Keyword : Miller\\''s algorithm


Efficient Algorithm for Tate Pairing of Composite Order
Yutaro KIYOMURA Tsuyoshi TAKAGI 
Publication:   IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2014/10/01
Vol. E97-A  No. 10 ; pp. 2055-2063
Type of Manuscript:  PAPER
Category: Cryptography and Information Security
Keyword: 
composite order pairingMiller's algorithmnon-adjacent Form (NAF)window hybrid binary-ternary form (w-HBTF)
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A Note on the Pairing Computation Using Normalized Miller Functions
Naoki OGURA Shigenori UCHIYAMA Naoki KANAYAMA Eiji OKAMOTO 
Publication:   IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2012/01/01
Vol. E95-A  No. 1 ; pp. 196-203
Type of Manuscript:  Special Section PAPER (Special Section on Cryptography and Information Security)
Category: Mathematics
Keyword: 
pairingMiller's algorithmrational functionsnormalization
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An Improvement of Twisted Ate Pairing Efficient for Multi-Pairing and Thread Computing
Yumi SAKEMI Yasuyuki NOGAMI Shoichi TAKEUCHI Yoshitaka MORIKAWA 
Publication:   IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2011/06/01
Vol. E94-A  No. 6 ; pp. 1356-1367
Type of Manuscript:  Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
Category: 
Keyword: 
twisted Ate pairingMiller's algorithmFrobenius mapmulti-pairingthread computing
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Integer Variable χ-Based Cross Twisted Ate Pairing and Its Optimization for Barreto-Naehrig Curve
Yasuyuki NOGAMI Yumi SAKEMI Hidehiro KATO Masataka AKANE Yoshitaka MORIKAWA 
Publication:   IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2009/08/01
Vol. E92-A  No. 8 ; pp. 1859-1867
Type of Manuscript:  Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
Category: Theory
Keyword: 
Ate pairingMiller's algorithm
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