NDLI: Counting equations in algebraic attacks on block ciphers

Content Provider	Springer Nature Link
Author	Knudsen, Lars R. Miolane, Charlotte V.
Copyright Year	2009
Abstract	This paper is about counting linearly independent equations for so-called algebraic attacks on block ciphers. The basic idea behind many of these approaches, e.g., XL, is to generate a large set of equations from an initial set of equations by multiplication of existing equations by the variables in the system. One of the most difficult tasks is to determine the exact number of linearly independent equations one obtain in the attacks. In this paper, it is shown that by splitting the equations defined over a block cipher (an SP-network) into two sets, one can determine the exact number of linearly independent equations which can be generated in algebraic attacks within each of these sets of a certain degree. While this does not give us a direct formula for the success of algebraic attacks on block ciphers, it gives some interesting bounds on the number of equations one can obtain from a given block cipher. Our results are applied to the AES and to a variant of the AES, and the exact numbers of linearly independent equations in the two sets that one can generate by multiplication of an initial set of equations are given. Our results also indicate, in a novel way, that the AES is not vulnerable to the algebraic attacks as defined here.
Starting Page	127
Ending Page	135
Page Count	9
File Format	PDF
ISSN	16155262
Journal	International Journal of Information Security
Volume Number	9
Issue Number	2
e-ISSN	16155270
Language	English
Publisher	Springer-Verlag
Publisher Date	2009-12-15
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Cryptology Block ciphers Algebraic attacks XL AES Communications Engineering, Networks Management of Computing and Information Systems Coding and Information Theory Operating Systems Computer Communication Networks Data Encryption
Content Type	Text
Resource Type	Article
Subject	Computer Networks and Communications Information Systems Safety, Risk, Reliability and Quality Software

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