The search functionality is under construction.

The search functionality is under construction.

This paper extends the Brezing-Weng method by parameterizing the discriminant *D* by a polynomial *D*(*x*). To date, the maximum of CM discriminant can be adequately addressed is about 14-digits. Thus the degree of the square free part of *D*(*x*) has to be sufficiently small. By making the square free part of *D*(*x*) a linear monomial, the degree of the square free part is small and by substituting *x* to some quadratic monomial, pairing-friendly curves with various discriminants can be constructed. In order that a square free part of *D*(*x*) is of the form *ax*, *ax* has to be a square element as a polynomial representation in a number field. Two methods are introduced to apply this construction. For *k* = 5, 8, 9, 15, 16, 20, 24 and 28, the proposed method gives smaller ρ value than those in previous studies.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E93-A No.6 pp.1032-1038

- Publication Date
- 2010/06/01

- Publicized

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.E93.A.1032

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

- Category
- Cryptography and Information Security

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.

Copy

Woo Sug KANG, Ki Taek KIM, "Pairing-Friendly Elliptic Curves with Various Discriminants" in IEICE TRANSACTIONS on Fundamentals,
vol. E93-A, no. 6, pp. 1032-1038, June 2010, doi: 10.1587/transfun.E93.A.1032.

Abstract: This paper extends the Brezing-Weng method by parameterizing the discriminant *D* by a polynomial *D*(*x*). To date, the maximum of CM discriminant can be adequately addressed is about 14-digits. Thus the degree of the square free part of *D*(*x*) has to be sufficiently small. By making the square free part of *D*(*x*) a linear monomial, the degree of the square free part is small and by substituting *x* to some quadratic monomial, pairing-friendly curves with various discriminants can be constructed. In order that a square free part of *D*(*x*) is of the form *ax*, *ax* has to be a square element as a polynomial representation in a number field. Two methods are introduced to apply this construction. For *k* = 5, 8, 9, 15, 16, 20, 24 and 28, the proposed method gives smaller ρ value than those in previous studies.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E93.A.1032/_p

Copy

@ARTICLE{e93-a_6_1032,

author={Woo Sug KANG, Ki Taek KIM, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Pairing-Friendly Elliptic Curves with Various Discriminants},

year={2010},

volume={E93-A},

number={6},

pages={1032-1038},

abstract={This paper extends the Brezing-Weng method by parameterizing the discriminant *D* by a polynomial *D*(*x*). To date, the maximum of CM discriminant can be adequately addressed is about 14-digits. Thus the degree of the square free part of *D*(*x*) has to be sufficiently small. By making the square free part of *D*(*x*) a linear monomial, the degree of the square free part is small and by substituting *x* to some quadratic monomial, pairing-friendly curves with various discriminants can be constructed. In order that a square free part of *D*(*x*) is of the form *ax*, *ax* has to be a square element as a polynomial representation in a number field. Two methods are introduced to apply this construction. For *k* = 5, 8, 9, 15, 16, 20, 24 and 28, the proposed method gives smaller ρ value than those in previous studies.},

keywords={},

doi={10.1587/transfun.E93.A.1032},

ISSN={1745-1337},

month={June},}

Copy

TY - JOUR

TI - Pairing-Friendly Elliptic Curves with Various Discriminants

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 1032

EP - 1038

AU - Woo Sug KANG

AU - Ki Taek KIM

PY - 2010

DO - 10.1587/transfun.E93.A.1032

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E93-A

IS - 6

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - June 2010

AB - This paper extends the Brezing-Weng method by parameterizing the discriminant *D* by a polynomial *D*(*x*). To date, the maximum of CM discriminant can be adequately addressed is about 14-digits. Thus the degree of the square free part of *D*(*x*) has to be sufficiently small. By making the square free part of *D*(*x*) a linear monomial, the degree of the square free part is small and by substituting *x* to some quadratic monomial, pairing-friendly curves with various discriminants can be constructed. In order that a square free part of *D*(*x*) is of the form *ax*, *ax* has to be a square element as a polynomial representation in a number field. Two methods are introduced to apply this construction. For *k* = 5, 8, 9, 15, 16, 20, 24 and 28, the proposed method gives smaller ρ value than those in previous studies.

ER -