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Practical Post-quantum Few-Time Verifiable Random Function with Applications to Algorand

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Financial Cryptography and Data Security (FC 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12675))

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Abstract

In this work, we introduce the first practical post-quantum verifiable random function (VRF) that relies on well-known (module) lattice problems, namely Module-SIS and Module-LWE. Our construction, named LB-VRF, results in a VRF value of only 84 bytes and a proof of around only 5 KB (in comparison to several MBs in earlier works), and runs in about 3 ms for evaluation and about 1 ms for verification.

In order to design a practical scheme, we need to restrict the number of VRF outputs per key pair, which makes our construction few-time. Despite this restriction, we show how our few-time LB-VRF can be used in practice and, in particular, we estimate the performance of Algorand using LB-VRF. We find that, due to the significant increase in the communication size in comparison to classical constructions, which is inherent in all existing lattice-based schemes, the throughput in LB-VRF-based consensus protocol is reduced, but remains practical. In particular, in a medium-sized network with 100 nodes, our platform records a 1.14\(\times \) to 3.4\(\times \) reduction in throughput, depending on the accompanying signature used. In the case of a large network with 500 nodes, we can still maintain at least 24 transactions per second. This is still much better than Bitcoin, which processes only about 5 transactions per second.

Z. Zhang—Work was done while with Algorand.

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Notes

  1. 1.

    https://github.com/zhenfeizhang/lb-vrf.

  2. 2.

    https://eprint.iacr.org/2020/1222.pdf.

  3. 3.

    https://github.com/zhenfeizhang/lb-vrf.

  4. 4.

    This is a rough estimation in September 2020. Since then, Algorand has upgraded its consensus for faster block generation time.

  5. 5.

    https://falcon-sign.info/.

  6. 6.

    https://www.pqcrainbow.org/.

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Acknowledgment

This work was supported in part by Australian Research Council Discovery Grant DP180102199 and also by use of the Nectar Research Cloud, a collaborative Australian research platform supported by the National Collaborative Research Infrastructure Strategy (NCRIS).

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Authors and Affiliations

  1. Monash University, Melbourne, Australia

    Muhammed F. Esgin, Amin Sakzad, Ron Steinfeld & Shifeng Sun

  2. CSIRO’s Data61, Melbourne, Australia

    Muhammed F. Esgin

  3. The University of Queensland, Brisbane, Australia

    Veronika Kuchta

  4. Manta Network, Boston, USA

    Zhenfei Zhang

  5. University of California, Santa Barbara, USA

    Shumo Chu

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  1. Muhammed F. Esgin
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Correspondence to Muhammed F. Esgin .

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Editors and Affiliations

  1. University of Illinois at Urbana-Champaign, Urbana, IL, USA

    Nikita Borisov

  2. KU Leuven, Leuven, Belgium

    Claudia Diaz

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Esgin, M.F. et al. (2021). Practical Post-quantum Few-Time Verifiable Random Function with Applications to Algorand. In: Borisov, N., Diaz, C. (eds) Financial Cryptography and Data Security. FC 2021. Lecture Notes in Computer Science(), vol 12675. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-64331-0_29

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