Algorithmic Aspects of Elliptic Curves
Faculty of Informatics, University of Debrecen, May 2007
Elliptic curves over Group law. Computing Mordell-Weil group.
Construction of curves with high rank.
Elliptic curves over finite fields: Implementation of operations.
Algorithms for determining the group order.
Elliptic Curve Cryptography: Public key cryptography based on discrete
logarithm problem. Menezes-Vanstone and ECDSA cryptosystems.
Elliptic curve discrete logarithm problem. Comparing ECC with other types of
Other applications of elliptic curves: Lenstra's elliptic curve factoring
method. Elliptic curve primality proving algorithm.
I. Blake, G. Seroussi, N. Smart: , Cambridge University Press, Cambridge, 1999.
Elliptic Curves in Cryptography
McGill University, 1999.
Elliptic Curve Handbook
J. E. Cremona: ,
Cambridge University Press, Cambridge, 1997.
Algorithms for Modular Elliptic Curves
D. Hankerson, A. Menezes, S. Vanstone:
Springer-Verlag, New York, 2004.
Guide to Elliptic Curve Cryptography
A. W. Knapp: ,
Princeton University Press, Princeton, 1992.
N. Koblitz: A Course in Number Theory and Cryptography,
Springer-Verlag, Berlin, 1994.
N. Koblitz, A. Menezes, S. A. Vanstone: , Designs, Codes and Cryptography
The State of Elliptic Curve Cryptography 19 (2000), pp. 173-193.
J. S. Milne: ,
BookSurge Publishers, 2006.
M. Rosing: ,
Manning, Greenwich, 1999.
Implementing Elliptic Curve Cryptography
S. Schmitt, H.G. Zimmer: Elliptic Curves. A Computational
Approach, de Gruyter, Berlin, 2003.
J. H. Silverman: Elliptic curves and cryptography,
in: P. Garrett, D. Lieman (Eds.): Public-Key Cryptography,
American Mathematical Society, Providence, 2005, pp.91-112.
J. H. Silverman, J. Tate: Rational Points on Elliptic Curves, Springer-Verlag, Berlin, 1992.
L.C. Washington: , CRC Press, Boca Raton, 2003.
Elliptic Curves: Number Theory and Cryptography
Some useful links
Web pages of some courses on elliptic curves
Elliptic Curves (Edray Goins)
Elliptic Curves (Jim Milne)
Elliptic Curves (Miles Reid)
Elliptic Curves (Helena Verrill)
Elliptic Curves and Applications (Andrej Dujella)
Elliptic Curves and Cryptography (Alan Silvester)
Elliptische Kurven (Franz Lemmermeyer)
Introduction to elliptic curves (Ian Kiming)
Number Theory of Cubic Curves (Jaap Top)
Selected Topics in Number Theory (Jerrold Tunnell)
Vorlesung uber Elliptische Kurven und Kryptographie
Andrej Dujella home page