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An Improved Twisted Ate Pairing over KSS Curves with k = 18

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Pairing-Based Cryptography – Pairing 2012 (Pairing 2012)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7708))

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Abstract

When implementing an efficient pairing calculation over KSS curves with embedding degree 18 and order r, the lower bound of the number of loop iterations of Miller’s algorithm is \(\frac{1}{6}\lfloor\log_2r\rfloor\). But the twisted Ate pairing requires \(\frac{1}{2}\lfloor\log_2r\rfloor\) loop iterations, and thus is slower than the optimal Ate pairing which achieves the lower bound. This paper proposes an improved twisted Ate pairing and uses multi-pairing techniques to compute it. Therefore, the number of loop iterations in Miller’s algorithm for the new pairing achieves the lower bound and it becomes faster than the original twisted Ate pairing by 30%.

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Authors and Affiliations

  1. SKLOIS, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, P.R. China

    Shan Chen, Kunpeng Wang & Dongdai Lin

  2. Graduate University of Chinese Academy of Sciences, Beijing, 100049, P.R. China

    Shan Chen

Authors
  1. Shan Chen
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  2. Kunpeng Wang
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  3. Dongdai Lin
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Editor information

Editors and Affiliations

  1. Départment d’Informatique, École Normale Supérieure and CNRS, 45 rue d’Ulm, 75005, Paris, France

    Michel Abdalla

  2. Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Tanja Lange

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Chen, S., Wang, K., Lin, D. (2013). An Improved Twisted Ate Pairing over KSS Curves with k = 18. In: Abdalla, M., Lange, T. (eds) Pairing-Based Cryptography – Pairing 2012. Pairing 2012. Lecture Notes in Computer Science, vol 7708. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36334-4_3

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  • DOI: https://doi.org/10.1007/978-3-642-36334-4_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36333-7

  • Online ISBN: 978-3-642-36334-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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