Faculty of Informatics, University of Debrecen, May 2007
Contents
Elliptic curves over Q: 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
cryptography.
Other applications of elliptic curves: Lenstra's elliptic curve factoring
method. Elliptic curve primality proving algorithm.
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.