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Using Term Rewriting to Solve Bit-Vector Arithmetic Problems (Poster Presentation)
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@MISC{Abal_usingterm,
author = {Iago Abal and Jorge Sousa Pinto},
title = {Using Term Rewriting to Solve Bit-Vector Arithmetic Problems (Poster Presentation)},
year = {}
}
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Abstract
Among many theories supported by SMT solvers, the theory of finite-precision bit-vector arithmetic is one of the most useful, for both hardware and software systems verification. This theory is also particularly useful for some specific domains such as cryptography, in which algorithms are naturally expressed in terms of bit-vectors. Cryptol is an example of a domain-specific language (DSL) and toolset for cryptography developed by Galois, Inc.; providing an SMT backend that relies on bit-vector decision procedures to certify the correctness of cryptographic specifications [3]. Most of these decision procedures use bit-blasting to reduce a bit-vector problem into pure propositional SAT. Unfortunately bit-blasting does not scale very well, especially in the presence of operators like multiplication or division. For example, the equality x 2 [n] − 1 [n] = (x [n] +1 [n]) × (x [n] − 1 [n]) is a simple consequence of distributivity and associativity laws; but even for small values of n the bit-level representation of this formula is so huge that it is intractable by current SAT solvers. The main reason for this is the loss of high-level algebraic structure present in the original
Keyphrases
bit-vector arithmetic problem term rewriting poster presentation simple consequence cryptographic specification decision procedure bit-level representation current sat solver high-level algebraic structure present finite-precision bit-vector arithmetic smt backend pure propositional sat smt solver many theory small value associativity law bit-vector problem specific domain bit-vector decision procedure main reason domain-specific language software system verification
