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Hashing into Twisted Jacobi Intersection Curves

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Book cover Information Security and Cryptology (Inscrypt 2017)

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Abstract

By generalizing Jacobi intersection curves introduced by D. V. Chudnovsky and G. V. Chudnovsky, Feng et al. proposed twisted Jacobi intersection curves, which contain more elliptic curves. Twisted Jacobi intersection curves own efficient arithmetics with regard to their group law and are resistant to timing attacks. In this paper, we proposed two hash functions indifferentiable from a random oracle, mapping binary messages to rational points on twisted Jacobi intersection curves. Both functions are based on deterministic encodings from \(\mathbb {F}_q\) to twisted Jacobi intersection curves. There are two ways to construct such encodings: (1) utilizing the algorithm of computing cube roots on \(\mathbb {F}_q\) when \(3\,|q+1\); (2) using Shallue-Woestijne-Ulas algorithm when \(4\,|q+1\). In both cases, our encoding methods are more efficient than existed ones. Moreover, we estimate the density of images of both encodings by Chebotarev theorem.

X. He—This work is supported in part by National Natural Science Foundation of China under Grant No. 61502487, 61672030.

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Authors and Affiliations

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

    Xiaoyang He, Wei Yu & Kunpeng Wang

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

    Xiaoyang He, Wei Yu & Kunpeng Wang

  3. University of Chinese Academy of Sciences, Beijing, China

    Xiaoyang He, Wei Yu & Kunpeng Wang

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  1. Xiaoyang He
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  2. Wei Yu
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  3. Kunpeng Wang
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Correspondence to Wei Yu .

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Editors and Affiliations

  1. Xidian University, Xi’an, China

    Xiaofeng Chen

  2. SKLOIS, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China

    Dongdai Lin

  3. Columbia University, New York, New York, USA

    Moti Yung

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He, X., Yu, W., Wang, K. (2018). Hashing into Twisted Jacobi Intersection Curves. In: Chen, X., Lin, D., Yung, M. (eds) Information Security and Cryptology. Inscrypt 2017. Lecture Notes in Computer Science(), vol 10726. Springer, Cham. https://doi.org/10.1007/978-3-319-75160-3_9

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  • DOI: https://doi.org/10.1007/978-3-319-75160-3_9

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