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Almost Injective and Invertible Encodings for Jacobi Quartic Curves

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Science of Cyber Security (SciSec 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14299))

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Abstract

This paper introduces a novel encoding scheme for hashing values from the finite field \(\mathbb {F}_p\) to points on Jacobi quartic curves. These curves possess efficient group law and are immune to timing attacks. The proposed encoding scheme achieves almost injective and invertible mappings of the input values into Jacobi quartic curves. When \(p \equiv 3 \mod 4\), our encoding saves \( 2 \textbf{I} + \textbf{D} - 8 \textbf{M} - 4 \textbf{S}\) compared to existing methods. This improvement amounts to approximately \(50\%\) on average when compared to existing methods. The encoding scheme can be used in a variety of cryptographic applications that rely on elliptic curves, such as identity-based encryption schemes and private set intersection protocols.

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, CAS, Beijing, China

    Xiuxiu Li, Wei Yu, Kunpeng Wang & Luying Li

  2. State Key Laboratory of Cryptology, P. O. Box 5159, Beijing, 100878, China

    Xiuxiu Li & Wei Yu

  3. School of Cyberspace Security, University of Chinese Academy of Sciences, Beijing, China

    Xiuxiu Li, Wei Yu, Kunpeng Wang & Luying Li

Authors
  1. Xiuxiu Li
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  2. Wei Yu
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  4. Luying Li
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Correspondence to Wei Yu .

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Editors and Affiliations

  1. Columbia University, New York, NY, USA

    Moti Yung

  2. RMIT University, Melbourne, VIC, Australia

    Chao Chen

  3. Technical University of Denmark, Kongens Lyngby, Denmark

    Weizhi Meng

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Li, X., Yu, W., Wang, K., Li, L. (2023). Almost Injective and Invertible Encodings for Jacobi Quartic Curves. In: Yung, M., Chen, C., Meng, W. (eds) Science of Cyber Security . SciSec 2023. Lecture Notes in Computer Science, vol 14299. Springer, Cham. https://doi.org/10.1007/978-3-031-45933-7_8

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  • DOI: https://doi.org/10.1007/978-3-031-45933-7_8

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