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Universally composable oblivious transfer from ideal lattice

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Abstract

As a fundamental cryptographic primitive, oblivious transfer (OT) is developed for the sake of efficient usability and combinational feasibility. However, most OT protocols are built upon some quantum non-immune cryptosystems by assuming the hardness of discrete logarithm or factoring problem, whose security will break down directly in the quantum setting. Therefore, as a subarea of post-quantum cryptography, lattice-based cryptography is viewed as a promising alternative and cornerstone to support for building post-quantum protocols since it enjoys some attractive properties, such as provable security against quantum adversaries and lower asymptotic complexity.

In this paper, we first build an efficient 1-out-of-2 OT protocol upon the hardness of ring learning with errors (RLWE) problem, which is at least as hard as some worst-case ideal lattice problems. We show that this 1-out-of-2 OT protocol can be universally composable and secure against static corruptions in the random oracle model. Then we extend it to a general case, i.e., 1-out-of-N OT with achieving the same level of security. Furthermore, on the basis of the above OT structure, we obtain two improved OT protocols using two improved lattice-based key exchange protocols (respectively relying on the RLWE problem and learning with errors (LWE) problem, and both achieving better efficiency by removing the Gaussian sampling for saving cost) as building blocks. To show that our proposed OT protocol indeed achieves comparable security and efficiency, we make a comparison with another two lattice-based OT protocols in the end of the paper.

With concerning on the potential threat from quantum computing and expecting on the practical use of OT with high efficiency, an efficient post-quantum OT protocol is pressing needed. As shown in this paper, our proposed OT protocols may be considered as post-quantum OT candidates since they can both preserve provable security relying on lattice problems and enjoy practical efficiency.

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Acknowledgements

This work is supported by the National Key R&D Program of China (2017YFB0802000), the National Natural Science Foundations of China (Grant Nos. 61472309, No.61672412), the National Cryptography Development Fund (MMJJ20170104), and the China Scholarship Council (201406960041).

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Authors and Affiliations

  1. State Key Laboratory of Integrated Service Networks, Xidian University, Xi’an, 710071, China

    Momeng Liu & Yupu Hu

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  1. Momeng Liu
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Correspondence to Momeng Liu.

Additional information

Momeng Liu is a PhD student who is supervised by Professor Yupu Hu at Xidian University, China. She earned her MS degree in cryptography from Xidian University, China in 2013 and her BS in telecommunications from Xi’an University, China in 2010. Her research interests mainly focus on analysing and designing schemes built upon lattice-based cryptography.

Yupu Hu is a professor and doctoral supervisor in the School of Telecommunications Engineering, Xidian University, China. He earned his doctorate in cryptography from Xidian University, China in 1999, and earned his MS and BS in mathematics from Xidian University, China in 1999 and 1987, respectively. His research interests focus on analysing and constructing schemes built upon lattice-based cryptography, multi-linear map and fully homomorphic encryption schemes.

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Liu, M., Hu, Y. Universally composable oblivious transfer from ideal lattice. Front. Comput. Sci. 13, 879–906 (2019). https://doi.org/10.1007/s11704-018-6507-4

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