Optimal pairing computation over families of pairing-friendly elliptic curves

Soo Kyung Eom; Hyang Sook Lee; Cheol Min Park

doi:10.1007/s00200-011-0146-4

Optimal pairing computation over families of pairing-friendly elliptic curves

Soo Kyung Eom, Hyang Sook Lee, Cheol Min Park

Department of Mathematics

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

Abstract

Vercauteren introduced the concept of optimal pairing, which by definition can be computed by using at most (log₂ r)/φ(k) + log₂ k basic Miller iterations, where r is the order of the groups involved and k is the embedding degree Vercauteren (IEEE Trans Inf Theory 56(1):455-461, 2010). Freeman et al. summarized and proposed all of the new constructions of pairing-friendly elliptic curves that currently exist Freeman et al. (J Cryptol 23(2):224-280, 2010). In this paper, we give an optimal pairing for each family of pairing-friendly curves in Freeman et al. (J Cryptol 23(2):224-280, 2010) by taking the Ate or R-ate pairing approach.

Original language	English
Pages (from-to)	235-248
Number of pages	14
Journal	Applicable Algebra in Engineering, Communications and Computing
Volume	22
Issue number	4
DOIs	https://doi.org/10.1007/s00200-011-0146-4
State	Published - Nov 2011

Keywords

Ate pairing
Elliptic curves
Pairing computation
R-ate pairing
Tate pairing

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abstract = "Vercauteren introduced the concept of optimal pairing, which by definition can be computed by using at most (log2 r)/φ(k) + log2 k basic Miller iterations, where r is the order of the groups involved and k is the embedding degree Vercauteren (IEEE Trans Inf Theory 56(1):455-461, 2010). Freeman et al. summarized and proposed all of the new constructions of pairing-friendly elliptic curves that currently exist Freeman et al. (J Cryptol 23(2):224-280, 2010). In this paper, we give an optimal pairing for each family of pairing-friendly curves in Freeman et al. (J Cryptol 23(2):224-280, 2010) by taking the Ate or R-ate pairing approach.",

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AU - Eom, Soo Kyung

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AB - Vercauteren introduced the concept of optimal pairing, which by definition can be computed by using at most (log2 r)/φ(k) + log2 k basic Miller iterations, where r is the order of the groups involved and k is the embedding degree Vercauteren (IEEE Trans Inf Theory 56(1):455-461, 2010). Freeman et al. summarized and proposed all of the new constructions of pairing-friendly elliptic curves that currently exist Freeman et al. (J Cryptol 23(2):224-280, 2010). In this paper, we give an optimal pairing for each family of pairing-friendly curves in Freeman et al. (J Cryptol 23(2):224-280, 2010) by taking the Ate or R-ate pairing approach.

KW - Ate pairing

KW - Elliptic curves

KW - Pairing computation

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KW - Tate pairing

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JO - Applicable Algebra in Engineering, Communications and Computing

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Optimal pairing computation over families of pairing-friendly elliptic curves

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Keywords

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