SMT Solving over Finite Field Arithmetic

19 pages•Published: June 3, 2023

Abstract

Non-linear polynomial systems over finite fields are used to model functional behavior of cryptosystems, with applications in system security, computer cryptography, and post- quantum cryptography. Solving polynomial systems is also one of the most difficult problems in mathematics. In this paper, we propose an automated reasoning procedure for deciding the satisfiability of a system of non-linear equations over finite fields. We introduce zero decomposition techniques to prove that polynomial constraints over finite fields yield finite basis explanation functions. We use these explanation functions in model constructing satisfiability solving, allowing us to equip a CDCL-style search procedure with tailored theory reasoning in SMT solving over finite fields. We implemented our approach and provide a novel and effective reasoning prototype for non-linear arithmetic over finite fields.

Keyphrases: finite fields, polynomial arithmetic, SMT solving, Triangular Sets

In: Ruzica Piskac and Andrei Voronkov (editors). Proceedings of 24th International Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 94, pages 238--256

Links:	https://easychair.org/publications/paper/KWWq
	https://doi.org/10.29007/4n6w