Explicit formula for optimal ate pairing over cyclotomic family of elliptic curves

Hoon Hong; Eunjeong Lee; Hyang Sook Lee

doi:10.1016/j.ffa.2014.12.007

Explicit formula for optimal ate pairing over cyclotomic family of elliptic curves

Hoon Hong, Eunjeong Lee, Hyang Sook Lee

Department of Mathematics

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

3 Scopus citations

Abstract

Pairings on elliptic curves play an important role in cryptography. We provide an explicit formula for vectors of polynomials describing optimal ate pairings over cyclotomic family of elliptic curves. The explicit formula is simple in that it only involves partitioning a certain cyclotomic polynomial. The simplicity of the formula allows us to analyze the sparsity of the vector.

Original language	English
Pages (from-to)	45-74
Number of pages	30
Journal	Finite Fields and their Applications
Volume	34
DOIs	https://doi.org/10.1016/j.ffa.2014.12.007
State	Published - Jul 2015

Bibliographical note

Funding Information:
Eunjeong Lee and Hyang-Sook Lee were 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 Number: 2012R1A2A1A03006706 ).

Publisher Copyright:
© 2014 Elsevier Inc. All rights reserved.

Keywords

Cyclotomic polynomial
Elliptic curve
Pairing-based cryptosystem

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10.1016/j.ffa.2014.12.007

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abstract = "Pairings on elliptic curves play an important role in cryptography. We provide an explicit formula for vectors of polynomials describing optimal ate pairings over cyclotomic family of elliptic curves. The explicit formula is simple in that it only involves partitioning a certain cyclotomic polynomial. The simplicity of the formula allows us to analyze the sparsity of the vector.",

keywords = "Cyclotomic polynomial, Elliptic curve, Pairing-based cryptosystem",

author = "Hoon Hong and Eunjeong Lee and Lee, {Hyang Sook}",

note = "Funding Information: Eunjeong Lee and Hyang-Sook Lee were 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 Number: 2012R1A2A1A03006706 ). Publisher Copyright: {\textcopyright} 2014 Elsevier Inc. All rights reserved.",

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AU - Lee, Hyang Sook

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N2 - Pairings on elliptic curves play an important role in cryptography. We provide an explicit formula for vectors of polynomials describing optimal ate pairings over cyclotomic family of elliptic curves. The explicit formula is simple in that it only involves partitioning a certain cyclotomic polynomial. The simplicity of the formula allows us to analyze the sparsity of the vector.

AB - Pairings on elliptic curves play an important role in cryptography. We provide an explicit formula for vectors of polynomials describing optimal ate pairings over cyclotomic family of elliptic curves. The explicit formula is simple in that it only involves partitioning a certain cyclotomic polynomial. The simplicity of the formula allows us to analyze the sparsity of the vector.

KW - Cyclotomic polynomial

KW - Elliptic curve

KW - Pairing-based cryptosystem

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JO - Finite Fields and their Applications

JF - Finite Fields and their Applications

ER -

Explicit formula for optimal ate pairing over cyclotomic family of elliptic curves

Abstract

Bibliographical note

Keywords

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