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Title:
fast tate pairing computation on twisted jacobi intersections curves
Author: Zhang Xusheng ; Chen Shan ; Lin Dongdai
Source: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Conference Name: 7th China International Conference on Information Security and Cryptography, Inscrypt 2011
Conference Date: November 30, 2011 - December 3, 2011
Issued Date: 2012
Conference Place: Beijing, China
Keyword: Security of data
Indexed Type: EI
ISSN: 0302-9743
ISBN: 9783642347030
Department: (1) SKLOIS Institute of Software Chinese Academy of Sciences Beijing China; (2) Graduate University Chinese Academy of Sciences Beijing China
Abstract: Recently there are lots of studies on the Tate pairing computation with different coordinate systems, such as twisted Edwards curves and Hessian curves coordinate systems. However, Jacobi intersections curves coordinate system, as another useful one, is overlooked in pairing-based cryptosystems. This paper proposes the explicit formulae for the doubling and addition steps in Miller's algorithm to compute the Tate pairing on twisted Jacobi intersections curves, as a larger class containing Jacobi intersections curves. Although these curves are not plane elliptic curves, our formulae are still very efficient and competitive with others. When the embedding degree is even, our doubling formulae are the fastest except for the formulae on Hessian/Selmer curves, and the parallel execution of our formulae are even more competitive with the Selmer curves case in the parallel manner. Besides, we give the detailed analysis of the fast variants of our formulae with other embedding degrees, such as the embedding degree 1, and the embedding degree dividing 4 and 6. At last, we analyze the relation between the Tate pairings on two isogenous elliptic curves, and show that the Tate pairing on twisted Jacobi intersections curves can be substituted for the Tate pairing on twisted Edwards curves completely. © 2012 Springer-Verlag Berlin Heidelberg.
English Abstract: Recently there are lots of studies on the Tate pairing computation with different coordinate systems, such as twisted Edwards curves and Hessian curves coordinate systems. However, Jacobi intersections curves coordinate system, as another useful one, is overlooked in pairing-based cryptosystems. This paper proposes the explicit formulae for the doubling and addition steps in Miller's algorithm to compute the Tate pairing on twisted Jacobi intersections curves, as a larger class containing Jacobi intersections curves. Although these curves are not plane elliptic curves, our formulae are still very efficient and competitive with others. When the embedding degree is even, our doubling formulae are the fastest except for the formulae on Hessian/Selmer curves, and the parallel execution of our formulae are even more competitive with the Selmer curves case in the parallel manner. Besides, we give the detailed analysis of the fast variants of our formulae with other embedding degrees, such as the embedding degree 1, and the embedding degree dividing 4 and 6. At last, we analyze the relation between the Tate pairings on two isogenous elliptic curves, and show that the Tate pairing on twisted Jacobi intersections curves can be substituted for the Tate pairing on twisted Edwards curves completely. © 2012 Springer-Verlag Berlin Heidelberg.
Language: 英语
Content Type: 会议论文
URI: http://ir.iscas.ac.cn/handle/311060/15818
Appears in Collections:软件所图书馆_会议论文

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Recommended Citation:
Zhang Xusheng,Chen Shan,Lin Dongdai. fast tate pairing computation on twisted jacobi intersections curves[C]. 见:7th China International Conference on Information Security and Cryptography, Inscrypt 2011. Beijing, China. November 30, 2011 - December 3, 2011.
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