Security of a Class of Knapsack Public-Key Cryptosystems against Low-Density Attack

Abstract

In 2003, Kobayashi et al. proposed a new class of knapsack public-key cryptosystems over Gaussian integer ring. This scheme using two-sequences as the public key. In 2005, Sakamoto and Hayashi proposed an improved version of Kobayashi's scheme. In this paper, we propose the knapsack PKC using l-sequences as the public key and present the low-density attack on it. We have described Schemes R and G for l = 2, in which the public keys are constructed over rational integer ring and over Gaussian integer ring, respectively. We discusses on the difference of the security against the low-density attack. We show that the security levels of Schemes R and G differ only slightly.