Exploring Crypto Dark Matter: New Candidate PRFs and their Applications

In this talk, I will present new and simple candidate PRFs introduced in a recent work. In this work, we depart from the traditional approaches for building PRFs used in provable security or in applied cryptography by exploring a new space of plausible PRF candidates. Our guiding principle is to maximize simplicity while optimizing complexity measures that are relevant to advanced cryptographic applications. Our primary focus is on weak PRFs computable by very simple circuits (depth-2 ACC circuits). 
The advantage of our approach is twofold. On the theoretical side, the simplicity of our candidates enables us to draw many natural connections between their hardness and questions in complexity theory or learning theory. On the applied side, the piecewise-linear structure of our candidates lends itself nicely to applications in secure multiparty computation (MPC). In particular, we construct protocols for distributed PRF evaluation that achieve better round complexity and/or communication complexity compared to protocols obtained by combining standard MPC protocols with practical PRFs (included MPC-friendly ones).
Finally, we introduce a new primitive we call an encoded-input PRF, which can be viewed as an interpolation between weak PRFs and standard (strong) PRFs. As we demonstrate, an encoded-input PRF can often be used as a drop-in replacement for a strong PRF, combining the efficiency benefits of weak PRFs and the security benefits of strong PRFs. We finally give a candidate EI-PRF based on our main weak PRF candidate.

Joint work with Dan Boneh, Yuval Ishai, Amit Sahai, and David J. Wu, published at TCC 2018