Constructing Elliptic Curves with Prescribed Embedding Degrees
 Paulo S. L. M. Barreto,
 Ben Lynn,
 Michael Scott
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Abstract
Pairingbased cryptosystems depend on the existence of groups where the Decision DiffieHellman problem is easy to solve, but the Computational DiffieHellman problem is hard. Such is the case of elliptic curve groups whose embedding degree is large enough to maintain a good security level, but small enough for arithmetic operations to be feasible. However, the embedding degree for most elliptic curves is enormous, and the few previously known suitable elliptic curves have embedding degree k ≤ 6. In this paper, we examine criteria for curves with larger k that generalize prior work by Miyaji et al. based on the properties of cyclotomic polynomials, and propose efficient representations for the underlying algebraic structures.
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 Title
 Constructing Elliptic Curves with Prescribed Embedding Degrees
 Book Title
 Security in Communication Networks
 Book Subtitle
 Third International Conference, SCN 2002 Amalfi, Italy, September 11–13, 2002 Revised Papers
 Pages
 pp 257267
 Copyright
 2003
 DOI
 10.1007/3540364137_19
 Print ISBN
 9783540004202
 Online ISBN
 9783540364139
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 2576
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
 Additional Links
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 Editors

 Stelvio Cimato ^{(4)}
 Giuseppe Persiano ^{(4)}
 Clemente Galdi ^{(5)}
 Editor Affiliations

 4. Dipartimento di Informatica ed Applicazioni, Università di Salerno
 5. Dept. of Computer Engineering and Informatics, Computer Technology Institute and University of Patras
 Authors

 Paulo S. L. M. Barreto ^{(6)}
 Ben Lynn ^{(7)}
 Michael Scott ^{(8)}
 Author Affiliations

 6. Laboratório de Arquitetura e Redes de Computadores (LARC) Escola Politécnica, Universidade de São Paulo, Brazil
 7. Computer Science Department, Stanford University, USA
 8. School of Computer Applications, Dublin City University, Dublin 9, Ballymun, Ireland
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