Comparative Analysis of the Merkle–Hellman Knapsack and RSA Public-Key Cryptosystems: Efficiency vs. Security

Abstract

This paper provides a targeted comparative analysis of the Merkle–Hellman knapsack cryptosystem and the RSA public-key scheme, aiming to evaluate their relative efficiency and practical relevance. The research investigates key generation complexity, encryption and decryption performance, and resistance to established cryptanalytic techniques. Based on an experimental implementation and benchmarking across different key sizes, the result indicate that the Merkle–Hellman approach achieves lower computational overhead in both encryption / decryption process, due to its reliance on superincreasing sequences. However, these efficiency advantages are counterbalanced by structural weaknesses in the key transformation process, which expose the system to polynomial-time attacks. By comparison, RSA, despite higher computational costs, preserves robust security grounded in the hardness of integer factorization. Overall, the analysis demonstrates the conclusion that Merkle–Hellman, despite its historical importance, fails to achieve a sustainable efficiency-security balance for modern applications, reinforcing RSA’s dominance in practical public-key cryptography.