From: thug@phantom.com (Murdering Thug) Since none of us have ever been inside the NSA, we cannot underestimate their power and resources. For all we know they may have 500 Intel Delta supercomputers linked together, each having 65,536 i860-XP/50mhz chips. We really don't know what kind of iron they possess. Thus we can't assume that they can't factor extremely large numbers easily.

Mr. Thug doesn't seem to understand the issue here. Your fear should be that the NSA knows something about number theory we don't, not that they possess a huge number of supercomputers. Consider that we believe the factoring problem to be exponential in the number of digits. That means that doubling the number of digits doesn't double the size of the problem -- it makes it far, far, far worse. Indeed, I suspect that it could be shown that using a key of only a few thousand digits, barring a change in factoring algorithm there would be no way to factor the number in the lifetime of the universe even were all the matter and energy in the universe given over to the factoring problem. There are problems that are known to be that size, by the way -- such as trying to do a complete search on the game tree for chess. So, if you are worried that the NSA might have 10,000 times the resources you suspected, you can just add a few more digits on to your key and defeat that possibility. Myself, I always use a key thats as long as possible to be safe, but I think that paranoia about their HARDWARE is wholely misplaced. The thing to be paranoid about is that they know something about factoring algorithms that we do not. Perry