The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Kertas ini membentangkan pendekatan baharu untuk mata prakiraan [3]P, [dua]P,..., [2k-1]P, untuk beberapa k ≥ 2 pada lengkung elips di atas Fp. Titik tersebut diperlukan untuk penilaian yang cekap bagi pendaraban skalar, operasi yang paling penting dalam kriptografi lengkung eliptik. Kaedah yang dicadangkan mengira mata dalam koordinat afin dan hanya memerlukan satu penyongsangan medan tunggal untuk pengiraan. Kaedah baru adalah lebih baik daripada semua kaedah yang diketahui yang juga menggunakan satu penyongsangan medan, jika memori yang diperlukan diambil kira. Berbanding dengan kaedah yang memerlukan beberapa penyongsangan medan untuk prapengiraan, kaedah yang dicadangkan adalah lebih pantas untuk julat luas nisbah penyongsangan medan dan pendaraban medan. Kaedah yang dicadangkan mendapat manfaat terutamanya daripada nisbah kerana ia berlaku pada kad pintar.
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Salinan
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
Salinan
@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},}
Salinan
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 -