@@ -304,10 +304,12 @@ We consider the following functions on the nodes of trees in $MT_{\lambda}$:
Problem: include the $l$-trick somehow (two trees?)
#### Another pathological case
#### Another pathological cases
The DCP problem for $f=x_1+x_2$ is easy on curves $E:y^2=x^3+ax$ over $\mathbb{F}_p$ for $p=1\pmod 4$. For such curves the map $(x,y)\mapsto(-x,iy)$, for $i=\sqrt{-1}$, is an endomorphism. The characteristic equation is $x^2+1=0 \pmod m$ where $m$ is the order of $(x_1,y_1)$ (found out experimentally). Here we are not considering the group order as the modulus as the curve never has a prime order (Why?). Anyway, if $k$ exists then it must be the root of the equation modulo some divisor of the group order.
For $f=x_1+x_2$ and curves $E:y^2=x^3+ax$ over $\mathbb{F}_p$ with $p=3\pmod 4$, the DCP doesn't have a solution as $y_1^2=-y_2^2$ but $-1$ is not a quadratic residue.
