Efficient and generalized pairing computation on Abelian varieties

Eunjeong Lee, Hyang Sook Lee, Cheol Min Park

Research output: Contribution to journalArticlepeer-review

107 Scopus citations


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 Atei pairing, and can be computed more efficiently. Using the R-ate pairing, the loop length in Miller's algorithm can be as small as (r1/φ(κ)) for some pairing-friendly elliptic curves which have not reached this lower bound. Therefore, we obtain savings of between 29% and 69% in overall costs compared to the Ate 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.

Original languageEnglish
Pages (from-to)1793-1803
Number of pages11
JournalIEEE Transactions on Information Theory
Issue number4
StatePublished - 2009


  • Ate pairing
  • Elliptic curves
  • Hyperelliptic curves
  • Pairing based cryptography
  • Tate pairing


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