# Quasigroups in cryptology

@article{Shcherbacov2009QuasigroupsIC, title={Quasigroups in cryptology}, author={Victor A. Shcherbacov}, journal={Comput. Sci. J. Moldova}, year={2009}, volume={17}, pages={193-228} }

We give a review of some known published applications of quasi- groups in cryptology. Keywords: cryptology, quasigroup, (r,s,t)-quasigroup, stream- cipher, secret-sharing system, zero knowledge protocol, authen- tication of a message, NLPN sequence, Hamming distance.

## 30 Citations

Quasigroup based crypto-algorithms

- Mathematics, Computer ScienceArXiv
- 2012

Modifications of Markovski quasigroup based crypto-algorithm have been proposed, some of which are based on the systems of orthogonal n-ary groupoids.

On some quasigroup cryptographical primitives

- Computer Science, MathematicsArXiv
- 2011

Using Vojvoda approach [34] we demonstrate that cryptographical primitives proposed in [26] are vulnerable relative to chosen ciphertext attack and chosen plaintext attack. We develop proposed in…

Block Cipher Defined by Matrix Presentation of Quasigroups

- Mathematics, Computer ScienceIACR Cryptol. ePrint Arch.
- 2021

This paper introduces a block cipher based on the quAsigroup transformations, which are defined by the matrix presentation of the quasigroup operations, which is suitable for constructing a block Cipher since it doesn’t require too much memory space to store all the necessary data.

Design of crypto primitives based on quasigroups Smile Markovski

- Computer Science, Mathematics
- 2015

This survey article will present how quasigroups can be used for construction of various crypto primitives, and especially what type of quAsigroups are used and how they can be constructed.

Super Optimal S-boxes Based on Pure Non-linear 3-quasigroups

- Mathematics, Computer Science
- 2017

The methodology is based on 3-quasigroup operations and it enables someone to get 44-bit S-boxes optimal in all the above four properties that PRESENT S-box has.

Post-Quantum Cryptography: A Zero-Knowledge Authentication Protocol

- Mathematics, Computer ScienceArXiv
- 2017

A simple bare-bones solution of a Zero-Knowledge authentication protocol which uses non-commutative algebra and a variation of the generalized symmetric decomposition problem (GSDP) as a one-way function is presented.

New Developments in Quasigroup-Based Cryptography

- Computer Science, Mathematics
- 2014

This chapter offers an overview of new developments in quasigroup-based cryptography, especially of new defined quasGovernments, including Multivariate Quadratic Quasigroups and MQQ public key schemes, because of their potential to become one of the most efficient pubic key algorithms today.

Non-associative public-key cryptography

- Mathematics, Computer ScienceAMS-EMS-SPM Joint Meeting
- 2016

It is shown that left selfdistributive systems appear in a natural special case of a generalized AAG-KEP for magmas, and it is proposed, among others instances, concrete realizations using $f$-conjugacy in groups and shifted conjugacy in braid groups.

An analogue of the ElGamal scheme based on the Markovski algorithm

- Computer ScienceArXiv
- 2021

This paper gives an analogue of the ElGamal encryption system based on the Markovski algorithm and states that it can be assigned to either the H2O/H2O or H2S/M2M bands.

Latin quandles and applications to cryptography

- Mathematics, Computer Science
- 2021

Four distinct cores of an Osborn loop (non-diassociative and non-power associative) were introduced and investigated and the necessary and sufficient conditions for these cores to be quasi-Latin quandles and involutory quandle were established.

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