Equivalent Secret Key Attack against Knapsack PKC based on Subset Sum Decision Problem

Abstract

The security of most of the knapsack type public key cryptosystem(PKC) depends on the computational subset sum problem. In 2012, a knapsack PKC based on the subset sum decision problem is proposed by Murakami, Hamasho and Kasahara. An attack against this type of knapsack PKC by computing alternative solutions of the knapsack problem is then proposed by Nagao and Morii. In 2016, a new knapsack PKC(M16 PKC) based on the subset sum decision problem for preventing Nagao and Morii attack is proposed by Murakami. In this paper, we propose the new effective attacks against M16 knapsack PKC. The proposed attacks compute the equivalent secret keys from the public key, and the ciphertext of M16 PKC can be decoded with the equivalent secret keys, in the same way as the decryption with the legitimate secret(decryption) keys.