IJPAM: Volume 40, No. 3 (2007)

POLYNOMIAL PERMUTATIONS ON FINITE
LATTICES RELATED TO CRYPTOGRAPHY

Dietmar Dorninger$^1$, Helmut Länger$^2$
$^{1,2}$Institute of Discrete Mathematics and Geometry
Vienna University of Technology
Wiedner Hauptstraße 8-10, Vienna, A-1040, AUSTRIA
$^1$e-mail: [email protected]
$^2$e-mail: [email protected]


Abstract.Motivated by cryptography, permutations induced by polynomial functions on finite lattices ${\mathcal L}=(L,\vee,\wedge,^*)$ with an antitone involution $^*$ are investigated. These permutations together with the operation of composition form a subgroup of the symmetric group on $L$. We describe the structure of this subgroup for different classes of lattices ${\mathcal L}$ and indicate possible applications by outlining a protocol for a symmetric cipher.

Received: September 29, 2007

AMS Subject Classification: 06C15, 08A40, 06D30

Key Words and Phrases: lattice, antitone involution, polynomial function, permutation, De Morgan algebra, polynomially complete, cryptographic protocol

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 40
Issue: 3