Paper Info
Title
Enhanced criteria on differential uniformity and nonlinearity of cryptographically significant functions
Abstract
The functions defined on finite fields with high nonlinearity are important primitives in cryptography. They are used as the substitution boxes in many block ciphers. To avoid the differential and linear attacks on the ciphers, the Sboxes must have low differential uniformity and high nonlinearity. In this paper, we generalize the notions of the differential uniformity and nonlinearity, which are called the - and the , to measure the nonlinear property of the functions. We show that the Sboxes endorsed by ZUC, SNOW 3G and some lightweight block ciphers have poor performances under these new criteria. The properties and characterizations of these new notions are presented. Another contribution of this paper is to study the nonlinearity of the functions with the form = ∘, where is from to and is a linear surjection from to . The motivation of this study is that such a substitution-permutation composition structure is widely used in the design of modern ciphers, which is to bring the confusion and diffusion to the ciphers. We determine the nonlinearity of for the linear function with certain property. Using this result, we compute the diversity of the nonlinearity for and . It is found that the former value is greatly amplified, which weakens the ciphers against the linear attack.
Year
DOI
Venue
2016
10.1007/s12095-015-0141-x
Cryptography and Communications
Keywords
Field
DocType
Substitution box,Almost perfect nonlinear function,Perfect nonlinear function,Truncated differential attack,06E30,94A60
Differential uniformity,Discrete mathematics,Finite field,Nonlinear system,Block cipher,Cryptography,Linear function,Mathematics,Surjective function,Confusion and diffusion
Journal
Volume
Issue
ISSN
8
2
1936-2447
Citations 
PageRank 
References 
1
0.38
23
Authors
3
Name
Order
Citations
PageRank
Yin Tan111.39
Guang Gong21717160.71
Bo Zhu322717.31