Block cipher defined by matrix presentation of quasigroups

Abstract

Designing new cryptosystems and their cryptanalysis is the basic cycle of advancement in the field of cryptography. In this paper we introduce a block cipher based on the quasigroup transformations, which are defined by the matrix presentation of the quasigroup operations. This type of quasigroup presentation is suitable for constructing a block cipher since it doesn’t require too much memory space to store all the necessary data, so it can be used even for lightweight cryptographic purposes. For now, we are considering only the quasigroups of order 4. Constructions with quasigroups of higer order and examination of the strengths and weaknesses of this design will be considered in next papers.