Abstract:
I will talk about the problem of using shared resources for private computations. This problem has been studied in two closely related models: locally random reductions (LRRs) and private information retrieval (PIR) schemes.

In both models, there are two parties that communicate with each other. The first party consists only of a single client and the other party consists of one or more resources (which could be, for instance, oracles or servers). The client wishes to solve some problem on an input that is private to the client by interacting with the information resources. The crucial privacy requirement is that at the end of all communication each resource must not learn anything about the actual input, except possibly the length of the input. It is considered infeasible for the resources to simply send all information (or computational aids) that would be required by the client to solve the problem on any possible input of a given length.

The solution to this puzzle makes use of randomness in a crucial way. Basically, for any given input the client sends different random queries to different resources and uses the answers to these queries to solve the problem. The probability distribution of the random query(ies) sent to a single resource depends only on the length of the input. If we assume that the resources do not collude to learn the input of the client and that thus each resource gets to know only its own queries, then the resources do not learn anything about the actual problem instance. The challenge in constructing good LRRs and PIR schemes is to devise mechanisms with as low as possible communication requirement.

I will explain and motivate these models, describe known results related to these models, and present my recent results on the complexity of languages that have locally random reductions (LRRs) of certain types.

Biography:
Dr. Rahul Tripathi is an assistant professor of Computer Science and Engineering at the University of South Florida (USF), Tampa, FL. His research interests are in algorithms and computational complexity theory. Dr. Tripathi holds a B.Tech. (2000) in Computer Science and Engineering from the Indian Institute of Technology, Kanpur, India, and an M.S. (2003) and Ph.D. (2005) in Computer Science from the University of Rochester, NY.