RFR(L): 8069539: RSA acceleration

[Andrew Haley]

Here is a prototype of what I propose:

http://cr.openjdk.java.net/~aph/rsa-1/

It is a JNI version of the fast algorithm I think we should use for
RSA.  It doesn't use any intrinsics.  But with it, RSA is already twice
as fast as the code we have now for 1024-bit keys, and almost three
times as fast for 2048-bit keys!

This code (montgomery_multiply) is designed to be as easy as I can
possibly make it to translate into a hand-coded intrinsic.  It will
then offer better performance still, with the JNI overhead gone and
with some carefully hand-tweaked memory accesses.  It has a very
regular structure which should make it fairly easy to turn into a
software pipeline with overlapped fetching and multiplication,
although this will perhaps be difficult on register-starved machines
like the x86.

The JNI version can still be used for those machines where people
don't yet want to write a hand-coded intrinsic.

I haven't yet done anything about Montgomery squaring: it's
asymptotically 25% faster than Montgomery multiplication.

I have only written it for x86_64.  Systems without a 64-bit multiply
won't benefit very much from this idea, but they are pretty much
legacy anyway: I want to concentrate on 64-bit systems.

So, shall we go with this?  I don't think you will find any faster way
to do it.

Andrew.