visualization Tools:

   • See the repeating patterns in 1/prime expansions
   • Watch how the nonlinear function transforms data
   • 3D view of the prime's cyclic behavior

Getting Started

Prerequisites

You'll need these Python libraries:

• matplotlib
• numpy
• sympy
• hashlib

Setup

1. Create a virtual environment:

python3 -m venv venv

2. Activate the environment:

source venv/bin/activate  # On Unix/macOS
# or
.\venv\Scripts\activate  # On Windows

3. Install dependencies:

pip install matplotlib numpy sympy

Usage

1. Basic Encryption and Decryption:

from main import CipherTest

message = "Hello, World!"
prime = 61    # A prime with good properties
key = 17      # Any number works
rounds = 10   # More rounds = more security
box_size = 256  # Size of substitution space

# Create cipher and run test
cipher = CipherTest(prime, key, rounds, box_size)
cipher.run_tests(message)

2. Visualizations:

from main import plot_decimal_pattern, plot_nonlinear_function, plot_3d_pattern

# View the patterns in 1/prime
plot_decimal_pattern(61)

# See how well inputs get scrambled
plot_nonlinear_function(61, range(1, 100))

# Look for patterns in 3D
plot_3d_pattern(61, get_decimal_sequence(61))

Core Functions

Encryption/Decryption

• encrypt_text(text, prime, key, rounds): Converts text to encrypted blocks
• decrypt_text(blocks, prime, key, rounds): Recovers original text from blocks

Key Generation

• generate_round_keys(key, rounds, prime): Creates round keys using SHA-256

Nonlinear Operations

• transform_value(x, prime): Three-stage nonlinear function
• substitute_value(value, prime): Maps inputs using prime patterns
• feistel_round(right, round_key, prime): Core Feistel network operation

Visualization

• plot_decimal_pattern(prime): Shows patterns in 1/prime
• plot_nonlinear_function(prime, range): Displays scrambling effectiveness
• plot_3d_pattern(prime, sequence): 3D view of patterns

Prime Number Tools

• find_reptend_primes(start, end): Finds primes with good properties
• get_decimal_sequence(prime): Gets patterns from 1/prime division

Testing

Run the test suite with:

python -m unittest test_encryption.py

The tests verify that:

1. Encryption followed by decryption recovers the original message
2. The process works with different message lengths
3. The cipher handles various prime numbers and key values