Highly nonlinear resilient functions play a crucial role in nonlinear combiners which are usual hardware oriented stream ciphers.During the past three decades,the main idea of construction of highly nonlinear resilient functions are bene-fited from concatenating a large number of affine subfunctions.However,these resilient functions as core component of ciphers usually suffered from the guess and determine attack or alge-braic attack since the n-variable nonlinear Boolean functions can be easily given rise to partial linear relations by fixing at most n/2 variables of them.How to design highly nonlinear resilient functions(S-boxes)without concatenating a large number of n/2 variables affine subfunctions appears to be an important task.In this article,a new construction of highly nonlinear resilient functions is proposed.These functions consist of two classes subfunctions.More specially,the first class(nonlinear part)contains both the bent functions with 2k variables and some affine subfunctions with n/2-k variables which are attained by using[n/2-k,m,d]disjoint linear codes.The second class(linear part)includes some linear subfunctions with n/2 variables which are attained by using[n/2,m,d]disjoint linear codes.It is illustrated that these resilient functions have high nonlinearity and high algebraic degree.In particular,It is different from previous well-known resilient S-boxes,these new S-boxes cannot be directly decomposed into some affine subfunctions with n/2 variables by fixing at most n/2 variables.It means that the S-boxes(vectorial Boolean functions)which use these resilient functions as component functions have more favourable cryptography properties against the guess and determine attack or algebraic attacks.

Haixia ZHAO;Yongzhuang WEI

Ministry of Education Key Laboratory of Cognitive Radio and Information Processing,Guilin University of Electronic Technology,Guilin 541004,China;School of Mathematics and Computing Science,Guilin University of Electronic Technology,Guilin 541004,China;Guangxi Key Laboratory of Cryptography and Information Security,Guilin University of Electronic Technology,Guilin 541004,China

计算机科学前沿

[1]Haixia ZHAO;Yongzhuang WEI-.New construction of highly nonlinear resilient S-boxes via linear codes)[J].计算机科学前沿,2022(03):170-176

combiners,fited,subfunctions,alge,braic

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