Cryptanalysis of Merkle-Hellman cipher using parallel genetic algorithm

TL;DR

This paper presents a parallel genetic algorithm approach to cryptanalyze the Merkle-Hellman cipher, demonstrating its effectiveness and comparing it with the LLL algorithm attack on the subset-sum problem.

Contribution

It introduces a novel parallel genetic algorithm tailored for breaking the Merkle-Hellman cryptosystem, addressing challenges in parameter adaptation and search space exploration.

Findings

The proposed PGA effectively breaks the MH cipher.

Experimental results outperform traditional LLL algorithm attack.

The method demonstrates robustness in solving NP-hard subset-sum problems.

Abstract

In 1976, Whitfield Diffie and Martin Hellman introduced the public key cryptography or asymmetric cryptography standards. Two years later, an asymmetric cryptosystem was published by Ralph Merkle and Martin Hellman called MH, based on a variant of knapsack problem known as the subset-sum problem which is proven to be NP-hard. Furthermore, over the last four decades, Metaheuristics have achieved a remarkable progress in solving NP-hard optimization problems. However, the conception of these methods raises several challenges, mainly the adaptation and the parameters setting. In this paper, we propose a Parallel Genetic Algorithm (PGA) adapted to explore effectively the search space of considerable size in order to break the MH cipher. Experimental study is included, showing the performance of the proposed attacking scheme and finally concluding with a comparison with the LLL algorithm attack.