20160325, 02:05  #1 
Nov 2014
3^{2} Posts 
Fast modular reduction for primes < 512 bits?
Hi,
I'm working on an implementation of Pollard's Rho for elliptic curves over prime fields. Currently it's using the Barrett Reduction but I'm wondering if there is anything faster for general primes (no special form) in the 128 to 512 bit range? Thanks 
20160325, 15:55  #2  
Tribal Bullet
Oct 2004
5×709 Posts 
Quote:
Otherwise Montgomery multiplication would probably outperform Barrett's method for moduli of these sizes. 

20160327, 00:37  #3 
Nov 2014
3^{2} Posts 
It's actually for any prime, not just the NIST ones :)
I'll look into Montgomery multiplication. The downside is that even the distinguished points would need to be stored in Montgomery form. 
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