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Hashing into Jacobi Quartic Curves

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Information Security (ISC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9290))

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Abstract

Jacobi quartic curves are well known for efficient arithmetics in regard to their group law and immunity to timing attacks. Two deterministic encodings from a finite field \(\mathbb {F}_q\) to Jacobi quartic curves are constructed. When \(q\equiv 3\pmod 4\), the first deterministic encoding based on Skalba’s equality saves two field squarings compared with birational equivalence composed with Fouque and Tibouchi’s brief version of Ulas’ function. When \(q\equiv 2\pmod 3\), the second deterministic encoding based on computing cube root costs one field inversion less than birational equivalence composed with Icart’s function at the cost of four field multiplications and one field squaring. It costs one field inversion less than Alasha’s encoding at the cost of one field multiplication and two field squarings. With these two deterministic encodings, two hash functions from messages directly into Jacobi quartic curves are constructed. Additionally, we construct two types of new efficient functions indifferentiable from a random oracle.

This research is supported in part by National Research Foundation of China under Grant No. 61379137, No. 61272040, and in part by National Basic Research Program of China(973) under Grant No.2013CB338001.

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Authors and Affiliations

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

    Wei Yu, Kunpeng Wang, Bao Li, Xiaoyang He & Song Tian

  2. Data Assurance and Communication Security Research Center, Chinese Academy of Sciences, Beijing, 100093, China

    Wei Yu

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  1. Wei Yu
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  2. Kunpeng Wang
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  3. Bao Li
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  4. Xiaoyang He
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  5. Song Tian
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Correspondence to Wei Yu .

Editor information

Editors and Affiliations

  1. University of Malaga, Malaga, Spain

    Javier Lopez

  2. Royal Holloway University of London, Egham, United Kingdom

    Chris J. Mitchell

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Yu, W., Wang, K., Li, B., He, X., Tian, S. (2015). Hashing into Jacobi Quartic Curves. In: Lopez, J., Mitchell, C. (eds) Information Security. ISC 2015. Lecture Notes in Computer Science(), vol 9290. Springer, Cham. https://doi.org/10.1007/978-3-319-23318-5_20

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  • DOI: https://doi.org/10.1007/978-3-319-23318-5_20

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-23318-5

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