Why doesn't the GCM spec use a more efficient multiplication algorithm? NIST SP 800-38D § 6.3 Multiplication Operation on Blocks describes a multiplication algorithm that, in my testing, appears to be a good amount slower then algorithm 2.40 (arbitrary reduction polynomials) in the Guide to Elliptic Curve Cryptography.

My question is...why? Does the algorithm described in NIST SP 800-38D provide better protection against timing attacks?
My question is... why?


There are a number of different algorithms that perform $GF(2^{128})$ multiplication, all with different trade-offs (speed on specific platforms, program size, memory usage, complexity, side channel resistance, etc).  NIST doesn't care which one you use, as long as you get the expected result at the end.

As for why NIST decided to put that specific algorithm as an example in the spec, well, I didn't write the spec, so I can't be certain.  My guess is that they decided on the goals of simplicity and clarity, and that algorithm was the best they could find that would meet those goals (whether it is actually simpler or clearer than algorithm 2.40 is, of course, debatable...)