On the nonlinearity of S-boxes and linear codes

For multi-output Boolean functions (also called S-boxes), various measures of nonlinearity have been widely discussed in the literature but many problems are left open in this topic. The purpose of this paper is to present a new approach to estimating the nonlinearity of S-boxes. A more fine-grained...

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Veröffentlicht in:Cryptography and communications Jg. 9; H. 3; S. 345 - 361
Hauptverfasser: Liu, Jian, Mesnager, Sihem, Chen, Lusheng
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.05.2017
Springer Nature B.V
Springer
Schlagworte:
Boolean functions
Boxes
Circuits
Coding and Information Theory
Communications Engineering
Computer Science
Data Structures and Information Theory
Encryption
Information and Communication
Lower bounds
Mathematics
Mathematics of Computing
Networks
Nonlinearity
Affine approximation attack
06E30
Symmetric cryptography
S-boxes
Linear codes
Nonlinearity
Multi-output Boolean functions
94A60
ISSN:1936-2447, 1936-2455
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Zusammenfassung:For multi-output Boolean functions (also called S-boxes), various measures of nonlinearity have been widely discussed in the literature but many problems are left open in this topic. The purpose of this paper is to present a new approach to estimating the nonlinearity of S-boxes. A more fine-grained view on the notion of nonlinearity of S-boxes is presented and new connections to some linear codes are established. More precisely, we mainly study the nonlinearity indicator (denoted by 𝒩 v ) for S-boxes from a coding theory point of view. Such a cryptographic parameter 𝒩 v is more related to best affine approximation attacks on stream ciphers. We establish a direct link between 𝒩 v and the minimum distance of the corresponding linear code. We exploit that connection to derive the first general lower bounds on 𝒩 v of non-affine functions from 𝔽 2 n to 𝔽 2 m for m dividing n . Furthermore, we show that 𝒩 v can be determined directly by the weight distribution of the corresponding linear code.
Bibliographie:ObjectType-Article-1
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ISSN:1936-2447
1936-2455
DOI:10.1007/s12095-015-0176-z