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- Title
Faster Ate Pairing Computation over Pairing-Friendly Ellipitic Curves Using GLV Decomposition.
- Authors
Soo Kyung Eom; Eunjeong Lee; Hyang-Sook Lee
- Abstract
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.
- Subjects
POLYNOMIALS; COMPLEX multiplication; ALGEBRAIC curves; ELLIPTIC curves; INTEGER programming; ENDOMORPHISMS
- Publication
ETRI Journal, 2013, Vol 35, Issue 5, p880
- ISSN
1225-6463
- Publication type
Article
- DOI
10.4218/etrij.13.0112.0756