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Old 2012-04-29, 23:54   #1
literka's Avatar
Mar 2010

110000002 Posts
Default ECM program for beginners.

Program of Literka "Elliptic Curve Method" is mainly for illustration of addition of rational points on an elliptic curve. It can be downloaded from Definitions and concepts were taken from the internet site "".

Use menu item New --> New curve to define a new curve. This curve must be of the form y^2=x^3+a*x+b (a,b - rational numbers), as it is defined in the quoted site. A graph of this curve should appear.

Find some rational points on this curve and add them to a curve using menu item New --> New point. They should appear on a screen. List of points, together with their coordinates will be seen after pressing menu item Points.

You can find sums of these points using the menu item New --> New equation. For example, assume that points A and B were defined. Adding the equation

C = A + B

we define a new point C on a curve, being the sum of A and B. As it was described before, we can see coordinates of C. Moreover, computer shows how C was obtained (as it was described on the quoted internet site). Hence the defined straight line will be seen, as well as its intersection with a curve. However, points with large coordinates will not be seen.

Program is not completely verified and was written for personal use only.

Last fiddled with by literka on 2012-04-29 at 23:59
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