SBN Explorer: An Empirical Study of Cryptographic Boolean Networks

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.