Cellular Automata in Cryptographic Random Generators

TL;DR

This paper evaluates the cryptographic suitability of cellular automata, introduces a new NP-Hard invertible automaton construction, and presents the Chasm pseudorandom generator with initial testing results.

Contribution

It provides a comprehensive analysis of cellular automata in cryptography, introduces a novel NP-Hard invertible automaton, and proposes the Chasm generator with experimental validation.

Findings

Cellular automata show limited provable security for cryptography.

A new finite state cellular automaton is NP-Hard to invert.

The Chasm generator passes initial NIST randomness tests.

Abstract

Cryptographic schemes using one-dimensional, three-neighbor cellular automata as a primitive have been put forth since at least 1985. Early results showed good statistical pseudorandomness, and the simplicity of their construction made them a natural candidate for use in cryptographic applications. Since those early days of cellular automata, research in the field of cryptography has developed a set of tools which allow designers to prove a particular scheme to be as hard as solving an instance of a well- studied problem, suggesting a level of security for the scheme. However, little or no literature is available on whether these cellular automata can be proved secure under even generous assumptions. In fact, much of the literature falls short of providing complete, testable schemes to allow such an analysis. In this thesis, we first examine the suitability of cellular automata as a primitive for building cryptographic primitives. In this effort, we focus on pseudorandom bit generation and noninvertibility, the behavioral heart of cryptography. In particular, we focus on cyclic linear and non-linear au- tomata in some of the common configurations to be found in the literature. We examine known attacks against these constructions and, in some cases, improve the results. Finding little evidence of provable security, we then examine whether the desirable properties of cellular automata (i.e. highly parallel, simple construction) can be maintained as the automata are enhanced to provide a foundation for such proofs. This investigation leads us to a new construction of a finite state cellular automaton (FSCA) which is NP-Hard to invert. Finally, we introduce the Chasm pseudorandom generator family built on this construction and provide some initial experimental results using the NIST test suite.