I have the following set of equations:
$M_1, M_2, x_1, y_1, x_2, y_2,$ are known and they are chosen from a $GF(2^m)$. I want to find $x_0,y_0$
Does the previous set of equations is solvable?
If I have the following set of equations:
where $x_0,y_0 x_1,y_1$ are the unknown GF elements.
As Dilip Sarwate clarified the set of equations is constructed by someone who " chose three distinct x0,x1,x2, as well as y0,y1,y2, then computed M1, M2, and finally revealed $M_1,M_2,x_1,y_1,x_2,y_2$ but not $x_0,y_0$ to us" i.e. it is known that the system has solution.
My question was: Can I recover the $x_0, y_0$ or in the second set of equations can I recover $x_0, x_1, y_0, y_1$ and generally in nonlinear sets to recover the respective $x_i, y_i$ by the provided info, on a GF? and the main point of my question: Does the fact that the set of equations is defined on a Galois Field impose any difficulties to find its solution?
I was not sure that it is possible to compute the solution of the problem with the aforementioned parameters on a Galois Field.
As Dilip Sarwate stated in his answer the solution of the previous problem can be recovered for linear and nonlinear equations.