New Frontiers in Information-Theoretic Secure Computation

Information-theoretic secure computation is a general-purpose technique for processing sensitive data without compromising its confidentiality or integrity even in the presence of a computationally-unbounded all-powerful adversary. This notion plays an important role in cryptography, both as a stand-alone object and as a tool for computational constructs. Despite its increasing importance, we have a very limited understanding of the *intrinsic complexity* of information-theoretic security, and some of the most central feasibility questions in this area have remained open for more than three decades.In this proposal, we aim to decipher the power and limitations of this notion. We will focus on three main objectives. First, we aim to improve the complexity of general *secret sharing schemes* and exploit such improvements towards realizing highly-efficient general-purpose zero-knowledge proofs. The second objective is to explore the complexity of Secure Non-Interactive Reductions and Multiparty Randomized Encoding -- a powerful generalization of information-theoretic garbled circuits that was recently presented by the PI. The third objective is to expand our theoretical understanding of constant-round information-theoretic protocols, optimize their round complexity, and study their concrete and asymptotic computational complexity.Being part of several recent exciting developments in these areas, we believe that it is now possible to make progress in some of these basic open problems. The suggested research will bridge across different regions of computer science such as coding theory, cryptography, and computational complexity. It is expected to impact central problems in cryptography, while enriching the general landscape of theoretical computer science.