https://github.com/bitbynik/substitution_cipher

SIL765 Assignment-1
https://github.com/bitbynik/substitution_cipher

cryptanalysis decipher iitd security substitution-cipher

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SIL765 Assignment-1

• Host: GitHub
• URL: https://github.com/bitbynik/substitution_cipher
• Owner: BitByNIK
• Created: 2025-01-09T08:59:41.000Z (about 1 year ago)
• Default Branch: main
• Last Pushed: 2025-01-19T10:44:34.000Z (12 months ago)
• Last Synced: 2025-01-19T11:29:22.387Z (12 months ago)
• Topics: cryptanalysis, decipher, iitd, security, substitution-cipher
• Language: Python
• Homepage:
• Size: 2.23 MB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

          
# Substitution Cipher Decoder

This project is a Python-based implementation of a substitution cipher decoder. It uses **hill climbing**, a search optimization algorithm, to iteratively improve decryption keys. By analyzing patterns in the ciphertext and comparing them with English language characteristics, the script deciphers encrypted text.

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## How It Works

A substitution cipher replaces each letter in plaintext with a specific character (e.g., numbers, symbols, or other letters). To decrypt such a cipher, the script finds the mapping between ciphertext characters and plaintext letters.

### Steps in the Decryption Process

1. **Initial Setup:**

   - The script starts with a **random key**, mapping ciphertext characters to plaintext letters.

   - A key represents how each ciphertext character translates into a plaintext letter.

2. **Fitness Calculation:**

   - The script evaluates how good the current key is by calculating a **fitness score**.

   - This score measures how similar the decrypted text is to English using the frequency of groups of four letters (called **quadgrams**).

   - Formula used for fitness:

     $$\text{Fitness} = \sum_{\text{quadgram}} \log(\text{QF}[\text{quadgram}])$$

     - **QF** represents the frequency of quadgrams in standard English text.

     - Taking the logarithm ensures to avoid underflow because frequencies can be small.

3. **Heuristic-Based Key Selection:**

   - A **heuristic function** is used to prioritize which parts of the key to adjust.

   - The heuristic identifies ciphertext characters whose frequencies differ the most from expected English frequencies.

   - Formula for the heuristic:

     $$H(b) = \max(1, |\text{FC}(b) - \text{FE}(\text{E}^{-1}(b))|)$$

     Where:

     - $$H(b)$$: Heuristic score for a ciphertext letter $$b$$.

     - $$\text{FC}(b)$$: Rank of $$b$$ in ciphertext frequencies.

     - $$\text{FE}(a)$$: Rank of the corresponding plaintext letter $$a$$ in English frequencies.

   - A ciphertext letter $$b$$ with a large heuristic value is **more likely to be swapped** because it is far from its expected frequency rank. The goal is to quickly minimize these differences.

   - Once a character $$b$$ is selected, it is swapped with another randomly chosen character in the key.

4. **Key Evaluation:**

   - The script decrypts the text using the modified key.

   - If the fitness score improves, the new key is kept. Otherwise, it is discarded.

5. **Stopping Condition:**

   - If the fitness score does not improve after \( T \) iterations, the process stops.

   - The entire procedure is repeated multiple times, and the best key across all attempts is chosen.

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## Why Use a Heuristic?

The heuristic focuses on ciphertext letters whose observed frequencies differ the most from expected English frequencies. This:

- **Speeds Up Convergence:** Quickly minimizes large frequency mismatches.

- **Improves Accuracy:** Guides the algorithm to better keys, especially for longer ciphertexts where frequency distributions are more reliable.

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## Features

- **Hill Climbing Optimization:** Iteratively improves the decryption key using fitness scoring.

- **Quadgram-Based Scoring:** Evaluates how "English-like" the decrypted text is.

- **Heuristic Guidance:** Targets the most impactful key adjustments to improve efficiency.

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## Requirements

- **Python 3.6 or Higher**

- A file containing a large sample of English text is required to calculate the letter and quadgram frequencies. Here, we have used big.txt, which should be a plain text file with diverse English content (e.g., books, articles). The quality of decryption improves with a larger and more representative reference text.

### Dependencies:

- Built-in Python libraries: `collections`, `math`, `random`.

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