Quasigroups and Quasigroups String Transformation

The cryptocodes considered in this monograph are based on quasigroups. Therefore, in this chapter, we give a brief overview of quasigroups and their properties. More details for quasigroups and their properties are given in Belousov (1972), Denes and Keedwell (1974) and Laywine and Mullen (1998). Using quasigroups, some string transformations have been defined in Markovski et al. (1999, 1997, 2001), Markovski (2003), Krapež (2010) and Dimitrova et al. (2012). They are called quasigroup string transformations. These quasigroup transformations are very useful for application in cryptography and coding theory, primarily for designing cryptographic primitives, error-detecting and error-correcting codes. The reasons for this are: the structure of quasigroups, their large number and their properties.