Low-Complexity Weak Pseudorandom Functions in AC0 [ MOD2 ]

Elette Boyle, Geoffroy Couteau, Niv Gilboa, Yuval Ishai, Lisa Kohl, Peter Scholl

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

A weak pseudorandom function (WPRF) is a keyed function fk: { 0, 1 }n→ { 0, 1 } such that, for a random key k, a collection of samples (x, fk(x) ), for uniformly random inputs x, cannot be efficiently distinguished from totally random input-output pairs (x, y). We study WPRFs in AC0 [ MOD2 ], the class of functions computable by AC0 circuits with parity gates, making the following contributions. WPRF by sparse polynomials. We propose the first WPRF candidate that can be computed by sparse multivariate polynomials over F2. We prove that it has subexponential security against linear and algebraic attacks.WPRF in AC0 ∘ MOD2. We study the existence of WPRFs computed by AC0 circuits over parity gates. We propose a modified version of a previous WPRF candidate of Akavia et al. (ITCS 2014), and prove that it resists the algebraic attacks that were used by Bogdanov and Rosen (ECCC 2017) to break the original candidate in quasipolynomial time. We give evidence against the possibility of using public parity gates and relate this question to other conjectures.Between Lapland and Cryptomania. We show that WPRFs in AC0 [ MOD2 ] imply a variant of the Learning Parity with Noise (LPN) assumption. We further show that WPRFs in a subclass of AC0 [ MOD2 ] that includes a recent candidate by Boyle et al. (FOCS 2020) imply, under a seemingly weak additional conjecture, public-key encryption.

Original languageEnglish
Title of host publicationAdvances in Cryptology – CRYPTO 2021 - 41st Annual International Cryptology Conference, CRYPTO 2021, Proceedings
EditorsTal Malkin, Chris Peikert
PublisherSpringer Science and Business Media Deutschland GmbH
Pages487-516
Number of pages30
ISBN (Print)9783030842581
DOIs
StatePublished - 1 Jan 2021
Event41st Annual International Cryptology Conference, CRYPTO 2021 - Virtual, Online
Duration: 16 Aug 202120 Aug 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12828 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference41st Annual International Cryptology Conference, CRYPTO 2021
CityVirtual, Online
Period16/08/2120/08/21

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