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Elliptic Curves

CSL

Hello Everyone,

The equation for an elliptic curve E is y^2 = x^3+ax+b mod n.
E is also equal to a set of points (x,y) such that x is <= n-1 and y can be found by plugging x into the equation mod n and solving that discrete log problem for y. Those points, what are they? Are they all of the points that make up the graph, meaning the domain consists of all integers <= n-1 and the range is the values gotten when plugging x in?

2 Replies

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Nermin Huskic13y ago
All those points make graph. I don't know for sure what really are you looking. explain better question. You can use Pari gp to find points on eliptic curves.
See here how they look like. http://web.math.pmf.unizg.hr/~duje/ecc/elipdef.html
I am sorry because that is article on my language, But translate it
Vulpes14y ago
I don't know much about elliptic curves but, on the face of it, if 'a', 'b' and 'n' are constants, then you can generate a series of points by iterating through all possible values of 'x' (0 <= x <= n-1) and calculating the corresponding value of 'y'.

Of course, if the RHS gives a positive number, then 'y' will have both a positive and a negative solution.