Privacy-free garbling schemes of Frederiksen et al. (Eurocrypt '15) are designed to satisfy only the authenticity criterion of Bellare et al. (ACM CCS '12) and to be more efficient than full-fledged garbling schemes. In this work, we improve the state-of-the-art privacy-free version of half-gates (HG) garbling of Zahur et al. (Crypto '15) by allowing an AND gate to be garbled with zero ciphertexts whenever at least one of its input wires is freely settable by the garbler. Our full solution, AuthOr, then combines the ideas from the information-theoretic garbling of Kondi and Patra (Crypto '17) with the improved HG-based scheme we obtain. AuthOr has a lower communication cost (i.e., garbled-circuit size) than HG garbling without any additional security assumptions. Theoretically, AuthOr's garbled-circuit size reduction over HG garbling ranges from 0% to 100%, with the exact improvement depending on the circuit structure. We have implemented our scheme and evaluated it on various circuits constructed by independent researchers. Our experimental results show that, in practice, the garbled-circuit size reduction can reach roughly 98%.

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