Markovski, Smile and Bakeva, Verica and Dimitrova, Vesna and Mileva, Aleksandra and Popovska-Mitrovik, Aleksandra and Mihajloska Trpcheska, Hristina (2023) Applications of Quasigroups in Cryptography and Coding Theory. In: Algebra without Borders – Classical and Constructive Nonassociative Algebraic Structures, Foundations and Applications. Springer Cham, pp. 419-489. ISBN 978-3-031-39333-4
Full text not available from this repository.Abstract
This survey article discusses some applications of quasigroups in cryptography and coding theory. Here mainly results obtained by the authors of this article are considered and obtained in the last quarter of the century. Not all of their results are presented; emphasis is given to those that were interested for the wider community. Security of the modern world is dependent on the many cryptographic products like block ciphers, stream ciphers, digital signatures and encryption schemes, hash functions, pseudo-random number generators, ... These products are mainly produced by using associative structures (number theory, group and finite field theory, Boolean algebras, etc.) The development of quantum computers questioned security based on associative structures. So, nowadays, the use of quasigroups for building cryptographic products is becoming more important. This short survey presents how quasigroups can be exploited for building suitable cryptographic primitives. For that aim, we define some types of quasigroups that are suitable for that purpose, we give the definitions of several kinds of quasigroup transformations, and we explain the constructions of some types of cryptographic primitives obtained by quasigroup transformations. (We notice that cryptographic properties are not discussed in this survey. The efficiency and security of the crypto products based on quasigroups is an open research problem for cryptographers and cryptanalysts.) The quasigroups are also suitable algebraic structures for building error detecting and error correcting code. We give one type of error detecting code based on quasigroups. Error correcting codes resistant to an intruder attack, so called RCBQ (Random Codes Based on Quasigroups) are given in details, as well as some of their applications in processing images and audio signals.
| Item Type: | Book Section |
|---|---|
| Subjects: | Natural sciences > Computer and information sciences |
| Divisions: | Faculty of Computer Science |
| Depositing User: | Aleksandra Mileva |
| Date Deposited: | 07 Dec 2023 10:07 |
| Last Modified: | 07 Dec 2023 10:07 |
| URI: | https://eprints.ugd.edu.mk/id/eprint/32792 |
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