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Forward-Secure Group Signatures from Lattices

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Post-Quantum Cryptography (PQCrypto 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11505))

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Abstract

Group signature is a fundamental cryptographic primitive, aiming to protect anonymity and ensure accountability of users. It allows group members to anonymously sign messages on behalf of the whole group, while incorporating a tracing mechanism to identify the signer of any suspected signature. Most of the existing group signature schemes, however, do not guarantee security once secret keys are exposed. To reduce potential damages caused by key exposure attacks, Song (ACMCCS 2001) put forward the concept of forward-secure group signature (FSGS), which prevents attackers from forging group signatures pertaining to past time periods even if a secret group signing key is revealed at the current time period. For the time being, however, all known secure FSGS schemes are based on number-theoretic assumptions, and are vulnerable against quantum computers.

In this work, we construct the first lattice-based FSGS scheme. Our scheme is proven secure under the Short Integer Solution and Learning With Errors assumptions. At the heart of our construction is a scalable lattice-based key evolving mechanism, allowing users to periodically update their secret keys and to efficiently prove in zero-knowledge that key evolution process is done correctly. To realize this essential building block, we first employ the Bonsai tree structure by Cash et al. (EUROCRYPT 2010) to handle the key evolution process, and then develop Langlois et al.’s construction (PKC 2014) to design its supporting zero-knowledge protocol.

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Notes

  1. 1.

    This set can be determined by the Nodeselect algorithm presented by Libert and Yung [42].

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Acknowledgements

The research is supported by Singapore Ministry of Education under Research Grant MOE2016-T2-2-014(S). Khoa Nguyen is also supported by the Gopalakrishnan – NTU Presidential Postdoctoral Fellowship 2018.

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Authors and Affiliations

  1. Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore

    San Ling, Khoa Nguyen, Huaxiong Wang & Yanhong Xu

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  1. San Ling
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Correspondence to Yanhong Xu .

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  1. University of Cincinnati, Cincinnati, OH, USA

    Jintai Ding

  2. Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL, USA

    Rainer Steinwandt

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Ling, S., Nguyen, K., Wang, H., Xu, Y. (2019). Forward-Secure Group Signatures from Lattices. In: Ding, J., Steinwandt, R. (eds) Post-Quantum Cryptography. PQCrypto 2019. Lecture Notes in Computer Science(), vol 11505. Springer, Cham. https://doi.org/10.1007/978-3-030-25510-7_3

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