Publication: IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences Publication Date: 2012/01/01 Vol. E95-ANo. 1 ;
pp. 196-203 Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security) Category: Mathematics Keyword: pairing, Miller's algorithm, rational functions, normalization,
Publication: IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences Publication Date: 2011/06/01 Vol. E94-ANo. 6 ;
pp. 1356-1367 Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications) Category: Keyword: twisted Ate pairing, Miller's algorithm, Frobenius map, multi-pairing, thread computing,
Publication: IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences Publication Date: 2009/08/01 Vol. E92-ANo. 8 ;
pp. 1859-1867 Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications) Category: Theory Keyword: Ate pairing, Miller's algorithm,