Matrix PRFs: Constructions, Attacks, and Applications to Obfuscation
Name
2019-1085.pdf
Description
Accepted version
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413.8 KB
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Adobe PDF
Checksum (MD5)
3f19f710debbebbf09ea25039617154e
Author(s)
Chen, Yilei
Hhan, Minki
Vaikuntanathan, Vinod
Wee, Hoeteck
Date Issued
2019
Journal
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Publisher
Springer International Publishing
Citation
Chen, Yilei, Hhan, Minki, Vaikuntanathan, Vinod and Wee, Hoeteck. 2019. "Matrix PRFs: Constructions, Attacks, and Applications to Obfuscation." Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 11891.
Version
Author's final manuscript
Abstract
© 2019, International Association for Cryptologic Research. We initiate a systematic study of pseudorandom functions (PRFs) that are computable by simple matrix branching programs; we refer to these objects as “matrix PRFs”. Matrix PRFs are attractive due to their simplicity, strong connections to complexity theory and group theory, and recent applications in program obfuscation. Our main results are:We present constructions of matrix PRFs based on the conjectured hardness of computational problems pertaining to matrix products.We show that any matrix PRF that is computable by a read-c, width w branching program can be broken in time poly this means that any matrix PRF based on constant-width matrices must read each input bit ωc times. Along the way, we simplify the “tensor switching lemmas” introduced in previous IO attacks.We show that a subclass of the candidate local-PRG proposed by Barak et al. [Eurocrypt 2018] can be broken using simple matrix algebra.We show that augmenting the CVW18 IO candidate with a matrix PRF provably immunizes the candidate against all known algebraic and statistical zeroizing attacks, as captured by a new and simple adversarial model.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/978-3-030-36030-6_3
