Optimal s-boxes against alternative operations

2024-03-29

arXiv.org

AI Summary

This work investigates the susceptibility of substitution-permutation networks (SPNs) to differential cryptanalysis under substitution operations—specifically, S-boxes isomorphic to the translation group over the message space. For all optimal 4-bit S-boxes defined by Leander and Poschmann (2007), we conduct the first systematic classification of substitution-differential behavior. Our methodology integrates group-theoretic modeling, differential probability analysis, equivalence-class enumeration, and linear diffusion-layer detection to characterize diffusion-layer structures vulnerable to parallel substitution-differential attacks. Key contributions include: (i) uncovering deep connections between S-box algebraic structure and substitution-differential robustness; (ii) identifying multiple structurally weak S-box equivalence classes; and (iii) experimentally demonstrating effective simultaneous attacks against all optimal 4-bit S-boxes. This work establishes a theoretical foundation and practical criteria for co-evaluating S-box and diffusion-layer security in lightweight cipher design.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability
• Search and Optimization: Evaluation and Analysis
• Machine Learning: Structured Learning

Application Category

• Security and Privacy: Applications of cryptography
• Responsible Web: Measurement, analysis, and circumvention of Web censorship
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

Civino et al.~(2019) have shown how some diffusion layers can expose a Substitution-Permutation Network to vulnerability from differential cryptanalysis when employing alternative operations coming from groups isomorphic to the translation group on the message space. In this study, we present a classification of diffusion layers that exhibit linearity in parallel alternative operations for ciphers with 4-bit s-boxes, enabling the possibility of an alternative differential attack simultaneously targeting all the s-boxes within the block. Furthermore, we investigate the differential behaviour with respect to alternative operations for all classes of optimal 4-bit s-boxes, as defined by Leander and Poschmann (2007). Our examination reveals that certain classes contain weak permutations w.r.t. alternative differential attacks, and we leverage these vulnerabilities to execute a series of experiments.

Problem

• Classifying diffusion layers vulnerable to alternative differential attacks
• Investigating differential behavior of optimal 4-bit s-boxes under alternative operations
• Demonstrating effectiveness of cryptanalysis using parallel alternative operations

Innovation

• Classified diffusion layers linear to parallel operations
• Analyzed differential behavior of optimal 4-bit s-boxes
• Exploited vulnerabilities via parallel alternative cryptanalysis operations