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EdSIDH: Supersingular Isogeny Diffie-Hellman Key Exchange on Edwards Curves

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Book cover Security, Privacy, and Applied Cryptography Engineering (SPACE 2018)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11348))

Abstract

Problems relating to the computation of isogenies between elliptic curves defined over finite fields have been studied for a long time. Isogenies on supersingular elliptic curves are a candidate for quantum-safe key exchange protocols because the best known classical and quantum algorithms for solving well-formed instances of the isogeny problem are exponential. We propose an implementation of supersingular isogeny Diffie-Hellman (SIDH) key exchange for complete Edwards curves. Our work is motivated by the use of Edwards curves to speed up many cryptographic protocols and improve security. Our work does not actually provide a faster implementation of SIDH, but the use of complete Edwards curves and their complete addition formulae provides security benefits against side-channel attacks. We provide run time complexity analysis and operation counts for the proposed key exchange based on Edwards curves along with comparisons to the Montgomery form.

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Acknowledgement

The authors would like to thank the reviewers for their comments. This work is supported in parts by awards NIST 60NANB16D246, NIST 60NANB17D184, and NSF CNS-1801341. Also, this research was undertaken thanks in part to funding from the Canada First Research Excellence Fund, Natural Sciences and Engineering Research Council of Canada, CryptoWorks21, Public Works and Government Services Canada, and the Royal Bank of Canada.

Author information

Authors and Affiliations

  1. Department of Computer and Electrical Engineering and Computer Science, Florida Atlantic University, Boca Raton, FL, USA

    Reza Azarderakhsh

  2. Department of Combinatorics and Optimization, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Elena Bakos Lang & David Jao

  3. Centre for Applied Cryptographic Research, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    David Jao

  4. evolutionQ, Inc., Waterloo, ON, Canada

    David Jao

  5. Texas Instruments, Dallas, TX, USA

    Brian Koziel

Authors
  1. Reza Azarderakhsh
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  2. Elena Bakos Lang
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  3. David Jao
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  4. Brian Koziel
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Corresponding author

Correspondence to Brian Koziel .

Editor information

Editors and Affiliations

  1. School of Computer Science and Engineering, Nanyang Technological University, Singapore, Singapore

    Anupam Chattopadhyay

  2. Indian Institute of Technology Madras, Chennai, India

    Chester Rebeiro

  3. University of Adelaide, Adelaide, Australia

    Yuval Yarom

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Azarderakhsh, R., Bakos Lang, E., Jao, D., Koziel, B. (2018). EdSIDH: Supersingular Isogeny Diffie-Hellman Key Exchange on Edwards Curves. In: Chattopadhyay, A., Rebeiro, C., Yarom, Y. (eds) Security, Privacy, and Applied Cryptography Engineering. SPACE 2018. Lecture Notes in Computer Science(), vol 11348. Springer, Cham. https://doi.org/10.1007/978-3-030-05072-6_8

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  • DOI: https://doi.org/10.1007/978-3-030-05072-6_8

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  • Print ISBN: 978-3-030-05071-9

  • Online ISBN: 978-3-030-05072-6

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