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Old 2005-08-25, 17:20   #6
R.D. Silverman
 
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Nov 2003

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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.

Your discussion of solving quadratics modulo a composite is irrelevant to
what you first asked.
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