0

Is there any way to plot xy diagram of points of elliptic curve (such as NIST p-192,p-224,p-256...) over finite field? I tried with p-256, but it has very big number of p thus when I use for loop it takes huge amount of time to go through the loop. Is there any other way to find all points of the curve such as y^2 = x^3 -3*x + 0xFFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F and plot in efficient way?

Alokin
  • 9
  • 2
  • 1
    You don't seem to appreciate how big these numbers are. No, there is no way to "plot" all the points because there are too many. Also, the x-y plot of an elliptic curve over a finite field will probably not reveal anything interesting as the points appear to be scattered randomly. It won't produce a nice visual like an elliptic curve over the reals. – President James K. Polk May 07 '22 at 12:56
  • So the only way to represent such a curve is over a real number, right? – Alokin May 07 '22 at 13:50
  • The wiki article for [elliptic curves](https://en.wikipedia.org/wiki/Elliptic_curve) includes images of the curves for real number and the scattered points for finite fields. Note the upper and lower halves of the xy plot for finite field are mirrors of each other. – rcgldr May 09 '22 at 00:57
  • `find all points or count number of points` - There is a related question and answer [here](https://crypto.stackexchange.com/q/27904). p-{192, 224, 256} => 2^{192, 224, 256). Let q = 2^{192, 224, or 256}, The range of the number of points is huge: q + 1 +/- (2 * sqrt(q)) . – rcgldr May 12 '22 at 02:48

0 Answers0