SMT Solving over Finite Field Arithmetic

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 is also one the most difficult problems mathematics. In this paper, we propose an automated reasoning procedure for deciding satisfiability a non-linear equations fields. We introduce zero decomposition techniques prove that constraints yield basis explanation functions. use these functions constructing solving, allowing us equip CDCL-style search tailored theory SMT solving implemented our approach provide novel effective prototype arithmetic