Garbling Scheme for Formulas with Constant Size of Garbled Gates

We provide a garbling scheme which creates garbled circuits of a very small constant size four bits per gate for circuits with fan-out 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 PRIV-security, a notion for deterministic searchable encryption. We prove our scheme secure in the programmable random oracle model.

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