fast tate pairing computation on twisted jacobi intersections curves

ISCAS OpenIR

	fast tate pairing computation on twisted jacobi intersections curves
	Zhang Xusheng; Chen Shan; Lin Dongdai
	2012
会议名称	7th China International Conference on Information Security and Cryptography, Inscrypt 2011
会议录名称	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
页码	210-226
会议日期	November 30, 2011 - December 3, 2011
会议地点	Beijing, China
收录类别	EI
ISSN	0302-9743
ISBN	9783642347030
部门归属	(1) SKLOIS Institute of Software Chinese Academy of Sciences Beijing China; (2) Graduate University Chinese Academy of Sciences Beijing China
摘要	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.; 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.
关键词	Security Of Data
语种	英语
内容类型	会议论文
URI标识	http://ir.iscas.ac.cn/handle/311060/15818
专题	中国科学院软件研究所
推荐引用方式 GB/T 7714	Zhang Xusheng,Chen Shan,Lin Dongdai. fast tate pairing computation on twisted jacobi intersections curves[C],2012:210-226.