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

Authors:
Hoon Hong;Eunjeong Lee;Hyang-Sook Lee;Cheol-Min Park
Affiliations:
Department of Mathematics, North Carolina State University, Raleigh, USA 27695-8205;Institute of Mathematical Sciences, Ewha Womans University, Seoul, South Korea 120-750;Department of Mathematics, Ewha Womans University, Seoul, South Korea 120-750;National Institute for Mathematical Sciences, Daejeon, South Korea 305-811
Venue:
Designs, Codes and Cryptography
Year:
2013

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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.