Quantum security analysis of a lattice-based oblivious transfer protocol

Because of the concise functionality of oblivious transfer （OT） protocols, they have been widely used as building blocks in secure multiparty computation and high-level protocols. The security of OT protocols built upon classical number theoretic problems, such as the discrete logarithm and factoring, however, is threatened as a result of the huge progress in quantum computing. Therefore, post-quantum cryptography is needed for protocols based on classical problems, and several proposals for post-quantum OT protocols exist. However, most post-quantum cryptosystems present their security proof only in the context of classical adversaries, not in the quantum setting. In this paper, we close this gap and prove the security of the lattice-based OT protocol proposed by Peikert et al. （CRYPTO, 2008）, which is universally composably secure under the assumption of learning with errors hardness, in the quantum setting. We apply three general quantum security analysis frameworks. First, we apply the quantum lifting theorem proposed by Unruh （EUROCRYPT, 2010） to prove that the security of the lattice-based OT protocol can be lifted into the quantum world. Then, we apply two more security analysis frameworks specified for post-quantum cryptographic primitives, i.e., simple hybrid arguments （CRYPTO, 2011） and game-preserving reduction （PQCrypto, 2014）.

不经意传输协议(oblivious transfer,OT)因其简易的密码功能广泛应用于安全多方计算。以往OT协议都是基于传统数论问题(例如,离散对数,大数分解问题)所构造的,随着量子计算技术的发展,基于传统困难问题的OT协议安全性受到极大的威胁。因此,人们转而考虑使用后量子密码技术替代以往OT协议所依赖的传统困难问题。目前,已有一些基于后量子密码体制的OT协议被提出。然而,大多数后量子密码构造只在假设传统敌手存在的环境下证明其方案安全性。在本文中,我们在量子敌手存在的环境下,证明一个基于格公钥密码的OT协议([PVW08])的安全性。首先我们使用量子平移定理([Unr10])证明该协议的安全性可以完全平移到量子环境中,此外,我们还使用其他两个专用于分析后量子密码原语的分析模型([HSS11],[Son14])从不同的角度对该协议进行安全性分析,从而保证我们给出的量子安全证明的正确性。我们的成果可以看作对后量子密码协议分析模型的一个实际应用实例。