Symplectic Geometry on Quantum Plane

A study of symplectic forms associated with two dimensional quantum planes and the quantum sphere in a three dimensional orthogonal quantum plane is provided. The associated Hamiltonian vector fields and Poissonian algebraic relations are made explicit.Comment: 12 pages, Late

Collaborative enforcement of firewall policies in virtual private networks

The widely deployed Virtual Private Network (VPN) tech-nology allows roaming users to build an encrypted tunnel to a VPN server, which henceforth allows roaming users to access some resources as if that computer is residing on their home organization’s network. Although the VPN technol-ogy is very useful, it imposes security threats to the remote network because their firewall does not know what traffic is flowing inside the VPN tunnel. To address this issue, we pro-pose VGuard, a framework that allows a policy owner and a request owner to collaboratively determine whether the re-quest satisfies the policy without the policy owner knowing the request and the request owner knowing the policy. We first present an efficient protocol, called Xhash, for oblivious comparison, which allows two parties, where each party has a number, to compare whether they have the same num-ber, without disclosing their numbers to each other. Then, we present the VGuard framework that uses Xhash as the basic building block. The basic idea of VGuard is to first convert a firewall policy to non-overlapping numerical rules and then use Xhash to check whether a request matches a rule. Comparing with the Cross-Domain Cooperative Fire-wall (CDCF) framework, which represents the state-of-the-art, VGuard is not only more secure but also orders of mag-nitude more efficient. On real-life firewall policies, for pro-cessing packets, our experimental results show that VGuard is 552 times faster than CDCF on one party and 5035 times faster than CDCF on the other party