This commit essentially rewrites all of the primitives needed to perform
the arithmetic for ECDSA signature verification of secp256k1 signatures to
significantly speed it up. Benchmarking has shown signature verification
is roughly 10 times faster with this commit over the previous.
In particular, it introduces a new field value which is used to perform the
modular field arithmetic using fixed-precision operations specifically
tailored for the secp256k1 prime. The field also takes advantage of
special properties of the prime for significantly faster modular reduction
than is available through generic methods.
In addition, the curve point addition and doubling have been optimized
minimize the number of field multiplications in favor field squarings
since they are quite a bit faster. They routines also now look for
certain assumptions such as z values of 1 or equivalent z values which
can be used to further reduce the number of multiplicaitons needed when
possible.
Note there are still quite a few more optimizations that could be done
such as using precomputation for ScalarBaseMult, making use of the
secp256k1 endomorphism, and using windowed NAF, however this work already
offers significant performance improvements.
For example, testing 10000 random signature verifications resulted in:
New btcec took 15.9821565s
Old btcec took 2m34.1016716s
Closesconformal/btcd#26.
