Analysis and Comparison of Known and Randomly Generated S-boxes for Block Ciphers

TL;DR

This paper compares mathematically constructed S-boxes with randomly generated ones in block ciphers, evaluating their cryptographic strength and performance to understand the trade-offs between theoretical guarantees and randomness.

Contribution

It provides a systematic comparison between algebraically constructed and random S-boxes, including performance metrics and cycle constraints, in a simple SPN cipher setting.

Findings

Mathematically constructed S-boxes exhibit stronger cryptographic properties.

Random S-boxes generally show weaker cryptographic strength.

Performance measures for random permutations are established and compared.

Abstract

Mathematically constructed S-boxes arise from algebraic structures and finite field theory to ensure strong, provable cryptographic properties. These mathematically grounded constructions allow for generation of thousands of S-Boxes with high nonlinearity, APN properties, and balanced avalanche characteristics, unlike fully random methods, which lack such theoretical guarantees in exchange for low complexity and more varied results. In this work, we compare mathematically constructed constructions with randomly generated ones to evaluate the relative weakness of the latter. We also establish an average measure of performance for randomly generated permutations, as well as random with forced cycle constraints, and compare them to well-established designs in a simple SPN setting.