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Further refinements of Miller's algorithm on Edwards curves.
- Source :
- Applicable Algebra in Engineering, Communication & Computing; Jun2016, Vol. 27 Issue 3, p205-217, 13p
- Publication Year :
- 2016
-
Abstract
- Recently, Edwards curves have received a lot of attention in the cryptographic community due to their fast scalar multiplication algorithms. Then, many works on the application of these curves to pairing-based cryptography have been introduced. In this paper, we investigate refinements to Miller's algorithm that play a central role in paring computation. We first introduce a variant of Miller function that leads to a more efficient variant of Miller's algorithm on Edwards curves. Then, based on the new Miller function, we present a refinement to Miller's algorithm that significantly improves the performance in comparison with the original Miller's algorithm. Our analyses also show that the proposed refinement is approximately 25 % faster than Xu-Lin's refinements (CT-RSA, 2010). Last but not least, our approach is generic, hence the proposed algorithms allow to compute both Weil and Tate pairings on pairing-friendly Edwards curves of any embedding degree. [ABSTRACT FROM AUTHOR]
- Subjects :
- ALGORITHMS
CURVES
CRYPTOGRAPHY
MATHEMATICAL functions
WEIL group
Subjects
Details
- Language :
- English
- ISSN :
- 09381279
- Volume :
- 27
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Applicable Algebra in Engineering, Communication & Computing
- Publication Type :
- Academic Journal
- Accession number :
- 117357310
- Full Text :
- https://doi.org/10.1007/s00200-015-0278-z