How to Circumvent the Two-Ciphertext Lower Bound for Linear Garbling Schemes

At EUROCRYPT 2015, Zahur et al. argued that all linear, and thus, efficient, garbling schemes need at least two k-bit elements to garble an AND gate with security parameter k. We show how to circumvent this lower bound, and propose an efficient garbling scheme which requires less than two k-bit elements per AND gate for most circuit layouts. Our construction slightly deviates from the linear garbling model, and constitutes no contradiction to any claims in the lower-bound proof. With our proof of concept construction, we hope to spur new ideas for more practical garbling schemes. Our construction can directly be applied to semi-private function evaluation by garbling XOR, XNOR, NAND, OR, NOR and AND gates in the same way, and keeping the evaluator oblivious of the gate function.