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Detail
Journal Article
Efficient Computation of Eta Pairing Over Binary Field with Vandermonde Matrix
- Authors
- Masaaki Shirase, Tsuyoshi Takagi, Doo Ho Choi, Dong Guk Han, Ho Won Kim
- Issue Date
- 2009-04
- Citation
- ETRI Journal, v.31, no.2, pp.129-139
- ISSN
- 1225-6463
- Publisher
- 한국전자통신연구원 (ETRI)
- Language
- English
- Type
- Journal Article
- Project Code
- 09MS5600, Development of the Technology of Side Channel Attack Countermeasure Primitives and Security Validation, Choi Doo Ho
- Abstract
- This paper provides an efficient algorithm for computing the ηTpairing on supersingular elliptic curves over fields of characteristic two. In the proposed algorithm, we deploy ploy a modified multiplication in F24nusing the Vandermonde matrix. For F, G;24nthe proposed multiplication method computes B . F .G instead ofF G . with some 棺.F.G because 棺 is eliminated by the final exponentiation of the pairing computation. The proposed multiplication method asymptotically requires only 7 multiplications in 2n F as n 8 , while the cost of the previously fastest Karatsuba method is 9 multiplications in 2n F . Consequently, the cost of the T pairing computation is reduced by 14.3%.
- KSP Keywords
- Binary fields, Efficient algorithms, Efficient computation, Final Exponentiation, Karatsuba method, Pairing computation, Supersingular elliptic curves, Vandermonde matrix