How to Use Elliptic Curve Cryptography to Find Inverses and Points on the Curve?

[vokoyo]

May I know how to solve the equation as below:

(1) y² = x³ + x + 1 mod 17

Finding Inverses
Finding Points on the Curve

(2) y² = x³ + 3x + 1 mod 13

Finding Inverses
Finding Points on the Curve

 

[I like Serena]

May I know how to solve the equation as below:

(1) y² = x³ + x + 1 mod 17

Finding Inverses
Finding Points on the Curve

Hi vokoyo,

How about filling in $x=0, ..., 16$.
Those are all the relevant possibilities for $x$.
After that the same results will appear periodically.

That way we find all the points on the curve.
And from the results we can also find all inverses, can't we?

 

[vokoyo]

Thank you very much for your advice and suggestion

Please show me your sample solution draft
so that I can improve my calculus skills

I fact I would like to draw the curve line or point by point