How to Combine Homomorphic Encryption and Garbled Circuits - Improved Circuits and Computing the Minimum Distance Efficiently
Vladimir Kolesnikov, Ahmad‐Reza Sadeghi, Thomas H. Schneider · 2009
Abstract. We show how two existing paradigms for two-party secure function evaluation (SFE) in the semi-honest model can be combined securely and efficiently – those based on additively homomorphic encryption (HE) with those based on garbled circuits (GC) and vice versa. Additionally, we propose new GC constructions for addition, subtraction, multiplication, and comparison functions. Our circuits are approximately two times smaller (in terms of garbled tables) than previous constructions. This implies corresponding computation and communication improvements in SFE of functions using the above building blocks (including the protocols for combining HE and GC). Based on these results, we present efficient constant-round protocols for secure integer comparison, and the related problems of minimum selection and minimum distance, which are crucial building blocks of many cryptographic schemes such as privacy preserving biometric authentication (e.g., face recognition, fingerprint matching, etc).