Low-level logical functions?

[Barukh Ziv]

Dear Paul,

Here's another question I've got: In the README file of the distribution, I
read:

Caution:
========
gcc versions 4.3.0 and 4.3.1 have a bug which affects gf2x in a an
unpredictable way. It is recommended to upgrade to at least 4.3.2.

Do you know if this bug exists also in version 4.2.2? There are certain
problems with compiling GMP on versions 4.3.x.

Regards,
Barukh.
On Sun, Nov 8, 2009 at 12:08 PM, Barukh Ziv <barukh.ziv at gmail.com> wrote:

>  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
>>
>>
>