A Public-Key Cryptosystem Based on Shift Register Sequences

Abstract

Various cryptosystems using finite field arithmetic have been introduced recently, e.g. cryptosystems based on permutations of finite fields (Lidl and Huller [8], Nöbauer [12]), cryptosystems of the knapsack type (Chor and Rivest [4], Niederreiter [11]), and cryptosystems based on discrete exponentiation in finite fields (Odlyzko [13], Wah and Wang [14]). Finite fields also play a role in the construction of stream ciphers (Beker and Piper [1], Beth et al. [2], Lidl and Niederreiter [10]). The security of cryptosystems based on discrete exponentiation has recently been diminished by significant progress on the discrete logarithm problem (Blake et al. [3], Coppersmith [5], Coppersmith et al. [6]). In this paper we propose a public-key cryptosystem that has a more complex structure than the corresponding discrete-exponentiation cryptosystem and is therefore potentially harder to break. This cryptosystem uses feedback shift register (FSR) sequences in finite fields and is thus easy to implement.