Security of Knapsack Cryptosystem Using Subset-Sum Decision Problem against Alternative-Solution Attack

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.