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Finding a generator of an elliptic curve effectively with huge numbers

ae flag

In cryptography I am facing the issue to find a generator of some elliptic curve given only the curve over given field and number of elements that the curve has.

The numbers used are enormous so I am struggling to implement any offered scenario how to find generator of an elliptic curve here in stackexchange. If anyone can help I would be thankful.

Maarten Bodewes avatar
in flag
What's the background of this? If the field is known then my first point of action was to try and see if it matches a known/named curve.
Daniel S avatar
ru flag
HINT: If you find a point on the curve, there's a pretty good chance it's a generator. How would you find a point? How would you check if it's a generator?
jakarta2000 avatar
ae flag
@MaartenBodewes there is no background this is the assignment to do it with Python code.
jakarta2000 avatar
ae flag
@DanielS but the number of points on a curve is x10^70+ so I think that would not be good approach. I know general rule that when the order of an elliptic curve is m, a point P is a generator if, and only if for all divisors d of m , dP ≠ 0 and mP = 0
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