2 research outputs found
Refinement of Two-Factor Factorizations of a Linear Partial Differential Operator of Arbitrary Order and Dimension
Given a right factor and a left factor of a Linear Partial Differential
Operator (LPDO), under which conditions we can refine these two-factor
factorizations into one three-factor factorization? This problem is solved for
LPDOs of arbitrary order and number of variables. A more general result for the
incomplete factorizations of LPDOs is proved as well.Comment: The final publication is available at http://www.springerlink.co
A New Primitive for a Diffie-Hellman-like Key Exchange Protocol Based on Multivariate Ore Polynomials
In this paper we present a new primitive for a key exchange protocol based on
multivariate non-commutative polynomial rings, analogous to the classic
Diffie-Hellman method. Our technique extends the proposed scheme of Boucher et
al. from 2010. Their method was broken by Dubois and Kammerer in 2011, who
exploited the Euclidean domain structure of the chosen ring. However, our
proposal is immune against such attacks, without losing the advantages of
non-commutative polynomial rings as outlined by Boucher et al. Moreover, our
extension is not restricted to any particular ring, but is designed to allow
users to readily choose from a large class of rings when applying the protocol.
Our primitive can also be applied to other cryptographic paradigms. In
particular, we develop a three-pass protocol, a public key cryptosystem, a
digital signature scheme and a zero-knowledge proof protocol