A New Digital Signature Scheme from Layered Cellular Automata

Abstract

Cellular Automata (CA) is one of the important tools to design cryptographic algorithms, and in the past years many researchers have explored several cryptographic algorithms based on CA. However, most of reported CAbased cryptographic algorithms focus on the symmetric key encryption schemes and few CA-based asymmetric encryption scheme has been proposed, let alone the CAbased digital signature scheme. In this paper, to fill this gap, we present a new digital signature scheme based on the layered CA technique. Specifically, in the proposed layered CA-based digital signature scheme, we combine the transition rules of some one-dimensional (1D) reversible CAs to generate the rules of a two-dimensional (2D) CA, where the reverse of the 1D transition rules are kept as the private key and the 2D transition rules are set as the corresponding public key. Based on the hardness assumption of the layered CA reversibility (LCAR) problem, we formally prove the proposed scheme is semantically secure against chosen-message attack in the random oracle model.