No abstract uploaded!

No abstract uploaded!

No abstract uploaded!

Soit$T$un courant positif fermé sur un voisinage de 0 dans$C$^{n}. Nous montrons que$T$admet un cône tangent (limite de la famille de ses homothétiques), dès que les masses projectives$v$_{T}(r) convergent assez vite vers$V$_{T}(0) pour que ($v$_{T}(r)−$v$_{T}(0))/$r$soit localement sommable en$r$=0. Cette condition suffisante est optimale: nous construisons des courants de bidegré (1, 1) n'ayant pas de cône tangent, tels que l'intégrale de ($v$_{T}(r)−$v$_{T}(0))/$r$soit aussi peu divergente qu'on le souhaite. Lorsque$T$est le courant d'intégration sur un ensemble analytique, on vérifie que$v$_{T}(r)−$v$_{T}(0)=0$r$^{ε}), ce qui redonne le théorème de Thie-King sur l'existence du cône tangent.

We use an RLWE-based key exchange scheme to construct a simple and efficient post-quantum oblivious transfer based on the Ring Learning with Errors assumption. We prove that our protocol is secure in the Universal Composability framework against static malicious adversaries in the random oracle model. The main idea of the protocol is that the receiver and the sender interact using the RLWE-based key exchange in such a way that the sender computes two keys, one of them shared with the receiver. It is infeasible for the sender to know which is the shared key and for the receiver to get information about the other one. The sender encrypts each message with each key using a symmetric-key encryption scheme and the receiver can only decrypt one of the ciphertexts. The protocol is extremely efficient in terms of computational and communication complexity, and thus a strong candidate for post-quantum applications.