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Insights Gained after a Decade of Cellular Automata-based Cryptography

Luca Mariot

TL;DR

The paper investigates whether cellular automata (CA) remain relevant for cryptography after a decade of CA-based work, focusing on stream and block ciphers. It argues that CA offer parallelism and rich dynamics but that many CA-centric studies rely on empirical testing and non-standard models, limiting cryptanalytic relevance. It reviews early CA PRG attempts, attacks on Wolfram's rule-30, and subsequent evolution toward larger diameters and asynchronous CA, extracting the need to align CA designs with CA-specific security notions (degree, immunity) and known cryptanalytic frameworks. For block ciphers, it surveys iterated-CA constructions and single-step CA approaches, highlighting diffusion limitations and recommending integrating CA as components within well-understood SPN/sponges designs, or pursuing diffusion via orthogonal arrays. The overarching goal is to foster collaboration between CA and cryptography communities, improve security-oriented evaluation, and identify concrete research directions that bridge conceptual gaps.

Abstract

Cellular Automata (CA) have been extensively used to implement symmetric cryptographic primitives, such as pseudorandom number generators and S-boxes. However, most of the research in this field, except the very early works, seems to be published in non-cryptographic venues. This phenomenon poses a problem of relevance: are CA of any use to cryptographers nowadays? This paper provides insights into this question by briefly outlining the history of CA-based cryptography. In doing so, the paper identifies some shortcomings in the research addressing the design of symmetric primitives exclusively from a CA standpoint, alongside some recommendations for future research. Notably, the paper remarks that researchers working in CA and cryptography often tackle similar problems, albeit under different perspectives and terminologies. This observation indicates that there is still ample room for fruitful collaborations between the CA and cryptography communities in the future.

Insights Gained after a Decade of Cellular Automata-based Cryptography

TL;DR

The paper investigates whether cellular automata (CA) remain relevant for cryptography after a decade of CA-based work, focusing on stream and block ciphers. It argues that CA offer parallelism and rich dynamics but that many CA-centric studies rely on empirical testing and non-standard models, limiting cryptanalytic relevance. It reviews early CA PRG attempts, attacks on Wolfram's rule-30, and subsequent evolution toward larger diameters and asynchronous CA, extracting the need to align CA designs with CA-specific security notions (degree, immunity) and known cryptanalytic frameworks. For block ciphers, it surveys iterated-CA constructions and single-step CA approaches, highlighting diffusion limitations and recommending integrating CA as components within well-understood SPN/sponges designs, or pursuing diffusion via orthogonal arrays. The overarching goal is to foster collaboration between CA and cryptography communities, improve security-oriented evaluation, and identify concrete research directions that bridge conceptual gaps.

Abstract

Cellular Automata (CA) have been extensively used to implement symmetric cryptographic primitives, such as pseudorandom number generators and S-boxes. However, most of the research in this field, except the very early works, seems to be published in non-cryptographic venues. This phenomenon poses a problem of relevance: are CA of any use to cryptographers nowadays? This paper provides insights into this question by briefly outlining the history of CA-based cryptography. In doing so, the paper identifies some shortcomings in the research addressing the design of symmetric primitives exclusively from a CA standpoint, alongside some recommendations for future research. Notably, the paper remarks that researchers working in CA and cryptography often tackle similar problems, albeit under different perspectives and terminologies. This observation indicates that there is still ample room for fruitful collaborations between the CA and cryptography communities in the future.
Paper Structure (13 sections, 2 equations, 3 figures)

This paper contains 13 sections, 2 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Background
  3. Cellular Automata
  4. Cryptography
  5. Stream Ciphers Based on CA
  6. Early Works
  7. Attacks on Wolfram's PRNG and Improvements
  8. Shortcomings and Insights
  9. Block Ciphers Based on CA
  10. Encryption by Iterating CA
  11. The Single-Step CA Approach
  12. Shortcomings and Insights
  13. An Outlook on Future Research

Figures (3)

  • Figure 1: NBCA
  • Figure 2: PBCA
  • Figure 4: Diagrams for Vernam-like stream ciphers and SPN block ciphers.