regarding these collaborative, "open" factorizations and cracking projects: I have been wondering about malicious hackers getting into these pools. would it be possible for them to contribute false data that screws up the end results? or are such anomalies easily discarded or disregarded by the final processes? there is a reduction step in the NFS (number field sieve, technique used to factor large numbers) in which all the collected data is mashed. how sensitive is this process to spurious data? i.e. if there was a little bit of bad data in its computation, does it completely screw it up, or is it robust and resistant to this kind of problem? it seems to me that in many cases, these collaborative projects virtually cannot check the validity of the supplied data without repeating the computation effort, although there may be good tests that tend to screen out "most" bad data. future implementors of these programs might amuse themselves with trying to create such safeguards or anticipate such "attacks" which are pretty significant the more the processes become distributed.