Tracing bit differences in strings transformed by linear quasigroups of order 4

Abstract

Quasigroups are simple algebraic structures whose application in cryptography is increasing rapidly, however not all quasigroups are suitable for cryptographic purposes. In this paper we investigate how a change of one bit in an input binary string affects the strings obtained by applying E-transformation as a multilevel encryptor based on linear quasigroups of order 4. We define a Boolean presentation of quasigroups and we show that for quasigroups of order 4 their Boolean presentations are of degree at most 2. We also give some properties for linear quasigroups and show that using these properties the number of linear quasigroups of order 4 can be easily computed.