@INCOLLECTION{Cohen-Handbook1,
author = {Roberto M. Avanzi and Tanja Lange},
title = {Introduction to Public-Key Cryptography},
editor = {Henri Cohen and Gerhard Frey},
booktitle = {Handbook of Elliptic and Hyperelliptic Curve Cryptography},
publisher = {Chapman \& Hall/CRC},
pages = {1--15},
year = {2006}
}
@INCOLLECTION{Cohen-Handbook13,
author = {Christophe Douce and Tanja Lange},
title = {Arithmetic of Elliptic Curves},
editor = {Henri Cohen and Gerhard Frey},
booktitle = {Handbook of Elliptic and Hyperelliptic Curve Cryptography},
publisher = {Chapman \& Hall/CRC},
pages = {267--302},
year = {2006}
}
@INCOLLECTION{Cohen-Handbook17,
author = {Reynald Lercier and David Lubicz and Frederik Vercauteren},
title = {Point Counting on Elliptic and Hyperelliptic Curves},
editor = {Henri Cohen and Gerhard Frey},
booktitle = {Handbook of Elliptic and Hyperelliptic Curve Cryptography},
publisher = {Chapman \& Hall/CRC},
pages = {407--453},
year = {2006}
}
@INCOLLECTION{Cohen-Handbook19,
author = {Roberto M. Avanzi},
title = {Generic Algorithms for Computing Discrete Logarithms},
editor = {Henri Cohen and Gerhard Frey},
booktitle = {Handbook of Elliptic and Hyperelliptic Curve Cryptography},
publisher = {Chapman \& Hall/CRC},
pages = {477--494},
year = {2006}
}
@INCOLLECTION{Cohen-Handbook20,
author = {Roberto M. Avanzi and Nicolas Th\'{e}riault},
title = {Index Calculus},
editor = {Henri Cohen and Gerhard Frey},
booktitle = {Handbook of Elliptic and Hyperelliptic Curve Cryptography},
publisher = {Chapman \& Hall/CRC},
pages = {495--509},
year = {2006}
}
@INCOLLECTION{Cohen-Handbook22,
author = {Gerhard Frey and Tanja Lange},
title = {Transfer of Discrete Logarithms},
editor = {Henri Cohen and Gerhard Frey},
booktitle = {Handbook of Elliptic and Hyperelliptic Curve Cryptography},
publisher = {Chapman \& Hall/CRC},
pages = {529--543},
year = {2006}
}
@BOOK{Cohen-Handbook,
author = {Henri Cohen and Gerhard Frey and Roberto Avanzi and Christophe Douce and Tanja Lange and Kim Nguyen and Frederik Vercautern},
title = {Handbook of Elliptic and Hyperelliptic Curve Cryptography},
publisher = {Chapman \& Hall/CRC},
year = {2006}
}
@BOOK{Silverman-Rational,
author = {Joseph H. Silverman and John Tate},
title = {Rational Points on Elliptic Curves},
publisher = {Springer-Verlag},
series = {Undergradute Texts in Mathematics},
year = {1992}
}
@MISC{Vercauteren-SEA,
author = {Frederik Vercauteren},
title = {The {SEA} Algorithm in Characteristic 2},
note = {\url{}}
}
@BOOK{Blake-Elliptic,
author = {Ian Blake and Gadiel Seroussi and Nigel Smart},
title = {Elliptic Curves in Cryptography},
publisher = {Springer-Verlag},
series = {Undergradute Texts in Mathematics},
year = {2006}
}
@ARTICLE{Schoof-Counting,
author = {Ren\'e Schoof},
title = {Counting points on elliptic curves over finite fields},
journal = {Journal de Th\'eorie des Nombres},
year = {1995},
volume = {7},
pages = {219--254}
}
@ARTICLE{Schoof-Elliptic,
author = {Ren\'e Schoof},
title = {Elliptic Curve Over Finite Fields and the Computation of Square Roots mod $p$},
journal = {Mathematics of Computation},
year = {1985},
month = {April},
volume = {44},
number = {170},
pages = {483--495}
}
@BOOK{Silverman-Arithmetic,
author = {Joseph H. Silverman},
title = {The Arithmetic of Elliptic Curves},
publisher = {Springer-Verlag},
series = {Gradute Texts in Mathematics},
year = {1986}
}
@BOOK{Lang-EllipticFunctions,
author = {Serge Lang},
title = {Elliptic Functions},
publisher = {Springer-Verlag},
series = {Gradute Texts in Mathematics},
edition = {2nd},
year = {1987}
}
@ARTICLE{Cassels-Diophantine,
author = {J.W.S. Cassels},
title = {Diophantine Equations with Special Reference to Elliptic Curves},
journal = {Journal of London Mathematical Society},
year = {1966},
volume = {41},
pages = {193--291}
}
@BOOK{Menezes-Handbook,
author = {Alfred J. Menzes and Paul C. van Oorschot and Scott A. Vanstone},
title = {Handbook of Applied Cryptography},
publisher = {CRC Press},
year = {1996}
}
@ARTICLE{Diffie-New,
author = {Whitfield Diffie and Martin E. Hellman},
title = {New Directions in Cryptography},
journal = {IEEE Transactions on Information Theory},
year = {1976},
month = {November},
volume = {IT-22},
number = {6},
pages = {644--654}
}
@MISC{Lopez-Overview,
author = {Julio L\'{o}pez and Ricardo Dahab},
title = {An Overview of Elliptic Curve Cryptography},
howpublished = {Institute of Computing, State University of Campinas},
year = {2000},
month = {May}
}
@TECHREPORT{NIST-Recommendation,
author = {Elaine Barker and William Barker and William Burr and William Polk and Miles Smid},
title = {Recommendation for Key Management---Part 1: General (Revised)},
institution = {National Institute of Standards and Technology},
number = {NIST Special Publication 800-57},
year = {2006},
month = {May}
}
@MISC{Lercier-Counting,
author = {Reynald Lercier and Fran\c{c}ois Morain},
title = {Counting Points on Elliptic Curves over $F_{p^n}$ Using Couveignes's algorithm},
year = {1996},
note = {\url{}}
}
@BOOK{Lang-EllipticCurves,
author = {Serge Lang},
title = {Elliptic Curves: Diophantine Analysis},
publisher = {Springer-Verlag},
series = {A Series of Comprehensive Studies in Mathematics 231},
year = {1978}
}
@BOOK{Silverman-Advanced,
author = {Joseph H. Silverman},
title = {Advanced Topics in the Arithmetic of Elliptic Curves},
publisher = {Springer-Verlag},
series = {Gradute Texts in Mathematics},
year = {1994}
}
@PHDTHESIS{Muller-Algorithmus,
author = {Volker M\"{u}ller},
title = {Ein Algorithmus zur Bestimmung der Punktanzahl elliptischer Kurven \"{u}ber endlichen K\"{o}rpern der Charakteristik gr\"{o}\ss er drei},
school = {Saarlandes University, Saarbr\"{u}cken},
year = {1995}
}
@TECHREPORT{ANSI-Public,
author = {ANSI},
title = {Public Key Cryptography for the Financial Services Industry: The Elliptic Curve Digital Signature Algorithm ({ECDSA})},
institution = {American National Standards Institute},
number = {ANSI X9.62},
year = {2005}
}
@MISC{Stein-Module,
author = {William Stein and David Kohel and Iftikhar Burhanuddin},
title = {Module of Supersingular Points},
year = {2006},
note = {\url{}}
}