[Lowerbounds, Upperbounds]

Algorithms are everywhere.

Title: Multi-Dimensional Range Query over Encrypted Data

Speaker: Elaine Shi, CSD

Location: NSH 1507
Time: 12-1 pm
Date: Friday, September 07, 2007

Abstract:

We design an encryption scheme called Multi-dimensional Range Query over Encrypted Data (MRQED), to address the privacy concerns related to the sharing of network audit logs and various other applications. Our scheme allows a network gateway to encrypt summaries of network flows before submitting them to an untrusted repository. When network intrusions are suspected, an authority can release a key to an auditor, allowing the auditor to decrypt flows whose attributes ( e.g., source and destination addresses, port numbers, etc.) fall within specific ranges. However, the privacy of all irrelevant flows are still preserved. We formally define the security for MRQED and prove the security of our construction under the decision bilinear Diffie-Hellman and decision linear assumptions in certain bilinear groups. We study the practical performance of our construction in the context of network audit logs. Apart from network audit logs, our scheme also has interesting applications for financial audit logs, medical privacy, untrusted remote storage, etc. In particular, we show that MRQED implies a solution to its dual problem, which enables investors to trade stocks through a broker in a privacy-preserving manner.

Title: Two applications of Szemeredi’s Regularity Lemma
Speaker: Oleg Pikhurko
When: September 6, 15:30-16:20pm
Where: Wean Hall, Room 5310
Abstract:

I will present two (short and unrelated) applications of Szemeredi’s Regularity Lemma.

In one (joint work with Benny Sudakov) we prove, for all large $n$, the conjecture of Lazebnik (1989) that among all graphs with n vertices and $m < n^2/4$ edges the maximum number of $3$-colorings is achieved by a semi-complete biparite graph.

Another application proves the conjecture of Aigner, Triesch, and Tuza (1995) that one can find an unknown acyclic orientation of any given graph of order $n$ by quering at most $(1/4+o(1))n^2$ edges.