A Taxonomy of Pairing-Friendly Elliptic Curves
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This paper gives a single coherent framework that encompasses all of the constructions of pairing-friendly elliptic curves currently existing in the literature and provides recommendations as to which pairing- friendly curves to choose to best satisfy a variety of performance and security requirements.Abstract:
Elliptic curves with small embedding degree and large prime-order subgroup are key ingredients for implementing pairing-based cryptographic systems. Such “pairing-friendly” curves are rare and thus require specific constructions. In this paper we give a single coherent framework that encompasses all of the constructions of pairing-friendly elliptic curves currently existing in the literature. We also include new constructions of pairing-friendly curves that improve on the previously known constructions for certain embedding degrees. Finally, for all embedding degrees up to 50, we provide recommendations as to which pairing-friendly curves to choose to best satisfy a variety of performance and security requirements.read more
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Optimal Pairings
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References
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The MAGMA algebra system I: the user language
TL;DR: MAGMA as mentioned in this paper is a new system for computational algebra, and the MAGMA language can be used to construct constructors for structures, maps, and sets, as well as sets themselves.
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Identity-Based Encryption from the Weil Pairing
Dan Boneh,Matthew K. Franklin +1 more
TL;DR: This work proposes a fully functional identity-based encryption (IBE) scheme based on bilinear maps between groups and gives precise definitions for secure IBE schemes and gives several applications for such systems.
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The Arithmetic of Elliptic Curves
TL;DR: It is shown here how Elliptic Curves over Finite Fields, Local Fields, and Global Fields affect the geometry of the elliptic curves.
Book ChapterDOI
Short Signatures from the Weil Pairing
Dan Boneh,Ben Lynn,Hovav Shacham +2 more
TL;DR: A short signature scheme based on the Computational Diffie-Hellman assumption on certain elliptic and hyperelliptic curves is introduced, designed for systems where signatures are typed in by a human or signatures are sent over a low-bandwidth channel.