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Two-Round PAKE Protocol over Lattices Without NIZK

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Information Security and Cryptology (Inscrypt 2018)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11449))

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  • 2014 Accesses

Abstract

Reducing the number of communication rounds of Password-based Authenticated Key Exchange (\(\textsf {PAKE} \)) protocols is of great practical significance. At PKC’15, Abdalla et al. relaxed the requirements of Gennaro-Lindell’s framework for three-round PAKE protocols, and obtained a two-round PAKE protocol under the traditional DDH-based smooth projective hash function (\(\mathsf {SPHF} \)). At ASIACRYPT’17, Zhang and Yu proposed a lattice-based two-round PAKE protocol via the approximate \(\mathsf {SPHF} \). However, the language of Zhang-Yu’s SPHF depends on simulation-sound non-interactive zero-knowledge (NIZK) proofs, for which there is no concrete construction without random oracle under lattice-based assumptions. To our knowledge, how to design a lattice-based two-round \(\textsf {PAKE} \) protocol via an efficient \(\mathsf {SPHF} \) scheme without NIZK remains a challenge. In this paper, we propose the first two-round \(\textsf {PAKE} \) protocol over lattices without NIZK. Our protocol is in accordance with the framework of Abdalla et al. (PKC’15) while attaining post-quantum security. We overcome the limitations of existing schemes by relaxing previous security assumptions (i.e., both the client and the sever need IND-CCA-secure encryption), and build two new lattice-based \(\mathsf {SPHF} \)s, one for IND-CCA-secure Micciancio-Peikert ciphertext (at the client side) and the other for IND-CPA-secure Regev ciphertext (at the server side). Particularly, our protocol attains provable security.

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Notes

  1. 1.

    Note that every \(\text {IND-CCA}2\)-secure scheme is also an \(\text {IND-PCA}\)-secure scheme.

  2. 2.

    The non-adaptive approximate \(\mathsf {SPHF} \) means the adversary can see the projective key \(ph \) before choosing the word \(W \).

  3. 3.

    They improved the Gennaro-Lindell framework to reduce the round number to two.

  4. 4.

    We use big-O notation to asymptotically bound the growth of a running time to within constant factors.

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Acknowledgments

The authors would like to thank the anonymous reviewers for their helpful advice and comments. This work was supported by the National Natural Science Foundation of China (No. 61802006 and No. 61802214).

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Authors and Affiliations

  1. College of Computer Science and Technology, Qingdao University, Qingdao, China

    Zengpeng Li

  2. School of EECS, Peking University, Beijing, 100871, China

    Ding Wang

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Correspondence to Ding Wang .

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  1. University of Wollongong, Wollongong, NSW, Australia

    Fuchun Guo

  2. Fujian Normal University, Fujian, China

    Xinyi Huang

  3. Columbia University, New York, NY, USA

    Moti Yung

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Li, Z., Wang, D. (2019). Two-Round PAKE Protocol over Lattices Without NIZK. In: Guo, F., Huang, X., Yung, M. (eds) Information Security and Cryptology. Inscrypt 2018. Lecture Notes in Computer Science(), vol 11449. Springer, Cham. https://doi.org/10.1007/978-3-030-14234-6_8

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