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Algebraic Insights into the Secret Feistel Network
Perrin, Léo Paul; Udovenko, Aleksei
2016In Peyrin, Thomas (Ed.) Fast Software Encryption - 23rd International Workshop, FSE 2016, Bochum, March 20-23, 2016
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Keywords :
secret-key cryptography; High-Degree Indicator Matrix; Feistel Network; ANF; Linear Approximation Table; Walsh Spectrum; Division Property; Integral Attack
Abstract :
[en] We introduce the high-degree indicator matrix (HDIM), an object closely related with both the linear approximation table and the algebraic normal form (ANF) of a permutation. We show that the HDIM of a Feistel Network contains very specific patterns depending on the degree of the Feistel functions, the number of rounds and whether the Feistel functions are 1-to-1 or not. We exploit these patterns to distinguish Feistel Networks, even if the Feistel Network is whitened using unknown affine layers. We also present a new type of structural attack exploiting monomials that cannot be present at round r-1 to recover the ANF of the last Feistel function of a r-round Feistel Network. Finally, we discuss the relations between our findings, integral attacks, cube attacks, Todo's division property and the congruence modulo 4 of the Linear Approximation Table.
Disciplines :
Computer science
Author, co-author :
Perrin, Léo Paul ;  University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT)
Udovenko, Aleksei  ;  University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT)
External co-authors :
no
Language :
English
Title :
Algebraic Insights into the Secret Feistel Network
Publication date :
2016
Event name :
23rd International Conference on Fast Software Encryption
Event organizer :
International Association for Cryptologic Research (IACR)
Event place :
Bochum, Germany
Event date :
20-23 March 2016
Audience :
International
Main work title :
Fast Software Encryption - 23rd International Workshop, FSE 2016, Bochum, March 20-23, 2016
Editor :
Peyrin, Thomas
Publisher :
Springer-Verlag Berlin Heidelberg
ISBN/EAN :
978-3-662-52992-8
Collection name :
Lecture Notes in Computer Science, 9783
Pages :
378-398
Peer reviewed :
Peer reviewed
Focus Area :
Security, Reliability and Trust
FnR Project :
FNR4009992 - Applied Cryptography For The Internet Of Things, 2012 (01/07/2013-30/06/2016) - Alex Biryukov
Funders :
FNR - Fonds National de la Recherche [LU]
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since 28 April 2016

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