SBN Explorer: An Empirical Study of Cryptographic Boolean Networks

TL;DR

This study systematically explores the design space of cryptographic Boolean networks by analyzing 64 architectural classes against resistance metrics, revealing optimal combinations of structural constraints.

Contribution

It formalizes a broad design space for cryptographic Boolean systems using six structural constraints and evaluates all classes against cryptanalytic resistance.

Findings

Best networks are sparse and have compatible structural constraints.

Classical cryptography has barely addressed epistatic constraint combinations.

Systematic evaluation reveals optimal constraint combinations for resistance.

Abstract

Boolean circuits form the foundational computational substrate of symmetric cryptography, yet the exploration of their architectural design space has remained largely confined to a handful of canonical paradigms - SPN, Feistel networks, and their immediate variants. This paper takes a deliberately broader perspective by formalizing the design space of cryptographic Boolean systems through six independent binary structural constraints: Stratification, Acyclicity, Regularity, Interleaving, Homogeneity, and Locality. These constraints generate a hypercube of $2^6 = 64$ distinct architectural classes defined over Synchronous Boolean Networks, a general model that subsumes both acyclic combinational circuits and recurrent synchronous systems. We systematically evaluate all 64 classes against three generic cryptanalytic fitness objectives - differential, linear and algebraic resistance - using a five-stage methodology centered on Formal Concept Analysis. The results reveal that the best Boolean networks are governed by the identification of sparse, mutually compatible combinations of constraints - a fundamentally epistatic problem that classical cryptography has barely addressed.