Cryptanalysis of Merkle-Hellman Cipher Using Parallel Genetic Algorithm

Kantour, Nedjmeeddine; Bouroubi, Sadek

doi:10.1007/s11036-019-01216-8

Cited by 6 publications

(2 citation statements)

References 15 publications

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“…For low-density cases, attacks are given by [3,4]. Intelligent algorithms such as genetic algorithm [5,6] and ant colony algorithm [7] are also used to crack the Merkle-Hellman cryptosystem. In 2019, Liu and Bi proposed an attack based on an orthogonal lattice, whose time complexity is lower than Shamir's [8].…”

Section: Introductionmentioning

confidence: 99%

A Simple and Efficient Attack on the Merkle-Hellman Knapsack Cryptosystem

Bi,

2024

Preprint

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The Merkle-Hellman knapsack cryptosystem was one of the two earliest public key cryptosystems, which was invented by Merkle and Hellman in 1978. One can recover the whole group of equivalent keys by using Shamir's method. The most time-consuming part of Shamir's attack is to recover the critical intermediate parameters by solving an integer programming problem with a fixed number of variables, whose worst-case complexity is exponential in the number of variables. In this paper, we present an improved algorithm to analyze the basic Merkle-Hellman public key cryptosystem. The main idea of our method is that we recover a partial super-increasing sequence as the equivalent private key, which is the main difference from Shamir's. More precisely, we first obtain a super-increasing sequence except for the first small part by invoking the LLL algorithm on a special lattice with a small dimension. After that, we can recover most part of the plaintext from the tail by solving the super-increasing knapsack method. Finally, we can recover the first part of plaintext from solving a size-reduced knapsack problem. Experimental data shows that one can recover the whole plaintext in less than 1 second on a laptop successfully for the typical parameters of the Merkle-Hellman cryptosystem, whose time complexity is reduced by a polynomial level compared with Shamir's algorithm.

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Section: Introductionmentioning

confidence: 99%

A Simple and Efficient Attack on the Merkle-Hellman Knapsack Cryptosystem

Bi,

2024

Preprint

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“…Recently, Abdel-Basset [8] suggested a whole optimization-based attack using a sigmoid function for discretizing the search space, and the results show that the proposed algorithm is an efficient and robust for cryptanalysis of the Merkle-Hellman knapsack cryptosystem (MHKC) more than other algorithms. Kantour [9] proposed a parallel genetic algorithm for breaking the MHKC, their proposed scheme is enhanced with a deliberate cooperation among the search entities (GAs) via the migration operator. We mention also many other attacks in [10]- [20].…”

Section: Introductionmentioning

confidence: 99%

Cryptanalysis of Merkle-Hellman cipher using ant colony optimization

Grari

Lamzabi

Azouaoui

et al. 2021

IJ-AI

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The Merkle-Hellman (MH) cryptosystem is one of the earliest public key cryptosystems, which is introduced by Ralph Merkle and Martin Hellman in 1978 based on an NP-hard problem, known as the subset-sum problem. Furthermore, ant colony optimization (ACO) is one of the most nature-inspired meta-heuristic optimization, which simulates the social behaviour of ant colonies. ACO has demonstrated excellent performance in solving a wide variety of complex problems. In this paper, we present a novel ant colony optimization (ACO) based attack for cryptanalysis of MH cipher algorithm, where two different search techniques are used. Moreover, experimental study is included, showing the effectiveness of the proposed attacking scheme. The results show that ACO based attack is more suitable than many other algorithms like genetic algorithm (GA) and particle swarm optimization (PSO).

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