16-Bit LFSR Simulator & Symmetric Stream Cipher Sandbox

An interactive desktop application built with Python and CustomTkinter designed to visualize the internal mechanics of a 16-bit Linear Feedback Shift Register (LFSR) Pseudo-Random Number Generator (PRNG) and demonstrate its real-time application in a symmetric stream cipher cryptographic algorithm.

---

🚀 Key Features

• Real-Time Matrix Visualization: Watch a $4 \times 4$ register grid update bit-by-bit dynamically. The final output gate (Index 15) is uniquely highlighted to track bit extrusion.
• Variable Speed Auto-Clock Engine: Features a precision clock engine toggle with an adjustable frequency slider spanning from manual single-stepping up to a rapid $20\text{ Hz}$ clock rate.
• Symmetric Encryption Sandbox: A cryptographically sound text-processing terminal that translates arbitrary plaintext string inputs into ASCII binary bits and encrypts them synchronously via bitwise XOR operations as the LFSR shifts.
• Infinite Keystream Tracker: Captures, holds, and auto-scrolls through the complete historical sequence of generated pseudo-random bits.

---

🧠 Core Cryptographic Concepts

Linear Feedback Shift Registers (LFSR)

An LFSR is a shift register whose input bit is a linear function of its previous state. The most common linear function is the Exclusive OR (XOR) logic gate. This simulator models a 16-bit system where the state updates on every clock pulse, shifting bits down the register line to produce a deterministic, pseudo-random sequence of bits with strong statistical properties.

The Stream Cipher Math

A stream cipher combines the plaintext digits with a pseudo-random cipher digit stream (the keystream). In this sandbox, encryption is achieved character-by-character using the bitwise Exclusive OR ($\oplus$) operator.

Each character typed into the input field is converted to its standard 8-bit ASCII binary equivalent. The cipher engine then processes individual bits using the classic symmetric rule:

$$Cipher_Bit = Plain_Bit \oplus Keystream_Bit$$

Because XOR is symmetric, passing the resulting ciphertext binary back through an identical keystream string decodes the message back to its original plaintext format perfectly:

$$Plain_Bit = Cipher_Bit \oplus Keystream_Bit$$

The output window automatically formats the ciphertext in clean 8-bit blocks (separated by spaces) to preserve readable byte boundaries.

---

🛠️ Installation & Setup

Prerequisites

• Python 3.8 or higher
• pip (Python package installer)

Step-by-Step Guide

1. Clone the Repository:

   git clone [https://github.com/Luke-Fu101/Multi-LFSR-PRNG.git](https://github.com/Luke-Fu101/Multi-LFSR-PRNG.git)
   cd Multi-LFSR-PRNG

2. Set Up a Virtual Environment (Recommended):

   python -m venv env
   source env/bin/activate        # macOS / Linux
   env\Scripts\activate           # Windows

3. Install Dependencies:

   pip install -r requirements.txt

4. Run the Application:

   python src/main.py