Browsing by Author "Louw, Gerard Jacques"

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    Elliptic curve cryptography
    (Stellenbosch : Stellenbosch University, 2016-12) Louw, Gerard Jacques; Breuer, Florian; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences
    ENGLISH ABSTRACT : In this thesis we present a selection of Diffie-Hellman cryptosystems, which were classically formulated using the multiplicative group of a finite field, but which may be generalised to use other group varieties such as elliptic curves. We also describe known attacks on special cases of such cryptosystems, which manifest as solutions to the discrete logarithm problem for group varieties, and the elliptic curve discrete logarithm problem in particular. We pursue a computational approach throughout, with a focus on the development of practical algorithms.