Thread: NFS and smooth norm MOD N ? View Single Post
2005-08-25, 17:20   #6
R.D. Silverman

Nov 2003

22·5·373 Posts

Quote:
 Originally Posted by bonju I believe that squares in the norm do not diminish smoothness (modulo algebraic stuff and terminology). Schnorr and Pollard gave efficient solution to bivariate quadratics modulo composite. solve a*t^2+b*t+c=3*v^2 for t,v let t=x/y. solve x-m*y=3
"I believe that squares in the norm do not diminish smoothness (modulo algebraic stuff and terminology)."

Non-sequitur. Where, in any of my prior response did I discuss "squares
in the norm". And "diminish smoothness" is meaningless gibberish.

We are discussing the SIZE of the norms taken mod N. For your "scheme"
to work, BOTH f(x,y) and x-m*y taken mod N need to be sufficiently
small so there is a reasonable change that they will be smooth. Furthermore,
to have any advantage over existing methods, the norms would need to
be *smaller* than what we can obtain currently.

I showed that for f(x,y) mod N to be small, that x,y needed to be near
or slightly larger than N^1/d. However, when this happens x - b*y
becomes much larger (near N^2/d instead of N^1/d) than we obtain
currently.