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An Improvement of Twisted Ate Pairing Using Integer Variable with Small HammingWeight
Yumi Sakemi,Hidehiro Kato,Yasuyuki Nogami,Yoshitaka Morikawa 대한전자공학회 2008 ITC-CSCC :International Technical Conference on Ci Vol.2008 No.7
Barreto?Naehrig (BN) curve has been introduced as a pairing-friendly elliptic curve over prime field Fp which has embedding degree 12. Characteristic and Frobenius trace are given as polynomials of integer variable χ. This paper proposes an improvement of Miller’s algorithm of twisted Ate pairing with BN curve by χ of small hamming weight. Then, in order to show the efficiency of the proposed method, twisted Ate pairings with BN curve of order r ? 2¹?? and r ? 2²?⁴ are simulated and it is shown that these twisted Ate pairings are carried out with 7.21 milliseconds and 16.5 milliseconds by Pentium4 (3.6㎓), respectively.
How to Generate a Secure Composite Order Ordinary Pairing-friendly Curve of Embedding Degree 3
Yasuyuki Nogami,Kazushi Nishii,Yumi Sakemi,Hidehiro Kato,Yoshitaka Morikawa 대한전자공학회 2009 ITC-CSCC :International Technical Conference on Ci Vol.2009 No.7
This paper proposes an efficient method for generating secure composite order ordinary pairing?friendly elliptic curves of embedding degree 3. It averagely takes about 22 minutes on Core 2 Duo (3.0㎓).