Extensions of the Cube Attack Based on Low Degree Annihilators

Authors:
Aileen Zhang;Chu-Wee Lim;Khoongming Khoo;Lei Wei;Josef Pieprzyk
Affiliations:
DSO National Laboratories, Singapore 118230;DSO National Laboratories, Singapore 118230;DSO National Laboratories, Singapore 118230;School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore;Department of Computing, Macquarie University, Australia
Venue:
CANS '09 Proceedings of the 8th International Conference on Cryptology and Network Security
Year:
2009

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Abstract

At Crypto 2008, Shamir introduced a new algebraic attack called the cube attack, which allows us to solve black-box polynomials if we are able to tweak the inputs by varying an initialization vector. In a stream cipher setting where the filter function is known, we can extend it to the cube attack with annihilators: By applying the cube attack to Boolean functions for which we can find low-degree multiples (equivalently annihilators), the attack complexity can be improved. When the size of the filter function is smaller than the LFSR, we can improve the attack complexity further by considering a sliding window version of the cube attack with annihilators. Finally, we extend the cube attack to vectorial Boolean functions by finding implicit relations with low-degree polynomials.