Homologie de morse et théorème de la signature

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

Signature of the interaction between dark energy and dark matter in galaxy clusters

We investigate the influence of ail interaction between dark energy and dark matter upon the dynamics of galaxy clusters. We obtain file general Layser-Irvine equation in the presence of interactions, and find how, in that case. the virial theorem stands corrected. Using optical, X-ray and weak lensing data from 33 relaxed galaxy clusters, we put constraints on the strength of the coupling between the dark sectors. Available data Suggests that this coupling is small but positive, indicating that dark energy might be decaying into dark matter. Systematic effects between the several mass estimates, however, should be better known, before definitive conclusions oil the magnitude and significance of this coupling could be established. (C) 2009 Published by Elsevier B.V.

Signature, positive Hopf plumbing and the Coxeter transformation

By a theorem of A'Campo, the eigenvalues of certain Coxeter transformations are positive real or lie on the unit circle. By optimally bounding the signature of tree-like positive Hopf plumbings from below by the genus, we prove that at least two thirds of them lie on the unit circle. In contrast, we show that for divide links, the signature cannot be linearly bounded from below by the genus.

Strong designated verifier signature in a multi-user setting

The security of strong designated verifier (SDV) signature schemes has thus far been analyzed only in a two-user setting. We observe that security in a two-user setting does not necessarily imply the same in a multi-user setting for SDV signatures. Moreover, we show that existing security notions do not adequately model the security of SDV signatures even in a two-user setting. We then propose revised notions of security in a multi-user setting and show that no existing scheme satisfies these notions. A new SDV signature scheme is then presented and proven secure under the revised notions in the standard model. For the purpose of constructing the SDV signature scheme, we propose a one-pass key establishment protocol in the standard model, which is of independent interest in itself.

A novel nonrepudiable threshold multi-proxy multi-signature scheme with shared verification

Tzeng et al. proposed a new threshold multi-proxy multi-signature scheme with threshold verification. In their scheme, a subset of original signers authenticates a designated proxy group to sign on behalf of the original group. A message m has to be signed by a subset of proxy signers who can represent the proxy group. Then, the proxy signature is sent to the verifier group. A subset of verifiers in the verifier group can also represent the group to authenticate the proxy signature. Subsequently, there are two improved schemes to eliminate the security leak of Tzeng et al.’s scheme. In this paper, we have pointed out the security leakage of the three schemes and further proposed a novel threshold multi-proxy multi-signature scheme with threshold verification.

Identity-based strong designated verifier signature schemes: Attacks and new construction

A strong designated verifier signature scheme makes it possible for a signer to convince a designated verifier that she has signed a message in such a way that the designated verifier cannot transfer the signature to a third party, and no third party can even verify the validity of a designated verifier signature. We show that anyone who intercepts one signature can verify subsequent signatures in Zhang-Mao ID-based designated verifier signature scheme and Lal-Verma ID-based designated verifier proxy signature scheme. We propose a new and efficient ID-based designated verifier signature scheme that is strong and unforgeable. As a direct corollary, we also get a new efficient ID-based designated verifier proxy signature scheme.