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Title:
New Smooth Projective Hashing For Oblivious Transfer
Authors: Bing Zeng
Abstract:Oblivious transfer is an important tool against malicious cloud server providers. Halevi-Kalai OT, 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. A natural question however, which so far has not been answered, is whether its security level can be improved, i.e., whether it can be made fully-simulatable. In this paper, we press a new SPH variant, which enables a positive answer to above question. In more details, it even makes fully-simulatable \mbox{OT}^{n}_{t} (n,t\in \mathbb{N} and n>t) possible. We instantiate this new SPH variant under not only the decisional Diffie-Hellman assumption, the decisional N-th residuosity assumption and the decisional quadratic residuosity assumption as currently existing SPH constructions, but also the learning with errors (LWE) problem. Before this paper, there is a folklore that it is technically difficult to instantiate SPH under the lattice assumption (e.g., LWE). Considering quantum adversaries in the future, lattice-based SPH makes important sense.
ePrint: https://eprint.iacr.org/2018/524
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