Galois field multiplicative inverse

[serhannn]

Hi,
How can I take the multiplicative inverse of a Galois field element? Actually, I achieved this by taking the natural logarithm in Matlab (log), but I didn't quite get the logic behind it. Why can I find it by simply taking the logarithm or am I missing something?

Thanks a lot.

 

[permute]

I don't follow.

if log(b) = k, then b^-1 = b^(q-k). This is because b*b^-1 = b^0 = b^q = 1.

This doesn't seem like it would work. Are you sure you aren't taking the log, computing the correct exponent, then finding the correct element in a second step?