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Isogeny-Based Key Compression Without Pairings

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Public-Key Cryptography – PKC 2021 (PKC 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12710))

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Abstract

SIDH/SIKE-style protocols benefit from key compression to minimize their bandwidth requirements, but proposed key compression mechanisms rely on computing bilinear pairings. Pairing computation is a notoriously expensive operation, and, unsurprisingly, it is typically one of the main efficiency bottlenecks in SIDH key compression, incurring processing time penalties that are only mitigated at the cost of trade-offs with precomputed tables. We address this issue by describing how to compress isogeny-based keys without pairings. As a bonus, we also substantially reduce the storage requirements of other operations involved in key compression.

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Notes

  1. 1.

    The actual SIKE setting matches this convention.

  2. 2.

    For the binary torsion, our methods require an extra table, \(\mathsf {L}_6\) or \(\mathsf {L}_6^*\), containing just 9 points over \(\mathbb {F}_{p^2}\), a small fraction of the space required for the other tables.

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Acknowledgements

This work is supported in part by NSERC, CryptoWorks21, Canada First Research Excellence Fund, Public Works and Government Services Canada.

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Authors and Affiliations

  1. University of Waterloo, Waterloo, Canada

    Geovandro C. C. F. Pereira

  2. evolutionQ Inc., Kitchener, Canada

    Geovandro C. C. F. Pereira

  3. University of Washington Tacoma, Tacoma, USA

    Paulo S. L. M. Barreto

Authors
  1. Geovandro C. C. F. Pereira
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  2. Paulo S. L. M. Barreto
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Corresponding author

Correspondence to Geovandro C. C. F. Pereira .

Editor information

Editors and Affiliations

  1. Texas A&M University, College Station, TX, USA

    Juan A. Garay

A The OptPath algorithm

A The OptPath algorithm

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Pereira, G.C.C.F., Barreto, P.S.L.M. (2021). Isogeny-Based Key Compression Without Pairings. In: Garay, J.A. (eds) Public-Key Cryptography – PKC 2021. PKC 2021. Lecture Notes in Computer Science(), vol 12710. Springer, Cham. https://doi.org/10.1007/978-3-030-75245-3_6

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  • DOI: https://doi.org/10.1007/978-3-030-75245-3_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-75244-6

  • Online ISBN: 978-3-030-75245-3

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