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We discuss multidoubling methods for efficient elliptic scalar multiplication. The methods allows computation of 2^{k} *P* directly from *P* without computing the intermediate points, where *P* denotes a randomly selected point on an elliptic curve. We introduce algorithms for elliptic curves with Montgomery form and Weierstrass form defined over finite fields with characteristic greater than 3 in terms of affine coordinates. These algorithms are faster than *k* repeated doublings. Moreover, we apply the algorithms to scalar multiplication on elliptic curves and analyze computational complexity. As a result of our implementation with respect to the Montgomery and Weierstrass forms in terms of affine coordinates, we achieved running time reduced by 28% and 31%, respectively, in the scalar multiplication of an elliptic curve of size 160-bit over finite fields with characteristic greater than 3.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E85-A No.5 pp.1075-1083

- Publication Date
- 2002/05/01

- Publicized

- Online ISSN

- DOI

- Type of Manuscript
- Special Section LETTER (Special Section on Discrete Mathematics and Its Applications)

- Category

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Yasuyuki SAKAI, Kouichi SAKURAI, "Speeding Up Elliptic Scalar Multiplication Using Multidoubling" in IEICE TRANSACTIONS on Fundamentals,
vol. E85-A, no. 5, pp. 1075-1083, May 2002, doi: .

Abstract: We discuss multidoubling methods for efficient elliptic scalar multiplication. The methods allows computation of 2^{k} *P* directly from *P* without computing the intermediate points, where *P* denotes a randomly selected point on an elliptic curve. We introduce algorithms for elliptic curves with Montgomery form and Weierstrass form defined over finite fields with characteristic greater than 3 in terms of affine coordinates. These algorithms are faster than *k* repeated doublings. Moreover, we apply the algorithms to scalar multiplication on elliptic curves and analyze computational complexity. As a result of our implementation with respect to the Montgomery and Weierstrass forms in terms of affine coordinates, we achieved running time reduced by 28% and 31%, respectively, in the scalar multiplication of an elliptic curve of size 160-bit over finite fields with characteristic greater than 3.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e85-a_5_1075/_p

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@ARTICLE{e85-a_5_1075,

author={Yasuyuki SAKAI, Kouichi SAKURAI, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Speeding Up Elliptic Scalar Multiplication Using Multidoubling},

year={2002},

volume={E85-A},

number={5},

pages={1075-1083},

abstract={We discuss multidoubling methods for efficient elliptic scalar multiplication. The methods allows computation of 2^{k} *P* directly from *P* without computing the intermediate points, where *P* denotes a randomly selected point on an elliptic curve. We introduce algorithms for elliptic curves with Montgomery form and Weierstrass form defined over finite fields with characteristic greater than 3 in terms of affine coordinates. These algorithms are faster than *k* repeated doublings. Moreover, we apply the algorithms to scalar multiplication on elliptic curves and analyze computational complexity. As a result of our implementation with respect to the Montgomery and Weierstrass forms in terms of affine coordinates, we achieved running time reduced by 28% and 31%, respectively, in the scalar multiplication of an elliptic curve of size 160-bit over finite fields with characteristic greater than 3.},

keywords={},

doi={},

ISSN={},

month={May},}

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TY - JOUR

TI - Speeding Up Elliptic Scalar Multiplication Using Multidoubling

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 1075

EP - 1083

AU - Yasuyuki SAKAI

AU - Kouichi SAKURAI

PY - 2002

DO -

JO - IEICE TRANSACTIONS on Fundamentals

SN -

VL - E85-A

IS - 5

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - May 2002

AB - We discuss multidoubling methods for efficient elliptic scalar multiplication. The methods allows computation of 2^{k} *P* directly from *P* without computing the intermediate points, where *P* denotes a randomly selected point on an elliptic curve. We introduce algorithms for elliptic curves with Montgomery form and Weierstrass form defined over finite fields with characteristic greater than 3 in terms of affine coordinates. These algorithms are faster than *k* repeated doublings. Moreover, we apply the algorithms to scalar multiplication on elliptic curves and analyze computational complexity. As a result of our implementation with respect to the Montgomery and Weierstrass forms in terms of affine coordinates, we achieved running time reduced by 28% and 31%, respectively, in the scalar multiplication of an elliptic curve of size 160-bit over finite fields with characteristic greater than 3.

ER -