New construction of highly nonlinear resilient S-boxes via linear codes  

作　　者：Haixia ZHAO Yongzhuang WEI 

机构地区：[1]Ministry of Education Key Laboratory of Cognitive Radio and Information Processing,Guilin University of Electronic Technology,Guilin 541004,China [2]School of Mathematics and Computing Science,Guilin University of Electronic Technology,Guilin 541004,China [3]Guangxi Key Laboratory of Cryptography and Information Security,Guilin University of Electronic Technology,Guilin 541004,China

出　　处：《Frontiers of Computer Science》2022年第3期175-181,共7页中国计算机科学前沿（英文版）

基　　金：The work was supported in part by the National Natural Science Foundation of China(Grant No.61872103);in part by Guangxi Science and Technology Foundation(Guike AB18281019,Guike AD18281026);in part by Guangxi Natural Science Foundation(2019GXNSFGA245004);in part by the Foundation of Ministry of Education Key Laboratory of Cognitive Radio and Information Processing(Guilin University of Electronic Technology)(CRKL180107).

摘　　要：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 benefited 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 algebraic attack since the n-variable nonlinear Boolean functions can be easily given rise to partial linear relations by fixing at most nil variables of them.How to design highly nonlinear resilient functions(S-boxes)without concatenating a large number of nil 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 nil 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 subftinctions with nil variables by fixing at most nil 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.

关 键 词：stream cipher S-BOX disjoint linear codes resiliency NONLINEARITY 

分 类 号：O17[理学—数学]