SPS结构大规模S盒设计与分析  

Large-scale S-box design and analysis of SPS structure

作　　者：张岚[1] 何良生 郁滨 ZHANG Lan;HE Liangsheng;YU Bin(Department of Cryptogram Engineering,Information Engineering University,Zhengzhou 450001,China;State Cryptography Administration,Beijing 100036,China)

机构地区：[1]信息工程大学密码工程学院,河南郑州450001 [2]国家密码管理局,北京100036

出　　处：《通信学报》2023年第2期27-40,共14页Journal on Communications

摘　　要：基于循环移位与异或运算构造了有限域(F2 m)4上的一类最优线性变换P,借鉴线性变换输入输出关系反证法的思想,提出将最优线性变换目标问题转化为若干个递进关系定理的证明方法,不仅解决了该类最优线性变换的证明,而且适用于任意线性变换的证明。通过小规模S盒与最优循环移位-异或型线性变换P,建立了2轮SPS结构的大规模S盒模型,设计了一系列密码学性质优良的轻量级大规模S盒,仅使用查表、循环移位、异或三类基本运算,提高了大规模S盒的线性度和差分均匀度。理论证明和实例分析表明,与已有大规模S盒构造方法相比,所提大规模S盒设计方案运算代价更加低廉,其差分、线性等密码学性质更加优良,适宜用于轻量级密码算法非线性置换设计。A class of optimal linear transformation P over a finite field(F2 m)4 was constructed based on cyclic shift and XOR operation.Using the idea of inverse proof of input-output relation of linear transformation for reference,a proof method was put forward that transformed the objective problem of optimal linear transformation into several theorems of progressive relation,which not only solved the proof of that kind of optimal linear transformation,but also was suitable for the proof of any linear transformation.By means of small-scale S-box and optimal cyclic shift-XOR linear transformation P,a large-scale S-box model with 2-round SPS structure was established,and a series of lightweight large-scale S-boxes with good cryptographic properties were designed.Only three kind of basic operations such as look-up table,cyclic shift and XOR were used in the proposed design scheme,which improved the linearity and difference uniformity of large-scale S-boxes.Theoretical proof and case analysis show that,compared with the existing large-scale S-box construction methods,the proposed large-scale S-box design scheme has lower computational cost and better cryptographic properties such as difference and linearity,which is suitable for the design of nonlinear permutation coding of lightweight cryptographic algorithms.

关 键 词：SPS结构 大规模S盒 循环移位-异或型线性变换 

分 类 号：TN918.1[电子电信—通信与信息系统]