### Comparison of cube attacks over diﬀerent vector spaces

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

##### Abstract

We generalise the cube attack of Dinur and Shamir (and the similar AIDA attack of Vielhaber) to a more general higher order di&#64256;erentiation attack, by summing over an arbitrary subspace of the space of initialisation vectors. The Moebius transform can be used for e&#64259;ciently 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 di&#64256;erentiation/ 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.

##### Metadata
Available format(s)
Category
Foundations
Publication info
Published elsewhere. LNCS IMACC 2015 Conference Proceedings
Keywords
CubeAIDA attackTriviumLinearity testingMoebius transformhigher order di&#64256erentiation
Contact author(s)
R Winter @ lboro ac uk
History
2015-09-15: received
Short URL
https://ia.cr/2015/894
License

CC BY

BibTeX

@misc{cryptoeprint:2015/894,
author = {Richard Winter and Ana Salagean and Raphael C. -W.  Phan},
title = {Comparison of cube attacks over diﬀerent vector spaces},
howpublished = {Cryptology ePrint Archive, Paper 2015/894},
year = {2015},
note = {\url{https://eprint.iacr.org/2015/894}},
url = {https://eprint.iacr.org/2015/894}
}

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