IEICE TRANSACTIONS on Fundamentals
Sole Inversion Precomputation for Elliptic Curve Scalar Multiplications
Summary :
This paper presents a new approach to precompute points [3]P, [5]P,..., [2k-1]P, for some k ≥ 2 on an elliptic curve over Fp. Those points are required for the efficient evaluation of a scalar multiplication, the most important operation in elliptic curve cryptography. The proposed method precomputes the points in affine coordinates and needs only one single field inversion for the computation. The new method is superior to all known methods that also use one field inversion, if the required memory is taken into consideration. Compared to methods that require several field inversions for the precomputation, the proposed method is faster for a broad range of ratios of field inversions and field multiplications. The proposed method benefits especially from ratios as they occur on smart cards.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E93-A No.6 pp.1140-1147
- Publication Date
- 2010/06/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E93.A.1140
- Type of Manuscript
- Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
- Category
- Cryptography and Information Security
Authors
Keyword
Latest Issue
Copyrights notice of machine-translated contents
The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.
Cite this
Copy
Erik DAHMEN, Katsuyuki OKEYA, "Sole Inversion Precomputation for Elliptic Curve Scalar Multiplications" in IEICE TRANSACTIONS on Fundamentals,
vol. E93-A, no. 6, pp. 1140-1147, June 2010, doi: 10.1587/transfun.E93.A.1140.
Abstract: This paper presents a new approach to precompute points [3]P, [5]P,..., [2k-1]P, for some k ≥ 2 on an elliptic curve over Fp. Those points are required for the efficient evaluation of a scalar multiplication, the most important operation in elliptic curve cryptography. The proposed method precomputes the points in affine coordinates and needs only one single field inversion for the computation. The new method is superior to all known methods that also use one field inversion, if the required memory is taken into consideration. Compared to methods that require several field inversions for the precomputation, the proposed method is faster for a broad range of ratios of field inversions and field multiplications. The proposed method benefits especially from ratios as they occur on smart cards.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E93.A.1140/_p
Copy
@ARTICLE{e93-a_6_1140,
author={Erik DAHMEN, Katsuyuki OKEYA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Sole Inversion Precomputation for Elliptic Curve Scalar Multiplications},
year={2010},
volume={E93-A},
number={6},
pages={1140-1147},
abstract={This paper presents a new approach to precompute points [3]P, [5]P,..., [2k-1]P, for some k ≥ 2 on an elliptic curve over Fp. Those points are required for the efficient evaluation of a scalar multiplication, the most important operation in elliptic curve cryptography. The proposed method precomputes the points in affine coordinates and needs only one single field inversion for the computation. The new method is superior to all known methods that also use one field inversion, if the required memory is taken into consideration. Compared to methods that require several field inversions for the precomputation, the proposed method is faster for a broad range of ratios of field inversions and field multiplications. The proposed method benefits especially from ratios as they occur on smart cards.},
keywords={},
doi={10.1587/transfun.E93.A.1140},
ISSN={1745-1337},
month={June},}
Copy
TY - JOUR
TI - Sole Inversion Precomputation for Elliptic Curve Scalar Multiplications
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1140
EP - 1147
AU - Erik DAHMEN
AU - Katsuyuki OKEYA
PY - 2010
DO - 10.1587/transfun.E93.A.1140
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E93-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 2010
AB - This paper presents a new approach to precompute points [3]P, [5]P,..., [2k-1]P, for some k ≥ 2 on an elliptic curve over Fp. Those points are required for the efficient evaluation of a scalar multiplication, the most important operation in elliptic curve cryptography. The proposed method precomputes the points in affine coordinates and needs only one single field inversion for the computation. The new method is superior to all known methods that also use one field inversion, if the required memory is taken into consideration. Compared to methods that require several field inversions for the precomputation, the proposed method is faster for a broad range of ratios of field inversions and field multiplications. The proposed method benefits especially from ratios as they occur on smart cards.
ER -
English
