New Frontiers in Secure Computation

The notion of secure computation is central to cryptography. Introduced in the seminal works of Yao [FOCS'82, FOCS'86] and Goldreich, Micali and Wigderson [STOC'87], secure multiparty computation allows a group of (mutually) distrustful parties to jointly compute any functionality over their individual private inputs in such a manner that the honest parties obtain the correct outputs and no group of malicious parties learn anything beyond their inputs and the prescribed outputs. General feasibility results for secure computation were given by Yao [FOCS'86] and Goldreich et al. [STOC'87] more than two decades ago. Subsequent to these works, designing secure computation protocols that can tolerate more powerful adversaries and satisfy stronger notions of security has been a very active area of research. In this dissertation, we study two such new frontiers in the area of secure computation. In the first part of this dissertation, we initiate a study of designing leakage-resilient interactive protocols. Specifically, we consider the scenario where an adversary, in addition to corrupting a subset of parties, can leak (potentially via physical attacks) arbitrary information from the secret state of any honest party. This is in contrast to the standard notion of secure computation where it is assumed that the adversary only has "black-box'' access to the honest parties. In particular, we formalize a meaningful definition of leakage-resilient zero knowledge proof systems and provide constructions that satisfy our notion. We also discuss various applications of our results. The second part of this dissertation concerns with the general question of whether it is possible to securely run cryptographic protocols over an insecure network environment such as the Internet. It is well-known that the standard notion of secure computation is only relevant to the "stand-alone" setting where a single protocol is being executed in isolation; as such it does not guarantee security when multiple protocol sessions may be executed concurrently under the control of an adversary who is present across all sessions. We consider the open problem of constructing secure password-based authenticated key exchange protocols in such a setting in the "plain model" (i.e., without assuming any trusted infrastructure or random oracles). We give the first construction of such a protocol based on standard cryptographic assumptions. Our results are in fact much more general, and extend to other functionalities w.r.t. a (necessarily) weakened notion of concurrently secure computation. The results presented in this dissertation stem from two papers which are joint works with Sanjam Garg and Amit Sahai, and with Vipul Goyal and Rafail Ostrovsky, respectively.