2026-09-21T16:43:42Z https://opus4.kobv.de/opus4-uni-passau/oai

oai:kobv.de-opus4-uni-passau:143 2025-08-13 bibliography:false doc-type:PhDThesis status-type:publishedVersion open_access ddc ddc:510

Weyl Gröbner Basis Cryptosystems Rashid Ali 510 Gröbner-Basis Weyl-Algebra Kryptologie Public Key Cryptosystem Non commutative Gröbner Basis In this thesis, we shall consider a certain class of algebraic cryptosystems called Gröbner Basis Cryptosystems. In 1994, Koblitz introduced the Polly Cracker cryptosystem that is based on the theory of Gröbner basis in commutative polynomials rings. The security of this cryptosystem relies on the fact that the computation of Gröbner basis is, in general, EXPSPACE-hard. Cryptanalysis of these commutative Polly Cracker type cryptosystems is possible by using attacks that do not require the computation of Gröbner basis for breaking the system, for example, the attacks based on linear algebra. To secure these (commutative) Gröbner basis cryptosystems against various attacks, among others, Ackermann and Kreuzer introduced a general class of Gröbner Basis Cryptosystems that are based on the difficulty of computing module Gröbner bases over general non-commutative rings. The objective of this research is to describe a special class of such cryptosystems by introducing the Weyl Gröbner Basis Cryptosystems. We divide this class of cryptosystems in two parts namely the (left) Weyl Gröbner Basis Cryptosystems and Two-Sided Weyl Gröbner Basis Cryptosystems. We suggest to use Gröbner bases for left and two-sided ideals in Weyl algebras to construct specific instances of such cryptosystems. We analyse the resistance of these cryptosystems to the standard attacks and provide computational evidence that secure Weyl Gröbner Basis Cryptosystems can be built using left (resp. two-sided) Gröbner bases in Weyl algebras. Universität Passau Passau Innstrasse 29, 94032 Passau Martin Kreuzer Prof. Dr. 2011-06-16 2011-06-22 PhDThesis Text publishedVersion urn:nbn:de:bvb:739-opus-23195 application/pdf eng Standardbedingung laut Einverständniserklärung thesis.doctoral Universität Passau Passau Fakultät für Informatik und Mathematik 1 https://opus4.kobv.de/opus4-uni-passau/oai/container/index/docId/143 https://opus4.kobv.de/opus4-uni-passau/frontdoor/index/index/docId/143