Chaos-Based Hash Function And Its Application In Message Authentication

The subject of this thesis is the study of chaos-based hash functions. With chaos theory, we described the behavior of certain dynamical systems that evolve with time. Such systems have been invoked in this thesis and are considered as primitive to the construction of chaos-based hash function.Protecting the authenticity of information has been a great challenge for cryptographers. The existing solutions have focused much on the importance of hash functions. In this thesis, the practicality of hash functions based on chaos is studied and an overview of the complexity theoretic definitions and constructions is given.Since many of the existing hash algorithms for message encryption have been proved to be not securely convenient, the contribution of this thesis, in that context, lies in the fulfillment of those shortcomings by (1) describing the role of chaos as primitive to the construction of suitable hash algorithms, (2) taking advantage of the complex behavior of chaotic dynamical systems to build robust encryption algorithms and (3) performing the study of practical design for one-way hash functions using chaotic systems. Hence, a new one-way chaos-based hash algorithm was proposed.Further, a general model for hash functions classification is detailed and taxonomy for attacks on hash functions is presented. Then all schemes in the literature are divided into two classes:keyed hash functions, and unkeyed hash functions. A key feature of hashing algorithms is that they are extremely sensitive to the message, i.e. changing even one bit of the input will change the output dramatically. This fact is also proven for our proposed hash algorithm based on chaos.It should be noticed that implementing the above algorithm involves minimum modifications to the existing schemes, therefore making it to meet the requirements of a suitable hashing algorithm.Finally, an outlook of hash functions applications is given with particular emphasis to message authentication where the concept of digital signature is well described.