Optimized interpolation attacks on LowMC

Itai Dinur, Yunwen Liu, Willi Meier, Qingju Wang

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

25 Scopus citations

Abstract

LowMC is a collection of block cipher families introduced at Eurocrypt 2015 by Albrecht et al. Its design is optimized for instantiations of multi-party computation, fully homomorphic encryption, and zero-knowledge proofs. A unique feature of LowMC is that its internal affine layers are chosen at random, and thus each block cipher family contains a huge number of instances. The Eurocrypt paper proposed two specific block cipher families of LowMC, having 80-bit and 128-bit keys. In this paper, we mount interpolation attacks (algebraic attacks introduced by Jakobsen and Knudsen) on LowMC, and show that a practically significant fraction of 2−38 of its 80-bit key instances could be broken 223 times faster than exhaustive search. Moreover, essentially all instances that are claimed to provide 128-bit security could be broken about 1000 times faster. In order to obtain these results we optimize the interpolation attack using several new techniques. In particular, we present an algorithm that combines two main variants of the interpolation attack, and results in an attack which is more efficient than each one.

Original languageEnglish
Title of host publicationAdvances in Cryptology – ASIACRYPT 2015 - 21st International Conference on the Theory and Application of Cryptology and Information Security, Proceedings
EditorsTetsu Iwata, Jung Hee Cheon
PublisherSpringer Verlag
Pages535-560
Number of pages26
ISBN (Print)9783662487990
DOIs
StatePublished - 1 Jan 2015
Externally publishedYes
Event21st International Conference on the Theory and Application of Cryptology and Information Security, ASIACRYPT 2015 - Auckland, New Zealand
Duration: 29 Nov 20153 Dec 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9453
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference21st International Conference on the Theory and Application of Cryptology and Information Security, ASIACRYPT 2015
Country/TerritoryNew Zealand
CityAuckland
Period29/11/153/12/15

Keywords

  • Block cipher
  • High-order differential cryptanalysis
  • Interpolation attack
  • LowMC

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