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.
Original language | English |
---|---|
Pages (from-to) | 880-888 |
Number of pages | 9 |
Journal | ETRI Journal |
Volume | 35 |
Issue number | 5 |
DOIs | |
State | Published - Oct 2013 |
Keywords
- Ate pairing
- Elliptic curves
- GLV decomposition
- Pairing computation