Math 290B (Lec 2) Winter 2006 schedule

Week 1

Organizational meeting. We will meet and decide what topics are most relevant to our research and plan a schedule of talks.

Week 2

Lecturer: Steve Lu

Abstract
Bilinear pairings (on elliptic curves) have come into play in many recent interesting developments in cryptography. One such pairing, the Tate-Lichtenbaum pairing, will be the focus of this talk. I will review the theory of divisors on elliptic curves. This will be followed by the definition of the pairing and some proofs of the bilinear properties it exhibits. Finally, I will present Miller's algorithm to acutally compute the pairing.

Week 3

Lecturer: Ryan Moriarty

Abstract
Given a 2-DNF formula on n variables, Boneh, Goh, and Nissim has shown how to construct a homorphic public key encryption scheme that allows for the public computation of the formula given only encryptions of the variables. I will present their construction of this encryption scheme and present a few of its applications. Finally, I will leave you with an open question on the natural augmentation of this scheme into a CCA1 secure scheme that has the same properties.

Week 4

Lecturer: Nishanth Chandran
Guest Lecturer: Brent Waters

Abstract
In this talk, I will be speaking about Brent Waters' paper on Identity Based Encryption (IBE). This is the first efficient IBE that is proven to be fully secure without the aid of Random Oracles. The scheme will be presented and the security of the scheme will be shown to reduce to the decisional Bilinear Diffie-Hellman (BDH) problem. Based on this IBE, a signature scheme that is secure under the computational Diffie-Hellman assumption without random oracles will be shown.

Week 5

Lecturer: Steve Lu

Abstract
Following the talk the previous week, I present an application of Waters' signature scheme to aggregate signatures. Using some of the properties of the signature scheme I was able to create an aggregate signature scheme without random oracles. I will exhibit some results due to joint work with Ostrovsky, Sahai, Shacham, Waters in this area.

Week 6

Lecturer: Anna Draganova

Abstract
Group signatures is a way for a person to sign anonymously on behalf of a group they are registered in. However, if a person does something wrong, there is a way to trace it back to him. The purpose of my talk is to introduce group signatures and how they may be constructed. The construction that is presented in my talk is based upon work by Boyen and Waters.

Week 7

Break

Week 8

Lecturer: Ryan Moriarty

Abstract
Ryan will present his TCC paper, Generalized Environmental Security from Number Theoretic Assumptions (joint work with Malkin, Yakovenko).

Week 9,10

Lecturer: Jens Groth

Abstract
Jens will present some of the recent work he has been doing. These involve non-interactive proofs and some great applications.