Comparison of cube attacks over different vector spaces

Richard Winter, Ana Salagean, Raphael C.W. Phan

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

8 Citations (Scopus)


We generalise the cube attack of Dinur and Shamir (and the similar AIDA attack of Vielhaber) to a more general higher order differentiation attack, by summing over an arbitrary subspace of the space of initialisation vectors. The Moebius transform can be used for efficiently examining all the subspaces of a big space, similar to the method used by Fouque and Vannet for the usual cube attack. Secondly we propose replacing the Generalised Linearity Test proposed by Dinur and Shamir with a test based on higher order differentiation/Moebius transform. We show that the proposed test provides all the information provided by the Generalised Linearity Test, at the same computational cost. In addition, for functions that do not pass the linearity test it also provides, at no extra cost, an estimate of the degree of the function. This is useful for guiding the heuristics for the cube/AIDA attacks. Finally we implement our ideas and test them on the stream cipher Trivium.

Original languageEnglish
Title of host publicationCryptography and Coding - 15th IMA International Conference, IMACC 2015, Proceedings
EditorsJens Groth
Number of pages14
ISBN (Print)9783319272382
Publication statusPublished - 2015
Externally publishedYes
EventIMA International Conference on Cryptography and Coding 2015 - Oxford, United Kingdom
Duration: 15 Dec 201517 Dec 2015
Conference number: 15th (Proceedings)

Publication series

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


ConferenceIMA International Conference on Cryptography and Coding 2015
Abbreviated titleIMACC 2015
Country/TerritoryUnited Kingdom
Internet address


  • Cube/AIDA attack
  • Higher order differentiation
  • Linearity testing
  • Moebius transform
  • Trivium

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