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在密码算法的设计中,S-盒有着信息混淆的重要功能.传统的S-盒的密码学指标一般包括线性偏差、差分特征、代数免疫度、不动点个数、雪崩效应等.2006年,Kocarev给出了有限集合上的离散混沌理论.本文借鉴该理论,在汉明距离的基础上给出了S-盒的Lyapunov指数的定义,利用该定义计算了几个密码算法中的S-盒的Lyapunov指数值,并进行了比较.证明了在欧氏距离上定义的Lvapunov指数最大的映射,按本文提出的S-盒的Lyapunov指数的定义其Lyapunov指数为0;讨论了S-盒的Lyapunov指数与S-盒的雪崩效应之间的关系,该关系实际上是混沌理论中的蝴蝶效应与密码学中的雪崩效应之间的关系.本文提出的S-盒的Lyapunov指数的定义可视为对传统的S-盒的密码学指标的补充.
In the design of cryptographic algorithms, S-boxes have the important function of information confusion.The traditional S-box cryptographic indexes generally include linear deviation, differential features, algebraic immunity, the number of fixed points, avalanche effect, etc. 2006 , Kocarev gives the theory of discrete chaos on a finite set.In this paper, based on the Hamming distance, this paper gives the definition of Lyapunov exponent of S-box. Using this definition, we calculate the S- The Lyapunov exponent value of the box is compared and compared.It is proved that the maximum Lvapunov exponent mapping on the Euclidean distance is defined by the Lyapunov exponent of the Lyapunov exponent of the S-box proposed in this paper, Lyapunov exponent and the avalanche effect of S-box, which is actually the relationship between the butterfly effect in chaos theory and the avalanche effect in cryptography.The definition of Lyapunov exponent of S-box proposed in this paper can be seen Complementing the traditional S-box cryptographic criteria.