A knapsack cryptosystem based on multiple knapsacks

In this paper, we propose a knapsack cryptosystem based on three knapsacks. Although one of the three secret knapsacks is superincreasing, the other two are non-superincreasing. On the encryption, a ciphertext is formed by multiplying the two non-superincreasing knapsacks together and then adding it to the superincreasing knapsack. Due to this structure of the cipher text, our knapsack cryptosystem is thought to be secure against all existing attacks, i.e., the low density attack and Shamir attack.