Paper 2008/040

Efficient and Generalized Pairing Computation on Abelian Varieties

Eunjeong Lee, Hyang-Sook Lee, and Cheol-Min Park


In this paper, we propose a new method for constructing a bilinear pairing over (hyper)elliptic curves, which we call the R-ate pairing. This pairing is a generalization of the Ate and Ate_i pairing, and also improves efficiency of the pairing computation. Using the R-ate pairing, the loop length in Miller's algorithm can be as small as ${\rm log}(r^{1 / \phi(k)})$ for some pairing-friendly elliptic curves which have not reached this lower bound. Therefore we obtain from 29 % to 69 % savings in overall costs compared to the Ate_i pairing. On supersingular hyperelliptic curves of genus 2, we show that this approach makes the loop length in Miller's algorithm shorter than that of the Ate pairing.

Available format(s)
Public-key cryptography
Publication info
Published elsewhere. Unknown where it was published
pairingelliptic curveshyperelliptic curvespairing based cryptographyTate pairing
Contact author(s)
ejlee @ kias re kr
2008-01-28: received
Short URL
Creative Commons Attribution


      author = {Eunjeong Lee and Hyang-Sook Lee and Cheol-Min Park},
      title = {Efficient and Generalized Pairing Computation on Abelian Varieties},
      howpublished = {Cryptology ePrint Archive, Paper 2008/040},
      year = {2008},
      note = {\url{}},
      url = {}
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