Some models of chaotic motion of particles and their application to cryptography

Abstract

In the paper reflection law models describing the motion of a free particle in a bounded domain are considered. Properties of such dynamical systems are strongly related to the boundary conditions, expressed by a map called a reflection law. We discuss recent results concerning the problem of transferring important properties like chaos, ergodicity and mixing from the reflection law to the motion of the particle. Then we present in a consistent way a method of construction of block cryptosystems, using chaotic reflection law models with appropriate properties. We also propose an application of the mechanical particle model (possessing the transferring property) for constructing pseudo-random numbers generator which can be applied in stream ciphers. The security of the cryptosystem based on particle's motion is due to the property of statistical independence of the actual location of the particle, after a number of reflections, of its initial location.