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Tate Pairing Computation on Generalized Hessian Curves

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Part of the Lecture Notes in Computer Science book series (LNSC,volume 7690)

Abstract

In this paper, we present explicit formulae for Miller’s algorithm to compute the Tate pairing on generalized Hessian curves using projective coordinates. Firstly, we propose the geometric interpretation of the group law and construct Miller function on generalized Hessian curves. The computation of Tate pairing using these functions in Miller’s algorithm costs 10m in addition steps and 5m+6s in doubling steps. Finally, we present the parallel algorithm for computing Tate pairing on generalized Hessian curves.

Keywords

  • Elliptic curves
  • Hessian curves
  • Tate pairing
  • Miller algorithm
  • Cryptography

Supported in part by the National Natural Science Foundation of China No. 11101002.

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Li, L., Zhang, F. (2012). Tate Pairing Computation on Generalized Hessian Curves. In: Lee, D.H., Yung, M. (eds) Information Security Applications. WISA 2012. Lecture Notes in Computer Science, vol 7690. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35416-8_9

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  • DOI: https://doi.org/10.1007/978-3-642-35416-8_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35415-1

  • Online ISBN: 978-3-642-35416-8

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