On Cryptographic Attacks Using Backdoors for SAT

TL;DR

This paper introduces a novel class of backdoor sets for SAT, called guess-and-determine, to improve cryptographic attacks by estimating attack hardness with SAT solvers, showing advantages over existing methods.

Contribution

It proposes a new backdoor set class for SAT in cryptanalysis, optimizing variable selection based on estimated attack difficulty, with experimental validation.

Findings

Proposed guess-and-determine backdoors outperform existing methods.

Experimental results show increased attack efficiency on cryptographic algorithms.

Backdoor-based approach improves estimated attack hardness.

Abstract

Propositional satisfiability (SAT) is at the nucleus of state-of-the-art approaches to a variety of computationally hard problems, one of which is cryptanalysis. Moreover, a number of practical applications of SAT can only be tackled efficiently by identifying and exploiting a subset of formula's variables called backdoor set (or simply backdoors). This paper proposes a new class of backdoor sets for SAT used in the context of cryptographic attacks, namely guess-and-determine attacks. The idea is to identify the best set of backdoor variables subject to a statistically estimated hardness of the guess-and-determine attack using a SAT solver. Experimental results on weakened variants of the renowned encryption algorithms exhibit advantage of the proposed approach compared to the state of the art in terms of the estimated hardness of the resulting guess-and-determine attacks.