This repository represents ongoing experimental research in lightweight cryptographic optimization and does not claim production-ready cryptographic security guarantees.
# Lightweight S-Box Optimization Framework

## Overview

This repository contains a modular cryptographic optimization framework for the discovery and analysis of lightweight S-boxes using a Memetic Algorithm.

The framework focuses on the generation, evaluation, and optimization of 5x5 S-boxes for lightweight cryptographic applications.

The project combines:

- Evolutionary computation
- Memetic optimization
- Cryptographic property evaluation
- Lightweight security analysis
- Logic complexity evaluation
- Linearly equivalent S-box transformations

The framework was developed as part of research into lightweight cryptography and secure S-box construction.

---

# Repository Structure

```text
project/
│
├── algorithms/
│   ├── helpers.py
│   ├── fitness.py
│   └── memetic_algorithm.py
│
├── metrics/
│   ├── differential_metrics.py
│   ├── linear_metrics.py
│   ├── bic_sac.py
│   ├── boomerang_uniformity.py
│   ├── logical_complexity.py
│   ├── utils.py
│   └── vto.py
│
├── transformations/
│   └── linear_equivalence.py
│
├── analysis/
│   ├── speed_analysis.py
│   ├── comparison_analysis.py
│   └── invariant_property_analysis.md
│
├── config/
│   └── settings.py
│
├── requirements.txt
├── README.md
└── .gitignore

---

Core Components

algorithms/

Contains the core optimization engine.

memetic_algorithm.py

Implements:

• population evolution
• mutation
• crossover
• elitism
• local search
• memetic improvement
• optimization orchestration

fitness.py

Implements the weighted fitness evaluation system used to score S-box candidates.

helpers.py

Contains reusable optimization helper functions such as:

• random S-box generation
• normalization and scaling functions

---

metrics/

Contains cryptographic evaluation metrics.

differential_metrics.py

Implements:

• differential branch number
• differential probability
• differential bound
• single-bit differential analysis

linear_metrics.py

Implements:

• linear approximation analysis
• maximal linear bias evaluation

bic_sac.py

Implements:

• Bit Independence Criterion (BIC)
• Strict Avalanche Criterion (SAC)

boomerang_uniformity.py

Implements:

• Boomerang Connectivity Table (BCT)
• Boomerang Uniformity (BU)

vto.py

Implements:

• Revisited Transparency Order (VTO)

logical_complexity.py

Implements:

• Espresso-based logic minimization
• logical complexity estimation

utils.py

Contains reusable utility functions used across metrics.

---

transformations/

Contains S-box transformation and equivalence operations.

linear_equivalence.py

Implements:

• linearly equivalent S-box generation
• random equivalent transformations
• canonical S-box generation
• permutation-XOR equivalence analysis

---

analysis/

Contains benchmarking, experimentation, and evaluation workflows.

speed_analysis.py

Implements:

• runtime benchmarking
• statistical timing analysis
• metric performance evaluation

comparison_analysis.py

Implements:

• S-box comparison workflows
• experimental evaluation pipelines
• cryptographic property comparison

invariant_property_analysis.md

Documents:

• invariant cryptographic properties
• variant cryptographic properties
• affine-equivalence behaviour
• optimization-aware property categorization

---

config/

Contains framework configuration files.

settings.py

Contains:

• optimization parameters
• population settings
• mutation rates
• cache sizes
• framework constants
• external tool paths

---

Main Features

• Modular memetic optimization framework
• Lightweight cryptographic analysis
• Multi-objective fitness evaluation
• Configurable optimization parameters
• Logic complexity estimation using Espresso
• Reusable transformation engine
• Support for cryptographic experimentation
• Structured framework architecture

---

Cryptographic Properties Evaluated

The framework evaluates several important cryptographic properties:

• Differential Branch Number
• Differential Probability
• Differential Bound
• Linear Approximation Bound
• Linear Bias
• Boomerang Uniformity
• BIC-SAC
• Revisited Transparency Order (VTO)
• Logic Complexity
• Single-Bit Differential Analysis

---

Requirements

Python Dependencies

The framework requires:

numpy
sage
matplotlib

Additional standard Python libraries used:

• functools
• random
• math
• subprocess
• logging
• statistics
• itertools
• time

---

External Dependencies

Espresso Logic Minimizer

The framework uses Espresso for logic minimization and logical complexity evaluation.

Example configuration:

ESPRESSO_PATH = "path/to/Espresso.exe"

Configured in:

config/settings.py

---

Example Execution

Run the Memetic Algorithm

python algorithms/memetic_algorithm.py

Run Speed Analysis

python analysis/speed_analysis.py

---

Example Output

The framework reports:

• best discovered S-box
• fitness score
• differential metrics
• linear metrics
• boomerang uniformity
• BIC-SAC
• VTO
• logical complexity
• statistical analysis results

---

Research Context

This framework was developed for research into:

• lightweight cryptography
• secure S-box design
• memetic optimization
• cryptographic property analysis
• lightweight security for constrained devices

The framework focuses primarily on 5x5 S-box optimization for lightweight applications.

---

Future Improvements

Potential future extensions include:

• GPU acceleration
• additional cryptographic metrics
• automated benchmarking
• machine learning guided optimization
• larger S-box dimensions
• visualization pipelines
• experiment tracking systems
• statistical reporting modules

---

Author

Meaad Tori

Research Areas:

• Lightweight Cryptography
• S-Box Optimization
• Memetic Algorithms
• Cryptographic Engineering
• Security Optimization Frameworks

This repository represents an active research framework and experimental cryptographic evaluation environment. Some components remain under ongoing refinement and validation.