SAT Solving Using XOR-OR-AND Normal Forms and Cryptographic Fault Attacks

The Boolean satisfiability problem (SAT) lies at the core of computational logic and has found many applications in verification, cryptography, and artificial intelligence. While conflict-driven SAT solvers (CDCL) excel on large industrial instances, they struggle with XOR-rich instances arising frequently in cryptanalysis, due to the inefficiency of CNF encodings of linear constraints. Conversely, algebraic approaches can work with linear XOR constraints naturally but fail to scale to relevant sizes. Bridging these complementary paradigms with a focus on cryptographic problems is at the heart of this thesis. On one hand, this dissertation advances SAT solving by introducing the XOR-OR-AND normal form (XNF) as a generalization of the conjunctive normal form (CNF), where literals are replaced by XOR chains of literals. This allows for a native representation of XOR constraints. We generalize the CDCL architecture to the richer language of XNFs. The underlying reasoning based on the proof system SRES which is shown to be exponentially stronger than classical resolution. An implementation demonstrates competitive performance and often surpasses state-of-the-art algebraic and logic solvers on random and cryptographic benchmarks. Furthermore, we prove that every XNF formula can be converted in polynomial time to a formula in 2-XNF, enabling a graph-based approach similar to 2-SAT. Building on this, we propose advanced in- and pre-processing techniques, and construct a simple DPLL-based solving framework. Our implementation, 2-Xornado, outperforms modern algebraic and logic solving approaches on many random and some structured cryptographic problems. On the other hand, we apply combined algebraic and logical techniques to cryptanalysis of stream ciphers. We introduce a formal guess-and-determine (GD) framework using a logical abstraction of the information flow in the internal state. From an algebraic point of view, we can then find optimal GD attacks utilizing a Gröbner basis. As a case study, we apply this method to aid in the construction of novel fault attacks on the ciphers KCipher-2 and Enocoro-128v2. Using ad hoc methods combining algebraic and logical approaches, we show that both ciphers are vulnerable to active side-channel attacks under rather weak fault models.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Passau

Year

2025

Author dc:creator

• Danner, Julian

Contributors dc:contributor

• Kreuzer, Martin
• Biere, Armin

Statement dc:rights

• Creative Commons - CC BY - Namensnennung 4.0 International

Repository record source_url

https://opus4.kobv.de/opus4-uni-passau/frontdoor/index/index/docId/1917

OAI identifier oai:identifier

oai:kobv.de-opus4-uni-passau:1917