Polynomial generating pairing and its criterion for optimal pairing

Eunjeong Lee; Hyang Sook Lee; Cheol Min Park

doi:10.1007/s00200-014-0225-4

Polynomial generating pairing and its criterion for optimal pairing

Eunjeong Lee
, Hyang Sook Lee
, Cheol Min Park

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We define a polynomial generating pairing (PGP) and propose a method to construct a family of pairing friendly curves from PGP. We show that a bilinear map over the family is directly determined by the coefficients of the PGP and the map is non-degenerate under a minor condition which is satisfied with cryptographic parameters. Finally, we provide a criterion for PGP to obtain an optimal pairing.

Original language	English
Pages (from-to)	227-247
Number of pages	21
Journal	Applicable Algebra in Engineering, Communications and Computing
Volume	25
Issue number	4
DOIs	https://doi.org/10.1007/s00200-014-0225-4
State	Published - 18 Aug 2014

Bibliographical note

Funding Information:
The authors would like to thank the anonymous referees for the helpful comments. Eunjeong Lee was supported by Basic Science Research Program (Grant No. 2011-0022600). Hyang-Sook Lee was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (Grant No. 2012R1A2A1A03006706).

Publisher Copyright:
© 2014, Springer-Verlag Berlin Heidelberg.

Keywords

Optimal pairing
Pairing-friendly elliptic curve
Polynomial generating pairing

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Cite this

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doi = "10.1007/s00200-014-0225-4",

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AU - Lee, Hyang Sook

AU - Park, Cheol Min

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PY - 2014/8/18

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N2 - We define a polynomial generating pairing (PGP) and propose a method to construct a family of pairing friendly curves from PGP. We show that a bilinear map over the family is directly determined by the coefficients of the PGP and the map is non-degenerate under a minor condition which is satisfied with cryptographic parameters. Finally, we provide a criterion for PGP to obtain an optimal pairing.

AB - We define a polynomial generating pairing (PGP) and propose a method to construct a family of pairing friendly curves from PGP. We show that a bilinear map over the family is directly determined by the coefficients of the PGP and the map is non-degenerate under a minor condition which is satisfied with cryptographic parameters. Finally, we provide a criterion for PGP to obtain an optimal pairing.

KW - Optimal pairing

KW - Pairing-friendly elliptic curve

KW - Polynomial generating pairing

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AN - SCOPUS:84939261647

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JO - Applicable Algebra in Engineering, Communications and Computing

JF - Applicable Algebra in Engineering, Communications and Computing

IS - 4

ER -

Polynomial generating pairing and its criterion for optimal pairing

Abstract

Bibliographical note

Keywords

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