Reference : Cryptanalysis of Feistel Networks with Secret Round Functions
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Cryptanalysis of Feistel Networks with Secret Round Functions
Biryukov, Alex mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC) >]
Leurent, Gaëtan mailto [Inria]
Perrin, Léo Paul mailto [University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT) > >]
Selected Areas in Cryptography -- SAC 2015, 21st International Conference, Sackville, NB, Canada, August 12-14, 2015, Revised Selected Papers
Dunkelman, Orr
Keliher, Liam
Springer International Publishing
Security and Cryptology, 8781
Selected Areas in Cryptography -- SAC 2015
August 12-14, 2015
[en] Feistel Network ; Yoyo ; Guess-and-Determine
[en] Generic distinguishers against Feistel Network with up to 5 rounds exist in the regular setting and up to 6 rounds in a multi-key setting. We present new cryptanalyses against Feistel Networks with 5, 6 and 7 rounds which are not simply distinguishers but actually recover completely the unknown Feistel functions.

When an exclusive-or is used to combine the output of the round function with the other branch, we use the so-called \textit{yoyo game} which we improved using a heuristic based on particular cycle structures. The complexity of a complete recovery is equivalent to $\bigO(2^{2n})$ encryptions where $n$ is the branch size. This attack can be used against 6- and 7-round Feistel Networks in time respectively $\bigO(2^{n2^{n-1}+2n})$ and $\bigO(2^{n2^{n}+2n})$. However when modular addition is used, this attack does not work. In this case, we use an optimized guess-and-determine strategy to attack 5 rounds with complexity $\bigO(2^{n2^{3n/4}})$.

Our results are, to the best of our knowledge, the first recovery attacks against generic 5-, 6- and 7-round Feistel Networks.
Researchers ; Professionals ; Students
FnR ; FNR4009992 > Alex Biryukov > ACRYPT > Applied Cryptography for the Internet of Things > 01/01/2013 > 31/12/2015 > 2012

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