New trapdoor sequences in modular knapsack cryptosystem

In the modular knapsack cryptosystem, many trapdoor sequences have been proposed. However, the various attacks against the conventional sequences have been proposed. In this paper, we first introduce three basic types of conventional trapdoor sequences, which are well-known as the super-increasing sequence proposed by Merkle and Hellman, the shifted-odd sequence proposed by Kasahara and Murakami and the combined sequence proposed by Nasako and Murakami. We second introduce the noisy super-increasing sequence proposed by Graham and Shamir and other noisy sequences. Finally, we propose a new noisy combined sequence and another type of combined sequence and show that both of the proposed sequences are secure against the conventional attacks.