A family of implementation-friendly BN elliptic curves

► We describe a new subfamily of BN elliptic curves for a wide platform scenario. ► Curves herein are simple to generate and suitable for efficient implementation. ► The implementation of the optimal ate pairing provided software speed records.. For the last decade, elliptic curve cryptography has g...

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Published inThe Journal of systems and software Vol. 84; no. 8; pp. 1319 - 1326
Main Authors Pereira, Geovandro C.C.F., Simplício, Marcos A., Naehrig, Michael, Barreto, Paulo S.L.M.
Format Journal Article
LanguageEnglish
Published New York Elsevier Inc 01.08.2011
Elsevier Sequoia S.A
Subjects
Boron nitride
Communities
Computational efficiency
Computer programs
Cryptography
Cybersecurity
Elliptic curve cryptosystems
Keys
Optimization
Pairing-based cryptosystems
Pairing-friendly curves
Software
Studies
Systems development
94A60
Elliptic curve cryptosystems
14G50
Pairing-based cryptosystems
Pairing-friendly curves
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Abstract ► We describe a new subfamily of BN elliptic curves for a wide platform scenario. ► Curves herein are simple to generate and suitable for efficient implementation. ► The implementation of the optimal ate pairing provided software speed records.. 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 pairing-friendly 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.
AbstractList 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 pairing-friendly 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.
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 pairing-friendly 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. [PUBLICATION ABSTRACT]
► We describe a new subfamily of BN elliptic curves for a wide platform scenario. ► Curves herein are simple to generate and suitable for efficient implementation. ► The implementation of the optimal ate pairing provided software speed records.. 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 pairing-friendly 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.
Author Pereira, Geovandro C.C.F.
Simplício, Marcos A.
Barreto, Paulo S.L.M.
Naehrig, Michael
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SSID ssj0007202
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Snippet ► We describe a new subfamily of BN elliptic curves for a wide platform scenario. ► Curves herein are simple to generate and suitable for efficient...
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...
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SubjectTerms Boron nitride
Communities
Computational efficiency
Computer programs
Cryptography
Cybersecurity
Elliptic curve cryptosystems
Keys
Optimization
Pairing-based cryptosystems
Pairing-friendly curves
Software
Studies
Systems development
Title A family of implementation-friendly BN elliptic curves
URI https://dx.doi.org/10.1016/j.jss.2011.03.083
https://www.proquest.com/docview/871576892
https://search.proquest.com/docview/896230873
Volume 84
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