Knapsack Public-Key Cryptosystem Using Chinese Remainder Theorem

The realization of the quantum computer will enable to break publickey cryptosystems based on factoring problem and discrete logarithm problem. It is considered that even the quantum computer can not solve NP -hard problem in a polynomial time. The subset sum problem is known to be NP -hard. Merkle and Hellman proposed a knapsack cryptosystem using the subset sum problem. However, it was broken by Shamir or Adleman because there exist the linearity of the modular transformation and the specialty in the secret keys. It is also broken with the lowdensity attack because the density is not sufficiently high. In this paper, we propose a new class of knapsack scheme without modular transformation. The specialty and the linearity can be avoidable by using the Chinese remainder theorem as the trapdoor. The proposed scheme has a high density and a large dimension to be sufficiently secure against a practical low-density attack.