Low-level logical functions?

[Barukh Ziv]

Dear Paul,

Thank you very much for the link to the library - I will try to use it. If
you permit, several questions:

1. Is there a documentation describing the interfaces?
2. Is there any interface between this library and GMP?

Sincerely,
B/
On Sat, Nov 7, 2009 at 10:57 PM, Paul Zimmermann
<Paul.Zimmermann at loria.fr>wrote:

>       Dear Barukh,
>
> > Date: Sat, 7 Nov 2009 19:58:39 +0200
> > From: Barukh Ziv <barukh.ziv at gmail.com>
>  >
> > Sincere all,
> >
> > Thank you very much for the prompt reply.
> >
> > If I understand correctly, internal functions cannot be called from
> outside
> > code?
> > Is there any planned date for v4.4 release?
> >
> > If you permit, I would like to ask another question: it looks like it may
> be
> > beneficial to have carry-less arithmetic over integers in GMP. An
> important
> > application of this is arithmetic over GF(2^m) (so called binary fields),
> > which are important in Elliptic Curve Cryptography (ECC).
> >
> > It is true that cary-less addition/subtraction may be efficiently
> > implemented by means of logical XOR. It's not the case for the
> > multiplicaition, though. Using hardware support, this may be greatly
> > optimized. Here's the message I received from Alfred Menezes, one of
> leading
> > specialists in ECC:
> > "Intel announced in 2008 that their future processors would be equipped
> with
> > a "PCLMULQDQ" instruction for fast "carryless" multiplication of 64-bit
> > binary polynomials. This instruction is very much anticipated because it
> > will greatly speed up computations on elliptic curves over binary fields
> > (including the so-called "Koblitz curves"). At present, elliptic curves
> over
> > prime fields have the advantage because of the fast integer
> multiplication
> > instructions available on Intel machines."
> >
> > As far as I know, a processor supporting the above instruction, is
> already
> > in the market.
> >
> > Sincerely,
> > Barukh.
>
> you might be interested by the GF2X library, which implements
> multiplication
> over GF(2)[x].
>
> Paul Zimmermann
>
> http://wwwmaths.anu.edu.au/~brent/gf2x.html
>
>