Secure computation has obtained significant attention in the literature recently. Classic architectures usually use either the Garbled Circuit (GC) or the Goldreich-Micali-Wigderson (GMW) protocols. So far, to reduce the complexity of communications in these protocols, various methods have been proposed. The best known work in both methods reduces the communication up to almost 2k-bits (k is the symmetric security parameter) for each AND gate, and using XOR gate is free. In this paper, by combining GC and GMW, we propose a scheme in the semi-honest adversary model. This scheme requires an Oblivious Transfer (OT) and a 2-bit data transfer for each AND gate, keeping XOR gates free. The analytical results on different applications, including AES, DES, SHA-1, SHA-256, MD5, multiplier, adder, and comparator show that the data transfer size can be reduced up to 52% and 41% when compared to the best known GC and GMW based methods, respectively.

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