Simple and exact formula for minimum loop length in Ate i pairing based on Brezing-Weng curves

Hoon Hong; Eunjeong Lee; Hyang Sook Lee; Cheol Min Park

doi:10.1007/s10623-011-9605-y

Simple and exact formula for minimum loop length in Ate _i pairing based on Brezing-Weng curves

Hoon Hong, Eunjeong Lee, Hyang Sook Lee, Cheol Min Park

Department of Mathematics

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

7 Scopus citations

Abstract

We provide a simple and exact formula for the minimum Miller loop length in Ate _i pairing based on Brezing-Weng curves, in terms of the involved parameters, under a mild condition on the parameters. It will also be shown that almost all cryptographically useful/meaningful parameters satisfy the mild condition. Hence the simple and exact formula is valid for them. It will also turn out that the formula depends only on essentially two parameters, providing freedom to choose the other parameters to address the design issues other than minimizing the loop length.

Original language	English
Pages (from-to)	271-292
Number of pages	22
Journal	Designs, Codes, and Cryptography
Volume	67
Issue number	2
DOIs	https://doi.org/10.1007/s10623-011-9605-y
State	Published - May 2013

Bibliographical note

Funding Information:
Acknowledgement Eunjeong Lee was supported by the Priority Research Centers Program through the National Research Foundation of Korea (NRF) grant funded by the Ministry of Education, Science and Technology (No. 2009-0093827). Hyang-Sook Lee and Cheol-Min Park were supported by the National Research Foundation of Korea (NRF) grant funded by the Ministry of Education, Science and Technology. (No.2010-0000402). We would like to thank the anonymous referees for their insightful and helpful suggestions.

Keywords

Elliptic curves
Miller algorithm
Pairing-based cryptosystem

Access to Document

10.1007/s10623-011-9605-y

Cite this

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title = "Simple and exact formula for minimum loop length in Ate i pairing based on Brezing-Weng curves",

abstract = "We provide a simple and exact formula for the minimum Miller loop length in Ate i pairing based on Brezing-Weng curves, in terms of the involved parameters, under a mild condition on the parameters. It will also be shown that almost all cryptographically useful/meaningful parameters satisfy the mild condition. Hence the simple and exact formula is valid for them. It will also turn out that the formula depends only on essentially two parameters, providing freedom to choose the other parameters to address the design issues other than minimizing the loop length.",

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