fastgf2m.txt

With the introduction of Intel 32nm i5/i7 processors, there
is support for a "carry-less" multiplication, also known as
"binary polynomial" multiplication. This support is in the form 
of the new 64-bit PCLMULQDQ instruction.

In fact such an instruction is also supported by some Sun and
Mips processors.

Support for this operation gives a big boost to the performance 
of any method that uses arithmetic over GF(2^m), in particular
elliptic curve cryptography, and pairing-based crypto using 
supersingular curves over GF(2^m).

To exploit the PCLMULQDQ instruction, using the Microsoft C
compiler, use the macro file clmul.mcs with the mex utility
to create the module mrcomba2.c, and define MR_COMBA2 in mirdef.h 
to the number of words required to represent m. Then link this 
module into the MIRACL library, and to your application.

For example if implementing standard elliptic curves over GF(2^283)
on a 64-bit PC, using MS C tools, then

c:\miracl>>mex 5 clmul mrcomba2

to create mrcomba2.c, and include into mirdef.h

#define MR_COMBA2 5

Then build a MIRACL library to include mrcomba2.c, and build and
link your application as normal, for an impressive speed boost.