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Old 2015-01-19, 01:41   #1
paul0
 
Sep 2011

3×19 Posts
Default NFS: Sieving the norm over ideals vs. integers

Hello, me again lol.

In Briggs paper, I am told to find prime ideals (r,p) such that f(r) = 0 mod p, and each prime ideal is "responsible" for dividing the norm, that is, each prime ideal has an entry on the matrix. Currently, my implementation instead just uses primes in Z to sieve the norm, so the norms are smooth over Z primes, and each prime has an entry on the matrix.

Is there a difference between two approaches? Some NFS papers say that I'm supposed to look for smooth norms, others say it has be smooth over prime ideals. Is the splitting of primes to different prime ideals just another technique to keep the sieved values smaller (since one prime is used multiple times), or will it break the algorithm if this isn't done?

Last fiddled with by paul0 on 2015-01-19 at 01:42
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