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Title: Comparison of cube attacks over different vector spaces
Authors: Winter, Richard
Salagean, A.M.
Phan, Raphael C.-W.
Keywords: Cube/AIDA attack
Linearity testing
Moebius transform
Higher order differentiation
Issue Date: 2015
Publisher: © Springer
Citation: WINTER, R., SALAGEAN, A.M. and PHAN, R.C-W., 2015. Comparison of cube attacks Over different vector spaces. Presented at the 15th IMA International Conference, (IMACC 2015), Oxford, UK, December 15-17, pp. 225-238.
Series/Report no.: Lecture Notes in Computer Science;9496
Abstract: 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.
Description: The final publication is available at http://dx.doi.org/10.1007/978-3-319-27239-9_14
Version: Accepted for publication
DOI: 10.1007/978-3-319-27239-9_14
URI: https://dspace.lboro.ac.uk/2134/20046
Publisher Link: http://dx.doi.org/10.1007/978-3-319-27239-9_14
ISBN: 9783319272382
ISSN: 0302-9743
Appears in Collections:Conference Papers and Presentations (Computer Science)

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