From my understanding of RSA UFOs, that is not true as Gnosis only received N and there is no way for him to figure out the factorization of N, which is two large unfactorable numbers P and Q. By combining multiple RSA UFOs, I think Anoncoin is using 13, it ensures that the person that solved one of the UFOs in the distributed computing project cannot know the final accumulator, and Gnosis can't either since he doesn't know the factorization of the 13 RSA UFOs. It makes sense to me how it works and you are incorrect in saying Gnosis knows the factorization of N, as without a LOT of computing power it is impossible for him to know that.
The only worry I have about the RSA UFO project is that possibly someone already knows the factorization of N (IE. The government), or someone will later find it out with faster processors in the future. I am not sure if this is a realistic thing to be worried about though, as the only thing I know about this stuff is from doing research on ZeroCoin/Zerocash/Anoncoin. I will try to reach out to the Zerocash Devs to get their opinion on the RSA UFO project, as I would trust their opinion over a random poster on these forums (no offense).
I was also concerned about this but Gnosis assured me that at any point in the future we can generate a larger set of RSA UFOs and upgrade the network with a hard fork if we had to.
That is good to know, so that alleviates one of my worries. I think it would go a long ways, as to my other concern of the government already knowing the factorization, to extend the RSA UFO project indefinitely. That way the security of the accumulator can be upgraded via a hard fork when bigger UFOS are found at a later date. That way over time the chance the NSA has already cracked the UFOs gets smaller and smaller.
Yes I think its a good idea. Hell, maybe we can build the RSA UFO generator right into the wallet, have everyone churning RSA UFOs all day if they want to, then do yearly hardforks to incorporate the new juicy UFOs.
That is a good idea, and I think it would go a long ways towards instilling trust in the RSA UFOs used to create the accumulator. Building it into the client would make it more likely that people would partake in the generation of the UFOs.
Even better, if we could figure out a way to incentivize people to do it they would be more likely to do so. If this could be figured out I think Anoncoin would have something really special here. By changing the PoW to RSA UFO generation it would incentivize them by rewarding them block rewards. I'm not sure what Anoncoin's block time is, but you could take the largest UFO generated per block and reward the finder with some Anoncoins. I would suggest switching from PoW to a form of PoS so it costs much less to secure the block chain. That would free up some Anoncoins in each block reward to be awarded to the person that generates the biggest UFO.
I don't have enough technical knowledge to figure out if this is plausible or not, but if it is possible then it could really help the long term sustainability and security of the project. There are already talks of switching to auxPoW, why not switch to something like ufoPoW if it is possible. Hopefully Gnosis or Meeh can comment as to if this would be possible to do in some way or another. Perhaps it could be done in another way and the way I stated is impossible... either way if it can be done I think it would be a great thing to do.