Relationship between weight of plaintext and successful attacks in knapsack cryptosystems

Abstract

The density is a very important parameter in knapsack public-key cryptosystems. It is known that the knapsack cryptosystem is broken with the low-density attack when the density is low. In 2005, Nguyen and Stern introduced the pseudo-density instead of the conventional density in order to evaluate CR and OTU cryptosystems. In 2008, Kunihiro introduced a new density in order to unify the conventional density and the pseudo-density. From Kunihiro's result, we can guess that the plaintext is disclosed with the low-density attack when the weight of the plaintext is low even in the conventional knapsack PKC. In this paper, we investigate the relationship between the weight of plaintext and successful attacks in conventional knapsack cryptosystems.