## Cryptology ePrint Archive: Report 2018/444

Founding Cryptography on Smooth Projective Hashing

Bing Zeng

Abstract: Oblivious transfer (OT) is a fundamental primitive in cryptography. Halevi-Kalai OT (Halevi, S. and Y. Kalai (2012), Journal of Cryptology 25(1)), which is based on smooth projective hash(SPH), is a famous and the most efficient framework for $1$-out-of-$2$ oblivious transfer ($\mbox{OT}^{2}_{1}$) against malicious adversaries in plain model. However, it does not provide simulation-based security. Thus, it is harder to use it as a building block in secure multiparty computation (SMPC) protocols. A natural question however, which so far has not been answered, is whether it can be can be made fully-simulatable. In this paper, we give a positive answer. Further, we present a fully-simulatable framework for general $\mbox{OT}^{n}_{t}$ ($n,t\in \mathbb{N}$ and $n>t$). Our framework can be interpreted as a constant-round blackbox reduction of $\mbox{OT}^{n}_{t}$ (or $\mbox{OT}^{2}_{1}$) to SPH. To our knowledge, this is the first such reduction. Combining Kilian's famous completeness result, we immediately obtain a black-box reduction of SMPC to SPH.

Category / Keywords: cryptographic protocols / oblivious transfer, secure multiparty computation, malicious adversaries, smooth projective hashing.