Constructing Elliptic Curves with Prescribed Embedding Degrees

By Paulo L. Barreto, Ben Lynn, Michael Scott. International Conference on Security and Cryptography for Networks, 2002

370 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Information Systems

View Paper: https://www.semanticscholar.org/paper/5f431d096f2db3ec1331fabf3553ca35c78eb9c0

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Citations in the corpus

Short Signatures from the Weil Pairing (2001, background): “Several constructions [5, 22, 14] show how to build elliptic curves E such that E(Fq) has a given security multiplier α.”
A One Round Protocol for Tripartite Diffie–Hellman (2000, background): “Allowing for slower key generation, larger values of k are possible (see [5] and [10]).”
Pairing-Friendly Elliptic Curves of Prime Order (2005, methodology): “Several methods have been proposed to construct curves with arbitrary k, including an algorithm credited to Cocks and Pinch [4, chapter 9] and related methods due to Barreto, Lynn, and Scott [1] and to Dupont, Enge, and Morain [9].”
Scalable Zero Knowledge Via Cycles of Elliptic Curves (2014, methodology): “In short, after breaking a pairing into its twomain parts, the Miller loop and the final exponentiation, and implementing both (using optimal pairings [110] and other methods [57,63,91]), they apply precomputation techniques to the verification key [27,53,95] and share subcomputations of the Miller ”
A Taxonomy of Pairing-Friendly Elliptic Curves (2010, methodology): “There are two principal strategies for constructing complete families, one due to Scott and Barreto [81] and the other due originally to Barreto, Lynn, and Scott [5], and in its fullest generality to Brezing and Weng [17].”
On Prime-Order Elliptic Curves with Embedding Degrees k = 3, 4, and 6 (2008, neutral): “Keywords: Elliptic curves, pairing-based cryptosystems, embedding degree, MNT curves.”
The Eta Pairing Revisited (2006, methodology): “See [3], [10] for methods to construct curves for pairing based systems with and such a small value of .”
Certificateless Public Key Cryptography (2003, neutral): “We refer to [2, 3, 6, 7, 9, 15, 17, 18] for a more comprehensive description of how these groups, pairings and other parameters should be selected in practice for efficiency and security.”