A new construction method of knapsack PKC using linear transformation and Chinese remainder theorem

It is required to invent the public-key cryptosystem(PKC) that is based on an NP-hard problem so that the quantum computer might be realized. The knapsack PKC is based on the subset sum problem which is NP-hard. In this paper, we propose a construction method of knapsack PKC using a linear transformation of the secret sequences over integer ring with the Chinese remainder theorem as the trapdoor. The proposed scheme is secure against Shamir´s attack and Adleman´s attack and invulnerable to the low-density attack.