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Paper 2006/261

Using Wiedemann's algorithm to compute the immunity against algebraic and fast algebraic attacks

Frederic Didier

Abstract

We show in this paper how to apply well known methods from sparse linear algebra to the problem of computing the immunity of a Boolean function against algebraic or fast algebraic attacks. For an $n$-variable Boolean function, this approach gives an algorithm that works for both attacks in $O(n2^{n} D)$ complexity and $O(n2^n)$ memory. Here $D = \binom{n}{d}$ and $d$ corresponds to the degree of the algebraic system to be solved in the last step of the attacks. For algebraic attacks, our algorithm needs significantly less memory than the algorithm in \cite{ACGKMR06} with roughly the same time complexity (and it is precisely the memory usage which is the real bottleneck of the last algorithm). For fast algebraic attacks, it does not only improve the memory complexity, it is also the algorithm with the best time complexity known so far for most values of the degree constraints.

Note: second submission : I removed the accents in my name because there was a problem...

Metadata
Available format(s)
PDF PS
Category
Secret-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Keywords
algebraic and fast algebraic attacksalgebraic immunityWiedemann's algorithm
Contact author(s)
frederic didier @ inria fr
History
2006-08-07: received
Short URL
https://ia.cr/2006/261
License
Creative Commons Attribution
CC BY
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