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A Note on Inverted Twisted Edwards Curve

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Information Security and Cryptology (Inscrypt 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13837))

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Abstract

This paper is a complementary work to the Edwards curve family. In this paper, we study the inverted Edwards coordinates on twisted Edwards curves (denoted by inverted twisted Edwards curves). We provide explicit addition, doubling, and tripling formulae on inverted twisted Edwards curves with projective coordinates and extended projective coordinates. Using the extended projective coordinates, the new explicit unified addition formulas cost \(9 \textbf{M}\).

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Acknowledgment

The authors would like to thank the anonymous reviewers for many helpful comments. This work is supported by the National Natural Science Foundation of China (No. 62272453, U1936209, 61872442, and 61502487).

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Authors and Affiliations

  1. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China

    Luying Li & Wei Yu

  2. School of Cyber Security, University of Chinese Academy of Sciences, Beijing, China

    Luying Li & Wei Yu

Authors
  1. Luying Li
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  2. Wei Yu
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Corresponding author

Correspondence to Wei Yu .

Editor information

Editors and Affiliations

  1. Institute of Information Engineering, CAS, Beijing, China

    Yi Deng

  2. Columbia University, New York, NY, USA

    Moti Yung

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Li, L., Yu, W. (2023). A Note on Inverted Twisted Edwards Curve. In: Deng, Y., Yung, M. (eds) Information Security and Cryptology. Inscrypt 2022. Lecture Notes in Computer Science, vol 13837. Springer, Cham. https://doi.org/10.1007/978-3-031-26553-2_15

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  • DOI: https://doi.org/10.1007/978-3-031-26553-2_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-26552-5

  • Online ISBN: 978-3-031-26553-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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