In mathematics the division polynomials provide a way to calculate multiples of points on elliptic curves and to study the fields generated byâ€¦Â (More)

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2017

2017

- Binglong Chen, Chuangqiang Hu, Chang-An Zhao
- IET Information Security
- 2017

Scalar multiplication is the most important and expensive operation in elliptic curve cryptosystems. In this study, the authorsâ€¦Â (More)

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2015

2015

- Binglong Chen, Chuangqiang Hu, Chang-An Zhao
- IACR Cryptology ePrint Archive
- 2015

Scalar multiplication is the most important and expensive operation in elliptic curve cryptosystems. In this paper we improve theâ€¦Â (More)

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2012

2012

- Johannes A. Buchmann, Harald Niederreiter, Andrew M. Odlyzko, Horst GÃ¼nter Zimmer, Michael E Laska, David G. Cantor
- 2012

On the Analogue of the Division Polynomials for Hyperelliptic CurvesÂ

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2012

2012

Assuming Langâ€™s conjectured lower bound on the heights of non-torsion points on an elliptic curve, we show that there exists anâ€¦Â (More)

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2011

2011

- Richard Moloney, Gary McGuire
- Applicable Algebra in Engineering, Communicationâ€¦
- 2011

This paper presents two kinds of division polynomials for twisted Edwards curves. Their chief property is that they characteriseâ€¦Â (More)

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2011

2011

- Dustin Moody
- ISSAC
- 2011

In this paper we find division polynomials for Jacobi quartics. These curves are an alternate model for elliptic curves to theâ€¦Â (More)

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2011

2011

We obtain nontrivial estimates of quadratic character sums of division polynomials Î¨n(P ), n = 1, 2, . . ., evaluated at a givenâ€¦Â (More)

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2008

2008

This paper presents division polynomials for twisted Edwards curves. Their chief property is that they characterise the n-torsionâ€¦Â (More)

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2006

2006

- Daniel Sadornil
- 2006

In [2], Verdure gives the factorisation patterns of division polynomials of elliptic curves defined over a finite field. Howeverâ€¦Â (More)

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2004

2004

For a fixed rational point P âˆˆ E(K) on an elliptic curve, we consider the sequence of values (Â

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