Generating huge quasigroups from small non-linear bijections via extended Feistel function

Markovski, Smile and Mileva, Aleksandra (2009) Generating huge quasigroups from small non-linear bijections via extended Feistel function. Quasigroups and related systems, 17 (1). pp. 91-106. ISSN 1561-2848

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Abstract

Quasigroups of huge order, like 2^256, 2^512, 2^1024, that can be effectively constructed,
have important applications in designing several cryptographic primitives. We
propose an effective method for construction of such huge quasigroups of order r = 2^s2^t for
small fixed values of s and arbitrary values of t; the complexity of computation of the quasigroup
multiplication is O(log(log(r))) = O(t). Besides the computational effectiveness,
these quasigroups can be constructed in such a way to have other desirable cryptographic
properties: do not satisfy the commutative law, the associative law, the idempotent law, to
have no proper subquasigroups, to be non-linear, etc. These quasigroups are constructed by
complete mappings generated by suitable bijections of order 2^s via extended Feistel network
functions.

Item Type:	Article
Subjects:	Natural sciences > Computer and information sciences Natural sciences > Matematics
Divisions:	Faculty of Computer Science
Depositing User:	Aleksandra Mileva
Date Deposited:	30 Oct 2012 18:03
Last Modified:	30 Oct 2012 18:03
URI:	https://eprints.ugd.edu.mk/id/eprint/101

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