Brauer Analysis of Some Time–Memory Trade-Off Attacks and Its Application to the Solution of the Yang–Baxter Equation

This paper is focused on some algebraic and combinatorial properties of a TMTO (Time–Memory Trade-Off) for a chosen plaintext attack against a cryptosystem with a perfect secrecy property. TMTO attacks aim to retrieve the preimage of a given one-way function more efficiently than an exhaustive search and with less memory than a dictionary attack. TMTOs for chosen plaintext attacks against cryptosystems with a perfect secrecy property are associated with some directed graphs, which can be defined by suitable collections of multisets called Brauer configurations. Such configurations induce so-called Brauer configuration algebras, the algebraic and combinatorial invariant analysis of which is said to be a Brauer analysis. In this line, this paper proposes formulas for dimensions of Brauer configuration algebras (and their centers) induced by directed graphs defined by TMTO attacks. These results are used to provide some set-theoretical solutions for the Yang–Baxter equation.