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 xm*y=3

"I believe that squares in the norm do not diminish smoothness (modulo algebraic stuff and terminology)."
Nonsequitur. 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 xm*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.
Your discussion of solving quadratics modulo a composite is irrelevant to
what you first asked.