Paper 2011/318 Original: eprint.iacr.org/2011/318 ↗
Scalar Multiplication on Koblitz Curves using $\tau^2-$NAF
Abstract
The paper proposes a $\tau^2-$NAF method for scalar multiplication on Koblitz curves, which requires asymptotically $0.215m$ point additions in $GF(2^m)$. For $\tau^2-$NAF method, point quading operation $(a\rightarrow a^4)$ is performed instead of point squarings. The proposed method is faster than normal $\tau-$NAF method, which requires around $\frac{m}{3}$ point additions. However, like width $w$ based $\tau-$NAF methods, there is an overhead of pre-computations in the $\tau^2-$NAF method. For extended binary fields of small size, the $\tau^2-$NAF based scalar multiplication requires almost same number of point additions as in width $4$ $\tau-$NAF method. Though, complexity wise, $\tau^2-$NAF based scalar multiplication and width $4-\tau-$NAF based scalar multiplication are similar, but the techniques are different.
Metadata
- Available format(s)
PDF- Category
- Implementation
- Publication info
- Preprint.
- History
- 2011-06-17: last updated
- 2011-06-17: published
- Short URL
- https://ia.cr/2011/318
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2011/318,
author = {Sujoy Sinha Roy and Chester Rebeiro and Debdeep Mukhopadhyay and Junko Takahashi and Toshinori Fukunaga},
title = {Scalar Multiplication on Koblitz Curves using $\tau^2-$NAF},
howpublished = {Cryptology {ePrint} Archive, Paper 2011/318},
year = {2011},
url = {https://eprint.iacr.org/2011/318}
}