复合离散混沌动力系统与Hash函数

在对一般的复合离散混池系统和一个由两个混池映射构成的特殊复合离散混池系统进行初步分析的基础上，建立了一个基于复合离散混池系统的带秘密密钥的Hash算法。算法以迭代初始点作为秘密密钥，以粗粒化的迭代轨迹作为其Hash值。该带秘密密钥的Hash函数满足一定的安全性要求，并且算法简单快速。

Composite Nonlinare Discrete Chaotic Dynamical Systems and Keyed Hash Functions

The aim of this paper is to deal with composite descrete chaotic dynamical systems and Keyed Hash based on it. The discrete chaotic dynamical systems is the iteration of a chaotic map. One of its characteristics is that the trajectory is sensitive to initial conditions and seems to be random though it is really a determinate process. The composite discrete chaotic dynamical system consists of some chaotic maps, and the iteration process is completely decided by one predetermined sequence called composite sequence. The trajectory of the composite discrete chaotic dynamical systems is not only sensitive to its initial conditions, but also relative with the composite sequence, which determines the choice of iterated function in the iterating process, so the trajectory is more complex than that of general discrete chaotic dynamical systems. After analyzing some basic properties of composite systems, we study a special one, which uses two chaotic maps and has special invariant distribution density function, and present a new approach to construct Keyed Hash function,with the composite sequences obtained from the message to be hashed. The approach uses the initial value of composite discrete chaotic dynamical system iteration as the secret key and the coarse graining trajectory as Hash value. Because of the sensitivity and randomicity of the iteration process, there is a very complex nonlinear relation between the Hash value and the corresponding message and secret key, and then every bit of the Hash value of the message M is relative with every bit of M . Furthermore, the algorithm is very fast and the Hash value is uniformly distributed in the Hash value space. Therefore, the keyed Hash function satisfies security requirements.