I want to be able to compute
g^x = g * g * g * ... * g (x times)
where g is in a finite field GF(2^m). Here m is rather large, m = 256, 384, 512, etc. so lookup tables are not the solution. I know that there are really fast algorithms for a similar idea, modpow for Z/nZ (see page 619-620 of HAC).
- What is a fast, non-table based way to compute cycles (i.e. g^x)?
- This is definitely a wishful question but here it comes: Can the idea of montgomery multiplication/exponentiation be 'recycled' to Galois fields? I would like to think so because of the isomorphic properties but I really don't know.
Remark: this is from my post on math.stackoverflow.com I suppose this is the best community to ask this question.