Integer Variable χ–Based Ate Pairing

Nogami, Yasuyuki; Akane, Masataka; Sakemi, Yumi; Kato, Harubumi; Morikawa, Yoshitaka

doi:10.1007/978-3-540-85538-5_13

Cited by 60 publications

(28 citation statements)

References 10 publications

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“…It admits several optimal derivations [8] of di erent Ate pairing [16] variants such as R-ate [17], Optimal Ate [8] and χ-ate [18]. Let E[n] be the subgroup of n-torsion points of E and E : y 2 = x 3 + b/ξ be a sextic twist of E with ξ not a cube nor a square in F p 2 .…”

Section: Preliminariesmentioning

confidence: 99%

Faster Explicit Formulas for Computing Pairings over Ordinary Curves

Aranha

Karabina²,

Longa

et al. 2011

Advances in Cryptology – EUROCRYPT 2011

135

176

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Abstract. We describe e cient formulas for computing pairings on ordinary elliptic curves over prime elds. First, we generalize lazy reduction techniques, previously considered only for arithmetic in quadratic extensions, to the whole pairing computation, including towering and curve arithmetic. Second, we introduce a new compressed squaring formula for cyclotomic subgroups and a new technique to avoid performing an inversion in the nal exponentiation when the curve is parameterized by a negative integer. The techniques are illustrated in the context of pairing computation over Barreto-Naehrig curves, where they have a particularly e cient realization, and also combined with other important developments in the recent literature. The resulting formulas reduce the number of required operations and, consequently, execution time, improving on the state-of-the-art performance of cryptographic pairings by 27%-33% on several popular 64-bit computing platforms. In particular, our techniques allow to compute a pairing under 2 million cycles for the rst time on such architectures.

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Section: Preliminariesmentioning

confidence: 99%

Faster Explicit Formulas for Computing Pairings over Ordinary Curves

Aranha

Karabina²,

Longa

et al. 2011

Advances in Cryptology – EUROCRYPT 2011

135

176

View full text Add to dashboard Cite

show abstract

“…(3) The concrete estimates in Tables 3 and 4 are for a specific BN curve. Other well-chosen BN curves, such as the one with BN parameter z = 4080000000000001 (in hexadecimal) [33] may have different performance characteristics. Nonetheless, we expect that our conclusions about the relative performance of the various signature schemes will not drastically change for well-chosen BN curves.…”

Section: Discussionmentioning

confidence: 99%

Comparing two pairing-based aggregate signature schemes

Chatterjee

Hankerson

Knapp

et al. 2009

Des. Codes Cryptogr.

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Abstract. In 2003, Boneh, Gentry, Lynn and Shacham (BGLS) devised the first provably-secure aggregate signature scheme. Their scheme uses bilinear pairings and their security proof is in the random oracle model. The first pairing-based aggregate signature scheme which has a security proof that does not make the random oracle assumption was proposed in 2006 by Lu, Ostrovsky, Sahai, Shacham and Waters (LOSSW). In this paper, we compare the security and efficiency of the BGLS and LOSSW schemes when asymmetric pairings derived from Barreto-Naehrig (BN) elliptic curves are employed.

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“…Our proposal has intersections with other interesting curve families that occur in the literature (e.g. [38,44]), offering additional benefits in those cases.…”

Section: Introductionmentioning

confidence: 92%

“…-facilitate the deployment of bilinear pairings at the 128-bit security level [15,37,8,2]; -enable all kinds of pairing-based cryptographic schemes and protocols (including short signatures) [19]; -be plentiful and easily found [35, Section 2.1.1]; -support a sextic twist, so pairing arguments can be defined over relatively small finite fields F p and F p 2 respectively [24]; -be amenable to twofold or threefold pairing compression [36]; -attain high efficiency for all pairing computation algorithms known, including the Tate [40], ate [24], eil [23], R-ate [30], Xate [38] and optimal [45] pairings; -admit optimizations based on endomorphisms and homomorphisms for all groups involved [18,20], thereby enabling fast nonpairing operations as well; -be suitable for software and hardware implementations on a wide range of platforms [16,21].…”

Section: Introductionmentioning

confidence: 99%

A family of implementation-friendly BN elliptic curves

Pereira

Simplício

Naehrig

et al. 2011

Journal of Systems and Software

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Abstract. For the last decade, elliptic curve cryptography has gained increasing interest in industry and in the academic community. This is especially due to the high level of security it provides with relatively small keys and to its ability to create very efficient and multifunctional cryptographic schemes by means of bilinear pairings. Pairings require pairingfriendly elliptic curves and among the possible choices, Barreto-Naehrig (BN) curves arguably constitute one of the most versatile families. In this paper, we further expand the potential of the BN curve family. We describe BN curves that are not only computationally very simple to generate, but also specially suitable for efficient implementation on a very broad range of scenarios. We also present implementation results of the optimal ate pairing using such a curve defined over a 254-bit prime field.

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Integer Variable χ–Based Ate Pairing

Cited by 60 publications

References 10 publications

Faster Explicit Formulas for Computing Pairings over Ordinary Curves

Faster Explicit Formulas for Computing Pairings over Ordinary Curves

Comparing two pairing-based aggregate signature schemes

A family of implementation-friendly BN elliptic curves

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