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Erschienen in:
The Realm of the Pairings Kapitel lesen Erstes Kapitel lesen

2014 | OriginalPaper | Buchkapitel

Exponentiating in Pairing Groups

verfasst von : Joppe W. Bos, Craig Costello, Michael Naehrig

Erschienen in: Selected Areas in Cryptography -- SAC 2013

Verlag: Springer Berlin Heidelberg

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Abstract

We study exponentiations in pairing groups for the most common security levels and show that, although the Weierstrass model is preferable for pairing computation, it can be worthwhile to map to alternative curve representations for the non-pairing group operations in protocols.

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Vorheriges Kapitel A High-Speed Elliptic Curve Cryptographic Processor for Generic Curves over
Nächstes Kapitel Faster Repeated Doublings on Binary Elliptic Curves
Fußnoten
1
We note that for particular KSS \(k=18\) curves, large savings may arise in this algorithm due to the fact that the \(\alpha = \sum _{i=0}^5 a_i\psi ^i\) (from Sect. 5.2 of [46]) have some of the \(a_i\) being zero. In the case of the KSS curve we use, around \(2/3\) of the computations vanish due to \(a_2=a_4=a_5=0\) and \(a_1=1\).
 
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Metadaten
Titel
Exponentiating in Pairing Groups
verfasst von
Joppe W. Bos
Craig Costello
Michael Naehrig
Copyright-Jahr
2014
Verlag
Springer Berlin Heidelberg
Buch
Selected Areas in Cryptography -- SAC 2013

Print ISBN: 978-3-662-43413-0

Electronic ISBN: 978-3-662-43414-7

Copyright-Jahr: 2014

DOI
https://doi.org/10.1007/978-3-662-43414-7_22

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