A Topological Study of Chaotic Iterations. Application to Hash Functions
This work addresses the need for secure and unpredictable hash functions in computer science security, though it appears incremental by applying existing chaotic theory to hash functions.
The paper conducted a topological analysis of chaotic iterations, demonstrating that they possess properties like topological mixing, expansivity, and high entropy, leading to unpredictable behavior. As an application, it proposed two versions of a chaotic hash function, with the second incorporating a chaotic artificial neural network.
Chaotic iterations, a tool formerly used in distributed computing, has recently revealed various interesting properties of disorder leading to its use in the computer science security field. In this paper, a comprehensive study of its topological behavior is proposed. It is stated that, in addition to being chaotic as defined in the Devaney's formulation, this tool possesses the property of topological mixing. Additionally, its level of sensibility, expansivity, and topological entropy are evaluated. All of these properties lead to a complete unpredictable behavior for the chaotic iterations. As it only manipulates binary digits or integers, we show that it is possible to use it to produce truly chaotic computer programs. As an application example, a truly chaotic hash function is proposed in two versions. In the second version, an artificial neural network is used, which can be stated as chaotic according to Devaney.