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Search: Posts Made By: bonju
Forum: Factoring 2005-08-26, 13:29
Replies: 9
Views: 1,575
Posted By bonju
Sure they are rare in Z, but they come at very...

Sure they are rare in Z, but they come at very reasonable price in Zn *if they can be used at all*.
Forum: Factoring 2005-08-26, 06:45
Replies: 9
Views: 1,575
Posted By bonju
I may be wrong, but if one finds "pseudo smooth"...

I may be wrong, but if one finds "pseudo smooth" relation, one may add (the ideal) "u" to the (algebraic) factor base. Since it is with even exponent, it seems that no additional algebraic relation...
Forum: Factoring 2005-08-26, 06:10
Replies: 9
Views: 1,575
Posted By bonju
For the sake of the flame, let's call...

For the sake of the flame, let's call p[k1]^e1*p[k2]^e2*p[ki]^ki*u^2, p[k] - prime in the prime base,
"pseudo smooth".

If you are sieving with quadratic and nfs, will you throw away "pseudo...
Forum: Factoring 2005-08-25, 16:05
Replies: 9
Views: 1,575
Posted By bonju
I believe that squares in the norm do not...

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.
...
Forum: Factoring 2005-08-25, 13:34
Replies: 9
Views: 1,575
Posted By bonju
I know they are smaller than N. Is of any...

I know they are smaller than N.

Is of any use this in some kind of modification of nfs:
1. f(x,y) > N
2. f(x,y) mod N is smooth
3. x-m*y mod N is smooth
(3 seems clear).
Forum: Factoring 2005-08-25, 08:16
Replies: 9
Views: 1,575
Posted By bonju
NFS and smooth norm MOD N ?

Is it possible the NFS to take advantage of ("pseudo") relations in which the
norm is smooth *MOD N*?

So if one is looking for smooth f(x,y)=sum(a[i]*x^i*y^(d-i)),
does smooth
f(x,y) mod n ...
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