# What should I change in my implementation to pass from a curve $y^2=x^3+1$ to $y^2=x^3+x$

I tried to change my implementation of pairing in curves $y^2 = x^3 + 1$ to use curves of the type $y^2 = x^3 + x$ but it didn't work.

I thought the only thing I had to change in my code was the irreducible polynomial and the transformation of points for the pairing. So I changed my polynomial from $x^2 + x + 1$ to $x^2 + 1$, I kept the root $\xi = x$ and I changed my mapping from $(x,y) \rightarrow (\xi x,y)$ to $(x,y) \rightarrow (-x,iy)$ where the $i$ is my $x$. Was I wrong somewhere or was there something other to do?

• What finite field $\mathbb{F}_p$ did you use? – Youssef El Housni Nov 30 '18 at 10:11