Re: symbol catenation and montgomery

[phr-2000]

   I measured a^b mod c for random 1024-bit numbers a, b, c:

     mpz_powm (1024)    16.375ms

That's pretty good!

   I then run "openssl speed 1024" on the same machine.  I don't know how
   to interpret these numbers:

     rsa 1024 bits   0.0066s   0.0004s    152.6   2660.1

The number of interest is 152.6.  It means openssl did 152.6 1024-bit
RSA decryptions (each consisting of two 512-bit modexps and a CRT
recombination) per second.  A 1024-bit modexp is maybe 3x as expensive
as a 1024 bit RSA decryption because of the CRT.  So that means
OpenSSL should do around 50 1024-bit modexps/sec or about 20 msec
each, which means GMP is actually beating OpenSSL.  I'm pleasantly
surprised.

Can I ask what cpu you did that test on?

You could also try "openssl speed rsa2048" which does 2048-bit RSA
operations (two 1024-bit modexps plus the recombination).  As the
operands get bigger the modexps should dominate the calculation more.