Open AccessFaster Ate Pairing Computation over Pairing‐Friendly Elliptic Curves Using GLV Decomposition
Author(s) -
Eom Soo Kyung,
Lee Eunjeong,
Lee HyangSook
Publication year - 2013
Publication title -
etri journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.295
H-Index - 46
eISSN - 2233-7326
pISSN - 1225-6463
DOI - 10.4218/etrij.13.0112.0756
Subject(s) - pairing , endomorphism , elliptic curve , mathematics , integer (computer science) , computation , pure mathematics , algorithm , computer science , physics , superconductivity , quantum mechanics , programming language
The preexisting pairings ate, ate i , 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 pairing‐friendly 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.