Stronger notions of secure computation

The concept of secure computation protocols was introduced in the seminal works of Yao and Goldreich et al. In this setting, a set of parties wish to compute a joint function of the inputs which they individually hold. The protocol for computation of this function should be such that it does not leak any information about the individual inputs (other than what is leaked by the output itself). General feasibility results for secure computation were obtained by Yao and Goldreich et al. in mid 1980's. Since then, designing secure computation protocols satisfying stronger security notions has been an active area of research. In this dissertation, we consider two different stronger notions of secure computation. We first consider the notion of resettable security where the security of a party should be maintained even if it uses the same randomness in multiple protocol executions. A well known problem left open by previous works in this area is whether it is possible to have a secure zero-knowledge protocol in which both parties may be resettable. We resolve this question in the positive by constructing such a protocol. At the heart of our construction is a novel non-black-box simulation strategy, which we believe to be of independent interest. We then consider the notion of covert computation where the parties can run a protocol without knowing if other parties are also participating in the protocol or not. At the end of the protocol, if all parties participated in the protocol and if the function output is favorable to all parties, only then the output is revealed. In this dissertation, we present the first construction for covert multi-party computation. In order to achieve this goal, we introduce a number of new techniques. One central technical contribution is the development of zero-knowledge proofs to garbled circuits technique. Along the way, we also develop a definition of covert computation as per the Ideal/Real model simulation paradigm. The results presented in this dissertation stem from two papers which are respectively joint work with Amit Sahai [GS08], and with Nishanth Chandran, Rafail Ostrovsky and Amit Sahai [CGO07].