Non-malleability against polynomial tampering

Marshall Ball, Eshan Chattopadhyay, Jyun Jie Liao, Tal Malkin, Li Yang Tan

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We present the first explicit construction of a non-malleable code that can handle tampering functions that are bounded-degree polynomials. Prior to our work, this was only known for degree-1 polynomials (affine tampering functions), due to Chattopadhyay and Li (STOC 2017). As a direct corollary, we obtain an explicit non-malleable code that is secure against tampering by bounded-size arithmetic circuits. We show applications of our non-malleable code in constructing non-malleable secret sharing schemes that are robust against bounded-degree polynomial tampering. In fact our result is stronger: we can handle adversaries that can adaptively choose the polynomial tampering function based on initial leakage of a bounded number of shares. Our results are derived from explicit constructions of seedless non-malleable extractors that can handle bounded-degree polynomial tampering functions. Prior to our work, no such result was known even for degree-2 (quadratic) polynomials.

Original languageEnglish (US)
Title of host publicationAdvances in Cryptology - CRYPTO 2020 - 40th Annual International Cryptology Conference, Proceedings
EditorsDaniele Micciancio, Thomas Ristenpart
PublisherSpringer
Pages97-126
Number of pages30
ISBN (Print)9783030568764
DOIs
StatePublished - 2020
Event40th Annual International Cryptology Conference, CRYPTO 2020 - Santa Barbara, United States
Duration: Aug 17 2020Aug 21 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12172 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference40th Annual International Cryptology Conference, CRYPTO 2020
Country/TerritoryUnited States
CitySanta Barbara
Period8/17/208/21/20

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science

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