Cryptology ePrint Archive: Report 2011/040
Simple and Exact Formula for Minimum Loop Length in Ate_i Pairing based on Brezing-Weng Curves
Hoon Hong, Eunjeong Lee, Hyang-Sook Lee and 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.
Category / Keywords: public-key cryptography / elliptic curve cryptosystem, pairing, number theory
Date: received 21 Jan 2011, last revised 21 Jan 2011
Contact author: ejlee127 at ewha ac kr
Available format(s): PDF | BibTeX Citation
Version: 20110121:184554 (All versions of this report)
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