The applications we use every day deal with privacy-sensitive data that come from different sources and entities, hence creating a tension between more functionality and privacy. Secure Multiparty Computation (MPC), a fundamental problem in cryptography, tries to resolve this tension.

A promising direction for making MPC practical is to consider realistic relaxations in security in exchange for better efficiency. I will focus on trading-off information leakage for better efficiency in the two-party setting. I start with a simple and efficient construction with security against malicious cheating that leaks an adversarially-chosen predicate of honest party's input. Then I show how to improve it by restricting the leakage in two orthogonal ways: (i) limiting leakage to a natural notion of "only computation leaks", and (ii) reducing probability of leakage using a tunable security parameter.