Details of Grant 

EPSRC Reference:	GR/L43275/01
Title:	DISCRETE LOGARITHMS IN ELLIPTIC CURVE GROUPS
Principal Investigator:	Piper, Professor F
Other Investigators:	Wild, Professor P Murphy, Professor S
Researcher Co-Investigators:
Project Partners:
Department:	Mathematics
Organisation:	Royal Holloway, Univ of London
Scheme:	Standard Research (Pre-FEC)
Starts:	21 July 1997	Ends:	20 October 1998	Value (£):	3,500
EPSRC Research Topic Classifications:	Logic & Combinatorics
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
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Summary on Grant Application Form
The discrete logarithm problem in the multiplicative group of a finite field has been studied extensively and algorithms that solve this problem in subexponential time have been given. It is believed that the discrete logarithm problem in elliptic curve groups is harder. For one class of curves, the super-singular elliptic curves, however, the problem can be reduced to that in an appropriate finite field. The main objective of this project is to determine whether such a reduction exists for non-supersingular elliptic curves and hyperelliptic curves. The project will undertake a determination of a classification of curves according to isomorphism classes of their associated groups. This will lead to an investigation of the implications of the Frey-Ruck reduction to the discrete logarithm problem on hperelliptic curves.
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