History of Elliptic curve

Difference (from prior major revision) (author diff)

Changed: 5c5

If we add a point at infinity, an elliptic curve forms an abelian group (as long as a certain constraint is met on the values of a and b, which ensures that the polynomial x³ + ax + b does not have a double zero). Each point on the curve is an element of the group, and a geometrical construction allows us to define addition of points in a consistent manner.

If we add a point at infinity, an elliptic curve forms an abelian group (as long as a certain constraint is met on the values of a and b, which ensures that the polynomial x³ + ax + b does not have a multiple zero and the curve does not have a singularity). Each point on the curve is an element of the group, and a geometrical construction allows us to define addition of points in a consistent manner.

	Revision 9 . . December 9, 2001 7:21 am by AxelBoldt
	Revision 8 . . December 9, 2001 7:20 am by AxelBoldt [link finite field]
	Revision 7 . . December 9, 2001 7:20 am by AxelBoldt [link finite field]
	Revision 6 . . December 9, 2001 6:13 am by Taw [see: ecc]
	Revision 5 . . (edit) December 9, 2001 5:46 am by The Anome [mentioned finite fields]
	Revision 4 . . December 9, 2001 5:46 am by The Anome [Mentioned use in cryptography]
	Revision 3 . . December 9, 2001 5:32 am by AxelBoldt
	Revision 2 . . (edit) December 9, 2001 5:27 am by Stuart Presnell [Formatting the superscript indices]
	Revision 1 . . December 9, 2001 5:23 am by Stuart Presnell [Very sketchy beginnings]