In 2012, Murakami, Hamasho and Kasahara proposed a knapsack PKC based on the subset sum decision problem. Nagao and Morii proposed an attack which is effective for this type of the knapsack scheme by computing integer solutions of the knapsack problem. This attack is referred to as alternative-solution attack. In 2016, Murakami proposed a new scheme of the knapsack PKCs(M16 schemes) based on the subset sum decision problem. In this paper, we shall evaluate the security of the M16 schemes against the alternative-solution attack by computer experiment. As the result, it is seen that M16 Basic Scheme can be broken with the alternative-solution attack and that M16 Weight-Limited Scheme can not be broken with the alternative-solution attack.

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.