Strongly average‐case secure obfuscation: achieving input privacy and circuit obscurity

Abstract

A program obfuscator is a compiling algorithm that takes a program/circuit as input and generates a new garbled circuit to implement the same functionality as before while obtaining hard‐to‐understand in some sense, that is, infeasible to learn information from the garbled circuit. In order to obtain a practical application, an obfuscation should satisfy equivalent in functionality, polynomial slowdown in efficiency, and virtual black‐box in security. In this paper, we model a stronger cryptographic obfuscation that does not only achieves the obfuscated circuit obscurity but also supports input re‐key privacy. In order to implement the re‐encryption obfuscation, we at first propose a key‐privacy two‐level encryption mechanism that implicitly supports the transformation from level‐2 ciphertext into level‐1 one, which provides an efficient method to re‐encrypt the ciphertext without explicitly decryption procedure. Under the mechanism of two‐level encryption and function of re‐encryption, we construct an obfuscation of re‐encryption that takes as input a probabilistic (keys) circuit and outputs a transformed circuit. We also give the proof that the obfuscator achieves the average‐case security for the circuit family under the extended DBDH assumption and Decisional Linear assumption in the standard model. Copyright © 2016 John Wiley & Sons, Ltd.