Linearly shift knapsack public-key cryptosystem

In this paper, we propose two algorithms to improve the Merkle-Hellman knapsack public-key cryptosystem. First, we propose an approach to transform a superincreasing sequence to a " high den-sity'' knapsack sequence. The algorithm is easy to implement and eliminates the redundancy of many knapsack cryptosystems. Second, a linearly shift method is used to improve the security of the knapsack public-key cryptosystem. We show that several knapsacks (e.g., the so-called ''useless " knapsack), which cannot be generated by using the Merkle-Hellman scheme, can be generated by the linearly shift method. Thus, Shamir's attack to the original knapsack, as well as the low density attack to the iterated knapsack, cannot apply to our system successfully. It is interesting to note that the concept of the requirement of being one-to-one in practical enciphering keys is not necessary for our system.