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

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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 www.literka.addr.com/mathcountry/numth/ecm.zip. Definitions and concepts were taken from the internet site "homepage.mac.com/ehgoins/notes/blackwell.pdf".

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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