Faster ate pairing computation over pairing-friendly elliptic curves using GLV decomposition

Soo Kyung Eom, Eunjeong Lee, Hyang Sook Lee

Research output: Contribution to journalArticlepeer-review


The preexisting pairings ate, atei, R-ate, and optimal-ate use q-expansion, where q is the size of the defining field for the elliptic curves. Elliptic curves with small embedding degrees only allow a few of these pairings. In such cases, efficiently computable endomorphisms can be used, as in [11] and [12]. They used the endomorphisms that have characteristic polynomials with very small coefficients, which led to some restrictions in finding various pairingfriendly curves. To construct more pairing-friendly curves, we consider μ-expansion using the Gallant-Lambert- Vanstone (GLV) decomposition method, where μ is an arbitrary integer. We illustrate some pairing-friendly curves that provide more efficient pairing from the μ-expansion than from the ate pairing. The proposed method can achieve timing results at least 20% faster than the ate pairing.

Original languageEnglish
Pages (from-to)880-888
Number of pages9
JournalETRI Journal
Issue number5
StatePublished - Oct 2013


  • Ate pairing
  • Elliptic curves
  • GLV decomposition
  • Pairing computation


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