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.

View More Papers

The Dark Side of E-Commerce: Dropshipping Abuse as a...

Arjun Arunasalam (Purdue University), Andrew Chu (University of Chicago), Muslum Ozgur Ozmen (Purdue University), Habiba Farrukh (University of California, Irvine), Z. Berkay Celik (Purdue University)

Read More

Security Attacks to the Name Management Protocol in Vehicular...

Sharika Kumar (The Ohio State University), Imtiaz Karim, Elisa Bertino (Purdue University), Anish Arora (Ohio State University)

Read More

Trim My View: An LLM-Based Code Query System for...

Sima Arasteh (University of Southern California), Pegah Jandaghi, Nicolaas Weideman (University of Southern California/Information Sciences Institute), Dennis Perepech, Mukund Raghothaman (University of Southern California), Christophe Hauser (Dartmouth College), Luis Garcia (University of Utah Kahlert School of Computing)

Read More