Further refinement of pairing computation based on Miller’s algorithm

Liu, Chao-Liang; Horng, Gwoboa; Chen, Te-Yu

doi:10.1016/j.amc.2006.11.135

Cited by 4 publications

(7 citation statements)

References 14 publications

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“…Then, Liu et al [15] presented a further refinement to the Miller's algorithm by using the Blake-Murty-Xu's method. Their improvement requires an additional algorithm for segmenting the binary representation of the order of subgroups r into 7 cases : (00) i , (00) i 0, (1) i , (01) i , 0(1) i , (1) i 0 and 0(1) i 0.…”

Section: Blake-murty-xu's Methodsmentioning

confidence: 99%

“…From the observations in [13,15] and by combining with the Eisenträger, Lauter and Montgomery's trick [17], we present a modification to Miller's algorithm that can eliminate all vertical lines.…”

Section: Our Refinementmentioning

confidence: 99%

“…In this paper we extend the Blake-Murty-Xu's method and show how to eliminate all of vertical lines in Miller's algorithm. Our algorithm is generically faster than the original Miller's algorithm, and its refinements [13,15] for all pairing-friendly curves with any embedding degree. As previous refinements, our algorithm does not eliminate denominators, but it improves the performance for both Weil and Tate pairings computation on general pairing-based elliptic curves.…”

Section: Introductionmentioning

confidence: 99%

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Refinements of Miller's Algorithm over Weierstrass Curves Revisited

Le¹,

Liu²

2011

The Computer Journal

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In 1986 Victor Miller described an algorithm for computing the Weil pairing in his unpublished manuscript. This algorithm has then become the core of all pairing-based cryptosystems. Many improvements of the algorithm have been presented. Most of them involve a choice of elliptic curves of a special forms to exploit a possible twist during Tate pairing computation. Other improvements involve a reduction of the number of iterations in the Miller's algorithm. For the generic case, Blake, Murty and Xu proposed three refinements to Miller's algorithm over Weierstrass curves. Though their refinements which only reduce the total number of vertical lines in Miller's algorithm, did not give an efficient computation as other optimizations, but they can be applied for computing both of Weil and Tate pairings on all pairing-friendly elliptic curves. In this paper we extend the Blake-Murty-Xu's method and show how to perform an elimination of all vertical lines in Miller's algorithm during Weil/Tate pairings computation on general elliptic curves. Experimental results show that our algorithm is faster about 25% in comparison with the original Miller's algorithm.

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Section: Blake-murty-xu's Methodsmentioning

confidence: 99%

Section: Our Refinementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Refinements of Miller's Algorithm over Weierstrass Curves Revisited

Le¹,

Liu²

2011

The Computer Journal

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show abstract

“…Following the basic ideas in [1] and [4], we propose an improved algorithm for computing the Tate pairing in characteristic three, which can reduce more lines in average cases. The savings could prove to be important for the performance of algorithms in the implementations of these cryptographic protocols.…”

Section: Introductionmentioning

confidence: 99%

“…In 1986, Victor Miller [5] proposed an efficient algorithm for computing the pairing and most current algorithms are based on it in some manner [1] [4]. Following the basic ideas in [1] and [4], we propose an improved algorithm for computing the Tate pairing in characteristic three, which can reduce more lines in average cases.…”

Section: Introductionmentioning

confidence: 99%