| On the approximation of S-boxes via Maiorana-McFarland functions |
| Wei, Yongzhuang (1); Pasalic, Enes (3)
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| 2013
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| Source | IET Information Security
 |
| ISSN | 17518709
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| Volume | 7Issue:2Pages:134-143 |
| English Abstract | Substitution boxes (S-boxes) are the key components of conventional cryptographic systems. To quantify the confusion property of S-boxes, different non-linearity criteria are proposed such as usual non-linearity (NF), unrestricted nonlinearity (UNF), generalised non-linearity (GN F), higher order non-linearity (HNF) and so on. Although these different criteria come from the idea of linear (or non-linear) approximation of S-boxes, the algebraic structures of Boolean functions that are used to approximate to S-boxes have not been considered yet. In this study, the concept of the extended non-linearity of S-boxes (denoted by ENF) is introduced by measuring the distance of a given function to a subset of Maiorana-McFarland functions. This approximation appears to be appealing because of a particular structure of this class of functions, namely their representation as a concatenation of affine functions. The complexity of computing the rth order extended non-linearity for S-boxes over GF(2) n is less than O ((n/r)2n-r), (r > 1). Moreover, a theoretical upper bound for the rth order extended nonlinearity is proved, which is much lower than previous generalised non-linearity which might give a rise to more efficient attacks that combine a generalised correlation approach with guess and determine techniques. Furthermore, the relationship between the r-order extended non-linearity and the generalised non-linearity is derived. © The Institution of Engineering and Technology 2013.; Substitution boxes (S-boxes) are the key components of conventional cryptographic systems. To quantify the confusion property of S-boxes, different non-linearity criteria are proposed such as usual non-linearity (NF), unrestricted nonlinearity (UNF), generalised non-linearity (GN F), higher order non-linearity (HNF) and so on. Although these different criteria come from the idea of linear (or non-linear) approximation of S-boxes, the algebraic structures of Boolean functions that are used to approximate to S-boxes have not been considered yet. In this study, the concept of the extended non-linearity of S-boxes (denoted by ENF) is introduced by measuring the distance of a given function to a subset of Maiorana-McFarland functions. This approximation appears to be appealing because of a particular structure of this class of functions, namely their representation as a concatenation of affine functions. The complexity of computing the rth order extended non-linearity for S-boxes over GF(2) n is less than O ((n/r)2n-r), (r > 1). Moreover, a theoretical upper bound for the rth order extended nonlinearity is proved, which is much lower than previous generalised non-linearity which might give a rise to more efficient attacks that combine a generalised correlation approach with guess and determine techniques. Furthermore, the relationship between the r-order extended non-linearity and the generalised non-linearity is derived. © The Institution of Engineering and Technology 2013. |
| Indexed Type | SCI
; EI
|
| Department | (1) State Key Laboratory of Information Security, Institute of Software, Chinese Academy of Sciences, Beijing 100190, China; (2) Guilin University of Electronic Technology, Guilin City, Guangxi Province 541004, China; (3) University of Primorska, FAMNIT and IAM, 6000, Koper, Slovenia
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| Language | 英语
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| WOS ID | WOS:000321701300010
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| Citation statistics |
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| Content Type | 期刊论文
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| URI | http://ir.iscas.ac.cn/handle/311060/16956
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| Collection | 中国科学院软件研究所
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Recommended Citation
GB/T 7714 |
Wei, Yongzhuang ,Pasalic, Enes . On the approximation of S-boxes via Maiorana-McFarland functions[J]. IET Information Security,2013,7(2):134-143.
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| APA |
Wei, Yongzhuang ,&Pasalic, Enes .(2013).On the approximation of S-boxes via Maiorana-McFarland functions.IET Information Security,7(2),134-143.
|
| MLA |
Wei, Yongzhuang ,et al."On the approximation of S-boxes via Maiorana-McFarland functions".IET Information Security 7.2(2013):134-143.
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