Authors: Krapež, Aleksandar 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Cryptographically suitable quasigroups via functional equations
Journal: Advances in Intelligent Systems and Computing
Volume: 207 AISC
First page: 265
Last page: 274
Conference: 4th ICT Innovations Conference on Secure and Intelligent Systems; Ohrid; North Macedonia; 12 September 2012 through 15 September 2012
Issue Date: 1-Jan-2013
ISBN: 978-3-642-37168-4
ISSN: 2194-5357
DOI: 10.1007/978-3-642-37169-1_26
The use of quasigroups in cryptography is increasingly popular. One method to find quasigroups suitable for cryptographic purposes is to use identity sieves, i.e. to find appropriate identities and check candidate quasigroups against them. We propose the use of functional equation approach to this problem. Namely, every identity can be considered as a functional equation and solutions to these equations as models of given identities. The identity i.e. functional equation can be transformed into related generalized functional equation which is suitable for algebraic treatment. A new method of solution of quadratic and parastrophically uncancelablle equations is given, using trees and dichotomies (a special equivalence relations). General solution is given by closed formulas. The quasigroups obtained can be further filtered using much simpler conditions.
Keywords: general solution | Identity sieve | quadratic functional equation | quasigroup
Publisher: Springer Link

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