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Extended Explicit Relations Between Trace, Definition Field, and Embedding Degree

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Algebraic Informatics (CAI 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9270))

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Abstract

An elliptic curve cryptosystem (ECC) is one of public key cryptosystem, whose security is based on elliptic curve discrete logarithm problem (ECDLP). An elliptic curve is uniquely determined by mathematical parameters such as j-invariant of an elliptic curve. By giving trace of elliptic curve, t, a definition field \(\mathbb F_{p}\), and discriminant D, an elliptic curve with order \(\sharp {E(\mathbb F_{p})} = n\) is determined. Therefore it is an open problem to determine explicit relations between the mathematical parameters and the embedding degrees k. Hirasawa and Miyaji presented concrete relations between the mathematical parameters and the embedding degrees. In this research, a new explicit relation between elliptic-curve parameters and embedding degrees is investigated by generalizing their research.

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Authors and Affiliations

  1. Japan Advanced Institute of Science and Technology, Asahidai 1–1, Nomi-shi, Ishikawa, 923–1292, Japan

    Atsuko Miyaji, Xiaonan Shi & Satoru Tanaka

  2. CREST, JST, Kawaguchi Center Building 4–1–8, Honcho, Kawaguchi-shi, Saitama, 332–0012, Japan

    Atsuko Miyaji

Authors
  1. Atsuko Miyaji
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  2. Xiaonan Shi
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  3. Satoru Tanaka
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Corresponding author

Correspondence to Satoru Tanaka .

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Editors and Affiliations

  1. Institut für Maschinelle, Universität Stuttgart, Stuttgart, Baden-Württemberg, Germany

    Andreas Maletti

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Miyaji, A., Shi, X., Tanaka, S. (2015). Extended Explicit Relations Between Trace, Definition Field, and Embedding Degree. In: Maletti, A. (eds) Algebraic Informatics. CAI 2015. Lecture Notes in Computer Science(), vol 9270. Springer, Cham. https://doi.org/10.1007/978-3-319-23021-4_15

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  • DOI: https://doi.org/10.1007/978-3-319-23021-4_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23020-7

  • Online ISBN: 978-3-319-23021-4

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