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Algebras, Lattices, Varieties - A Conference in Honor of Walter Taylor
August 15-18, 2004
University of Colorado
Boulder, Colorado, USA |
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Organizers
Jennifer Hyndman, Keith Kearnes, Ralph McKenzie, George McNulty, Ágnes Szendrei, Ross Willard
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Applications of the dynamical properties of quasigroups
by
Smile Markovski
Institute of Informatics, Ss Ciryl and Methodius University, Skopje, Macedonia
Given a finite quasigroup (Q, *), we consider the transformations
E, D : Q+ --> Q+ on the set of all nonempty strings
Q+={x1... xn | xi in Q, n > 0 } defined by
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E(x1... xn)=(y1... yn) <===> yi = yi-1*xi, |
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D(x1... xn)=(y1... yn) <===> yi = xi-1*xi, |
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where xi in Q and y0, x0 in Q are fixed. Then E, D are
permutations on Q+ and E-1=D for y0 = x0. The
sets of iterated strings {E(n)(A) | n=0, 1, 2, ...} and
{D(n)(A) | n=0, 1, 2, ...}, where A in Q+,
have properties of 'uniformity' and 'fractalness' and these properties
can be used for defining suitable applications in cryptography
(pseudo-random string generators, stream ciphers, hash functions),
coding theory (stream codes), design theory, classification of
quasigroups.
Date received: July 5, 2004
Copyright © 2004 by the author(s).
The author(s) of this document and the organizers of the conference
have granted their consent to include this abstract in
Atlas Conferences Inc.
Document # caoc-11.