Feb, 2009
Fast Ate Pairing Computation of Embedding Degree 12 Using Subfield-Twisted Elliptic Curve
IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES
- ,
- ,
- Volume
- E92A
- Number
- 2
- First page
- 508
- Last page
- 516
- Language
- English
- Publishing type
- DOI
- 10.1587/transfun.E92.A.508
- Publisher
- IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG
This paper presents implementation techniques of fast Ate pairing of embedding degree 12. In this case, we have no trouble in finding a prime order pairing friendly curve E such as the Barreto-Naehrig curve y(2) = x(3) + a, a is an element of F-p. For the curve, an isomorphic substitution from G(2) is an element of E(F-p(12)) into G(2)'in subfield-twisted elliptic curve E'(F-p(2)) speeds up scalar multiplications over G(2) and wipes out denominator calculations in Miller's algorithm. This paper mainly provides about 30% improvement of the Miller's algorithm calculation using proper subfield arithmetic operations. Moreover, we also provide the efficient parameter settings of the BN curves. When p is a 254-bit prime, the embedding degree is 12, and the processor is Pentium4 (3.6 GHz), it is shown that the proposed algorithm computes Ate pairing in 13.3 milli-seconds including final exponentiation.
- Link information
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- DOI
- https://doi.org/10.1587/transfun.E92.A.508
- Web of Science
- https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000265701000022&DestApp=WOS_CPL
- Scopus
- https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=70449513811&origin=inward
- Scopus Citedby
- https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=70449513811&origin=inward
- ID information
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- DOI : 10.1587/transfun.E92.A.508
- ISSN : 0916-8508
- eISSN : 1745-1337
- SCOPUS ID : 70449513811
- Web of Science ID : WOS:000265701000022