一类轻量级最优S盒的构造方法

S盒是对称密码算法中主要的非线性部件,其密码性质的好坏将直接影响到密码算法的整体安全性。给出了一类4比特最优S盒的构造方法,证明了此类最优S盒属于同一仿射等价类G₁,统计给出其差分、线性和代数次数等密码学性质,计算出此类S盒的硬件实现平均等效门数为25.6。在此基础上,通过带轮密钥的3轮MISTY结构和Feistel结构构造了一类8比特S盒,给出了结构最优性的定义,并给出8比特S盒达到结构最优性的一个充分条件。

Construction methods for a class of lightweight optimal S-boxes

S-boxes are fundamental nonlinear components used in symmetric ciphers. The security of the ciphers is directly affected by the cryptographic properties of the S-boxes. This paper presents a construction method for a class of 4-bit optimal S-boxes, and proves that these optimal S-boxes can be classified into the same affine equivalent class G1. For each optimal S-boxes, we count their differential, linear properties and algebraic degree, then get the average number of equivalent gate of 25.6 in hardware implement. Furthermore, utilizing three-round MISTY and Feistel structure with sub-keys, we investigate the problem of constructing 8 bit S-boxes. Using a new definition called structure-optimality, we put forward a sufficient condition when 8-bit S-boxes reach the structure-optimality.