Use Non-Adjacent Form (NAF) of large numbers to reduce ScalarMult computation times.
Preliminary results indicate around a 8-9% speed improvement according to BenchmarkScalarMult.
The algorithm used is 3.77 from Guide to Elliptical Curve Crytography by Hankerson, et al.
This closes#3
This implements a speedup to ScalarMult using the endomorphism available to secp256k1.
Note the constants lambda, beta, a1, b1, a2 and b2 are from here:
https://bitcointalk.org/index.php?topic=3238.0
Preliminary tests indicate a speedup of between 17%-20% (BenchScalarMult).
More speedup can probably be achieved once splitK uses something more like what fieldVal uses. Unfortunately, the prime for this math is the order of G (N), not P.
Note the NAF optimization was specifically not done as that's the purview of another issue.
Changed both ScalarMult and ScalarBaseMult to take advantage of curve.N to reduce k.
This results in a 80% speedup to large values of k for ScalarBaseMult.
Note the new test BenchmarkScalarBaseMultLarge is how that speedup number can
be checked.
This closes#1
Code uses a windowing/precomputing strategy to minimize ECC math.
Every 8-bit window of the 256 bits that compose a possible scalar multiple has a complete map that's pre-computed.
The precomputed data is in secp256k1.go and the generator for that file is in gensecp256k1.go
Also fixed a spelling error in a benchmark test.
Results so far seem to indicate the time taken is about 35% of what it was before.
Closes#2
