Computing A^x (mod n)

Décio Luiz Gazzoni Filho decio at
Sat Oct 2 19:42:31 CEST 2004

On Saturday 02 October 2004 13:57, Philip Lee wrote:
> I'm just wondering the algorithm behind mpz_powm().  It can't be doing
> the calculation (mod n) inside whatever loop it's running, because if
> I take a a 572-bit number and raise it to a 576-bit number modulo a
> 576-bit number, the program will terminate. I'm guessing it is doing
> the exponential junk first and then just taking the modulus right?
> Because this would cause an extreme overflow in such a case as mine.
> (As you can tell, I'm doing some RSA stuff ).
> So my question is, "if the mpz_powm() function isn't doing a running
> calculation (mod n ), why is it not?" As I said, this would cause
> overflows which would be prevented if it was instead doing a running
> calculation (mod n). Anyways, just wondering.

mpz_powm() does reduce modulo n after each multiplication/squaring. I speak 
from experience, but it's also mentioned in the manual (though not 

If your program is crashing, it's because there's something wrong with your 


PS: it's almost insulting to suggest that the GMP guys would have implemented 
modular exponentiation without reduction after each step. Better put your 
asbestos suit on.
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