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Comparing AI Algorithms for Optimizing Elliptic Curve Cryptography Parameters in e-Commerce Integrations: A Pre-Quantum Analysis

Felipe Tellez, Jorge Ortiz

TL;DR

The paper compares Genetic Algorithms (GA) and Particle Swarm Optimization (PSO) for optimizing Elliptic Curve Cryptography (ECC) parameters in a simulated pre-quantum e-commerce environment with third-party integrations. Using a unified fitness function that includes curve validity, Hasse bounds, and resistance to Pollard's rho, the study finds GA yields faster convergence and higher fitness values than PSO, while both methods produce secure, 256-bit-like parameters. In simulations of ECC-based encryption and ECDH/HMAC workflows, GA and PSO perform comparably in speed, with no successful attacks observed within extended timeframes; GA shows superior efficiency and practicality. The work demonstrates the viability of bio-inspired optimization for ECC parameter selection in real-world-like e-commerce contexts and highlights future directions, including hybrid approaches and post-quantum considerations.

Abstract

This paper presents a comparative analysis between the Genetic Algorithm (GA) and Particle Swarm Optimization (PSO), two vital artificial intelligence algorithms, focusing on optimizing Elliptic Curve Cryptography (ECC) parameters. These encompass the elliptic curve coefficients, prime number, generator point, group order, and cofactor. The study provides insights into which of the bio-inspired algorithms yields better optimization results for ECC configurations, examining performances under the same fitness function. This function incorporates methods to ensure robust ECC parameters, including assessing for singular or anomalous curves and applying Pollard's rho attack and Hasse's theorem for optimization precision. The optimized parameters generated by GA and PSO are tested in a simulated e-commerce environment, contrasting with well-known curves like secp256k1 during the transmission of order messages using Elliptic Curve-Diffie Hellman (ECDH) and Hash-based Message Authentication Code (HMAC). Focusing on traditional computing in the pre-quantum era, this research highlights the efficacy of GA and PSO in ECC optimization, with implications for enhancing cybersecurity in third-party e-commerce integrations. We recommend the immediate consideration of these findings before quantum computing's widespread adoption.

Comparing AI Algorithms for Optimizing Elliptic Curve Cryptography Parameters in e-Commerce Integrations: A Pre-Quantum Analysis

TL;DR

The paper compares Genetic Algorithms (GA) and Particle Swarm Optimization (PSO) for optimizing Elliptic Curve Cryptography (ECC) parameters in a simulated pre-quantum e-commerce environment with third-party integrations. Using a unified fitness function that includes curve validity, Hasse bounds, and resistance to Pollard's rho, the study finds GA yields faster convergence and higher fitness values than PSO, while both methods produce secure, 256-bit-like parameters. In simulations of ECC-based encryption and ECDH/HMAC workflows, GA and PSO perform comparably in speed, with no successful attacks observed within extended timeframes; GA shows superior efficiency and practicality. The work demonstrates the viability of bio-inspired optimization for ECC parameter selection in real-world-like e-commerce contexts and highlights future directions, including hybrid approaches and post-quantum considerations.

Abstract

This paper presents a comparative analysis between the Genetic Algorithm (GA) and Particle Swarm Optimization (PSO), two vital artificial intelligence algorithms, focusing on optimizing Elliptic Curve Cryptography (ECC) parameters. These encompass the elliptic curve coefficients, prime number, generator point, group order, and cofactor. The study provides insights into which of the bio-inspired algorithms yields better optimization results for ECC configurations, examining performances under the same fitness function. This function incorporates methods to ensure robust ECC parameters, including assessing for singular or anomalous curves and applying Pollard's rho attack and Hasse's theorem for optimization precision. The optimized parameters generated by GA and PSO are tested in a simulated e-commerce environment, contrasting with well-known curves like secp256k1 during the transmission of order messages using Elliptic Curve-Diffie Hellman (ECDH) and Hash-based Message Authentication Code (HMAC). Focusing on traditional computing in the pre-quantum era, this research highlights the efficacy of GA and PSO in ECC optimization, with implications for enhancing cybersecurity in third-party e-commerce integrations. We recommend the immediate consideration of these findings before quantum computing's widespread adoption.
Paper Structure (61 sections, 4 figures, 7 tables, 15 algorithms)

This paper contains 61 sections, 4 figures, 7 tables, 15 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. Objective
  4. Scope and Limitations
  5. Structure and Contributions
  6. Literature Review
  7. ECC Parameter Optimization
  8. AI Techniques for ECC Parameter Optimization
  9. E-commerce and Third-party Integrations
  10. Types of E-commerce Integrations
  11. The Role of AI in ECC and Third-Party Integrations
  12. Pre-Quantum Developments in ECC Optimization
  13. Limitations of Similar Research
  14. Materials and Methods
  15. ECC Optimization Parameters
  16. ...and 46 more sections

Figures (4)

  • Figure 1: A high-level diagram of the environment's architecture
  • Figure 2: Interaction between Entity A (e-commerce) and Entity B (ERP server)
  • Figure 3: Fitness Progression over Generations - GA
  • Figure 4: Fitness Progression over Iterations - PSO