Arnau Gàmez-Montolio (City, University of London; Activision Research), Enric Florit (Universitat de Barcelona), Martin Brain (City, University of London), Jacob M. Howe (City, University of London)

Polynomials over fixed-width binary numbers (bytes, Z/2 wZ, bit-vectors, etc.) appear widely in computer science including obfuscation and reverse engineering, program analysis, automated theorem proving, verification, errorcorrecting codes and cryptography. As some fixed-width binary numbers do not have reciprocals, these polynomials behave differently to those normally studied in mathematics. In particular, polynomial equality is harder to determine; polynomials having different coefficients is not sufficient to show they always compute different values. Determining polynomial equality is a fundamental building block for most symbolic algorithms. For larger widths or multivariate polynomials, checking all inputs is computationally infeasible. This paper presents a study of the mathematical structure of null polynomials (those that evaluate to 0 for all inputs) and uses this to develop efficient algorithms to reduce polynomials to a normalized form. Polynomials in such normalized form are equal if and only if their coefficients are equal. This is a key building block for more mathematically sophisticated approaches to a wide range of fundamental problems.

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Frank Capobianco (The Pennsylvania State University), Quan Zhou (The Pennsylvania State University), Aditya Basu (The Pennsylvania State University), Trent Jaeger (The Pennsylvania State University, University of California, Riverside), Danfeng Zhang (The Pennsylvania State University, Duke University)

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