New Techniques for Private Function Evaluation
Seyed Saeed Sadeghian
In this thesis, we study the problem of general-purpose private function evaluation (PFE) wherein a single party P1 holds a circuit C, while each Pi for 1<=i<=m holds a private input xi, and the goal is for a subset (or all) of the parties to learn C(x1,…,xm) but nothing else. We pursue the design of PFE with better concrete and/or asymptotic complexity for a variety of settings. We put forth a general framework for designing PFE as the first alternative general approach to universal circuits. In this framework, the task of hiding the circuit topology and securely evaluating its gates are addressed independently through two functionalities we call CTH (Circuit Topology Hiding) and PGE (Private Gate Evaluation). We instantiate our framework using the building blocks of several well-known general MPC constructions, obtaining more efficient PFE than prior work for two-party PFE, multi-party PFE and PFE for arithmetic circuits. Next, we propose the first general framework for designing actively secure PFE, not based on universal circuits. On the theoretical side, our framework yields the first actively secure PFE with linear complexity in the circuit size. On the practical side, we obtain the first actively secure PFE for arithmetic circuits with O(glogg) complexity where g is the circuit size, significantly improving over previous constructions with complexity O(g^5). Despite its inefficiency, we identify various advantages for PFE based on universal circuits. Valiant's construction (STOC 1976) yields universal circuits with the optimal asymptotic complexity, and has been employed in several recent works. But somewhat surprisingly, no implementations of the construction exist. We look back at this construction, and provide a more approachable description. This enables us to provide constant factor improvements and the first implementation. A more accurate comparison made possible through our implementation shows that the improved Valiant's UC performs better than the theoretical estimate, and in fact is almost always smaller than the UC construction of Kolesnikov and Schneider (FC 2008). We also observe, for the first time, that the same construction can be adapted to yield size-optimized universal arithmetic circuits (UAC).
•Jan 1, 2015•4 citations