I need to solve the usual cubic equation x^3 + ax^2 + bx + c = 0 over a finite field GF(2^n). This is to avoid doing a brute-force Chien search in a BCH decoder.

I read in a paper about an easy way to reduce the equation to z^3 + z + k = 0 where k = (a * b + c) / (a^2 + b) ^ (3/2). Then a lookup table can be used for all the values of k. However as far as I can tell this approach will not work when (a^2 + b) happens to not have a square root in the field. An example for GF(2^5) would be x^3 + 08*x + 1a = 0.

Can someone help?

Regards,  
-Dimitri