article · 1999

Quasigroup String Processing

Smile Markovski, Danilo Gligoroski, Verica Bakeva

Cited by 0Abstract and details only

Abstract

Given afi set A we consider quasigroup operations 1 # 2 #:::# n on A and we use them todefi transformations E #D : A ,whereA is the set of allfil strings with members from A.We show that the mappings E and D haveseveral useful properties, suitable for many purposes in cryptography, coding theory, defi and improving (pseudo) random generators, ... . Key words: Markovchain, quasigroup, quasigroup string processing, uniform distribution AMS Mathematics Subject Classification (1991): 20N05, 60J10, 60J20 1 Preliminaries It was noticed in [4] and [5] that quasigroups can be very useful for cryptographic purposes, mainly because there is a huge number of quasigroups operations on a given finite set, and it is easy to define the encoding and decoding functions by using the quasigroup operations as well. In this paper we are treating transformations of the( finite) stings with members of a given finite set A by using quasigroup operations on A,andwe are proving several useful properties of these transformations, confirming the suggestions stated in [4] and [5]. Muchmore, the results that we present here mayhavemany other useful applications. Recall that a Q# ) is a groupoid( i.e. algebra with one binary operation on the set Q) satisfying the law: 8u# v 2 9!x# y 2 x u = v &amp; u y = v)( In fact(c says that the equations x u = v# u y = v for eachgiven u# v 2 Q and x# y unknown, have unique solutions. This implies that any Q# ) allows another quasigroup operation n on Q defined by x n y = z () y = x z(andthenthefollowing equalities are identities in the algebra( Q# # n): x x n y)=y = x x y):( We note that by( 2) the operations and n are mutually defined, i.e. one of these two operations uniquely determines the other one. The usefulness of the q...

Cite this paper

APA 7

Markovski, S., Gligoroski, D., & Bakeva, V. (1999). Quasigroup String Processing.

MLA 9

Markovski, Smile, et al. “Quasigroup String Processing.” 1999.

Chicago

Markovski, Smile, Danilo Gligoroski, and Verica Bakeva. 1999. “Quasigroup String Processing.”

Harvard

Markovski, S., Gligoroski, D. and Bakeva, V. (1999) ‘Quasigroup String Processing’.

BibTeX

@article{markovski1999quasigroup,
  title = {{Quasigroup String Processing}},
  author = {Markovski, Smile and Gligoroski, Danilo and Bakeva, Verica},
  year = {1999}
}

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