Garbling scheme for formulas with constant size of garbled gates

Abstract

We provide a garbling scheme which creates garbled circuits of a very small constant size (four bits per gate) for circuits with fanout one (formulas). For arbitrary fan-out, we additionally need only two ciphertexts per additional connection of each gate output wire. We make use of a trapdoor permutation for which we define a generalized notion of correlation robustness. We show that our notion is implied by PRIVsecurity, a notion for deterministic (searchable) encryption.We prove our scheme secure in the programmable random oracle model.