Hashing into Twisted Jacobi Intersection Curves

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10726)


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.


Elliptic curves Twisted Jacobi intersection curves Character sum Hash function Random oracle 


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Authors and Affiliations

  1. 1.State Key Laboratory of Information Security, Institute of Information EngineeringChinese Academy of SciencesBeijingChina
  2. 2.Data Assurance and Communication Security Research CenterChinese Academy of SciencesBeijingChina
  3. 3.University of Chinese Academy of SciencesBeijingChina

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