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KDM-Secure Public-Key Encryption from Constant-Noise LPN

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Book cover Information Security and Privacy (ACISP 2017)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10342))

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Abstract

The Learning Parity with Noise (LPN) problem has found many applications in cryptography due to its conjectured post-quantum hardness and simple algebraic structure. Over the years, constructions of different public-key primitives were proposed from LPN, but most of them are based on the LPN assumption with low noise rate rather than constant noise rate. A recent breakthrough was made by Yu and Zhang (Crypto’16), who constructed the first Public-Key Encryption (PKE) from constant-noise LPN. However, the problem of designing a PKE with Key-Dependent Message (KDM) security from constant-noise LPN is still open.

In this paper, we present the first PKE with KDM-security assuming certain sub-exponential hardness of constant-noise LPN, where the number of users is predefined. The technical tool is two types of multi-fold LPN on squared-log entropy, one having independent secrets and the other independent sample subspaces. We establish the hardness of the multi-fold LPN variants on constant-noise LPN. Two squared-logarithmic entropy sources for multi-fold LPN are carefully chosen, so that our PKE is able to achieve correctness and KDM-security simultaneously.

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Acknowledgments

We would like to thank Yunhua Wen for a careful proofreading, and the reviewers for valuable comments. The authors are supported by the National Natural Science Foundation of China Grant (Nos. 61672346, 61373153).

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Shuai Han & Shengli Liu

  2. State Key Laboratory of Cryptology, P.O. Box 5159, Beijing, 100878, China

    Shuai Han & Shengli Liu

  3. Westone Cryptologic Research Center, Beijing, 100070, China

    Shengli Liu

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  1. Shuai Han
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  1. Queensland University of Technology, Brisbane, Queensland, Australia

    Josef Pieprzyk

  2. Queensland University of Technology, Brisbane, Queensland, Australia

    Suriadi Suriadi

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Han, S., Liu, S. (2017). KDM-Secure Public-Key Encryption from Constant-Noise LPN. In: Pieprzyk, J., Suriadi, S. (eds) Information Security and Privacy. ACISP 2017. Lecture Notes in Computer Science(), vol 10342. Springer, Cham. https://doi.org/10.1007/978-3-319-60055-0_3

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