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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Peizhuo Lv (Institute of Information Engineering, Chinese Academy of Sciences, China; School of Cyber Security, University of Chinese Academy of Sciences, China), Pan Li (Institute of Information Engineering, Chinese Academy of Sciences, China; School of Cyber Security, University of Chinese Academy of Sciences, China), Shenchen Zhu (Institute of Information Engineering, Chinese Academy of Sciences, China;…

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Guangke Chen (ShanghaiTech University), Yedi Zhang (National University of Singapore), Fu Song (Institute of Software, Chinese Academy of Sciences; University of Chinese Academy of Sciences)

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Yuki Hayakawa (Keio University), Takami Sato (University of California, Irvine), Ryo Suzuki, Kazuma Ikeda, Ozora Sako, Rokuto Nagata (Keio University), Qi Alfred Chen (University of California, Irvine), Kentaro Yoshioka (Keio University)

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