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Title:
Simple and Exact Formula for Minimum Loop Length in Ate_i Pairing based on Brezing-Weng Curves
Authors: Hoon Hong, Eunjeong Lee, Hyang-Sook Lee, Cheol-Min Park
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 be also shown that almost all cryptographically useful 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 two parameters, providing freedom to choose the other parameters to address the design issues other than minimizing the loop length.
ePrint: https://eprint.iacr.org/2011/040
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