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: http://eprints.ugd.edu.mk/id/eprint/101

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