Group Analysis of Differential Equations and Integrable Systems − 2018


Maryna Nesterenko (Institute of Mathematics of NAS of Ukraine, Kyiv, Ukraine)

Simple Lie groups in quasicrystalls

Abstract:
Quasicrystalls constructed as model sets of semisimple Lie groups are applied to cryptography and discrete analysis of almost periodic functions.

Namely: a method for finite discrete analysis of almost periodic functions that is entirely based on group theoretical methods, primarily finite groups and their duals is developed (the method is practical and computable and examples of functions based on the standard Fibonacci quasicrystal are proposed); and a symmetric encryption method based on one-dimensional quasicrystals is proposed (the advantages of the cipher are stability, strict aperiodicity and everywhere discontinuous property as well as the high speed of computation and simplicity of implementation).