[1 1; 1 0]^n = [Fn+1 Fn; Fn Fn-1] So you could rewrite n as a sum of m powers of 2 (just write it in binary), then for each "1" there, send it to a separate pr

[1 1; 1 0]^n = [Fn+1 Fn; Fn Fn-1] So you could rewrite n as a sum of m powers of 2 (just write it in binary), then for each "1" there, send it to a separate processor to compute [1 1; 1 0]^k using exponentiation by squaring (where k is the corresponding power of 2). Your reduce step multiplies the resulting matrices together. Note: this is just the first thing that comes to mind, I have no idea if this is what you were thinking of, or if it's even a good idea.