Actively Secure Private Function Evaluation.

We propose the first general framework for designing actively secure private function evaluation (PFE), not based on universal circuits. Our framework is naturally divided into pre-processing and online stages and can be instantiated using any generic actively secure multiparty computation (MPC) protocol. Our framework helps address the main open questions about efficiency of actively secure PFE. 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(g . log g) complexity where g is the circuit size. The best previous construction (of practical interest) is based on an arithmetic universal circuit and has complexity O(g(5)). We also introduce the first linear Zero-Knowledge proof of correctness of "extended permutation" of ciphertexts (a generalization of ZK proof of correct shuffles) which maybe of independent interest.