We optimize the communication (and, indirectly, computation) complexity of two-party secure function evaluation (SFE). We propose a new approach, which relies on the information-theoretic (IT) Garbled Circuit (GC), which is more efficient than Yao's GC on shallow circuits. When evaluating a large circuit, we "slice" it into thin layers and evaluate them with IT GC. Motivated by the client-server setting, we propose two variants of our construction: one for semi-honest model (relatively straightforward), and one secure against a semi-honest server and covert client (more technically involved). One of our new building blocks, String-selection Oblivious Transfer (SOT), may be of independent interest.#R##N##R##N#Our approach offers asymptotic improvement over the state-of-the-art GC, both in communication and computation, by a factor logκ, where κ is a security parameter. In practical terms, already for today's κ∈{128,256} our (unoptimized) algorithm offers approximately a factor 2 communication improvement in the semi-honest model, and is only a factor ≈1.5 more costly in setting with covert client.
['Vladimir Kolesnikov', 'Ranjit Kumaresan']
Improved secure two-party computation via information-theoretic garbled circuits