No, you don't need to trust anyone. You can verify how the accumulator works before compiling your code if you like. (ignore back on.)
We will be able to verify how the accumulators works with the opensource code but the problem is no that.
The problem is that Gnosis will generate the keys (RSA) of these accumulators.There is nothing trustless. You need to trust that Gnosis is honest and will not keep the factors to forge zerocoin proofs and then infinite ANC.
Source:
https://wiki.anoncoin.net/Zerocoin#Zerocoin_in_practice (Section: Criticisms, fourth paragraph)
If gnosis has his own rsa ufos - with factors - then he had 8 core years squirrelled away in his basement ? get real !!! You cannot fake the numbers nor the work needed to work them out.
But, even if Gnosis had an alternative set of RSA UFOs, these wouldn't work with Zerocoin. The ZC mint transactions use the agreed upon value of N (the rsa ufo), and the spend transaction uses the same value of N. Miners verify that this is done correctly. There is no back door.
You turn around too. You try to invalidate my arguments trying to divert the issue.
As I said before, in the opensource code, it will be not possible to see if Gnosis hold the factors (P and Q) of the RSA keys or not. You will see only the N number in the opensource code.According to the anoncoin wiki:
https://wiki.anoncoin.net/Zerocoin#Zerocoin_in_practice (Section: Criticisms, fourth paragraph)
If Gnosis knows the factors, he will be able to forge zerocoin proofs and then infinite ANC. And there is no way to be sure he destroy these factors. You need to trust Gnosis.
Excuse me for being blunt, but you really don't know what you are talking about it. If N was chosen using Sanders method of generating RSA UFOs, there is no way that anyone could know the factorization of N. Since we are using Sander generated RSA UFOs for N, which are generated in a deterministic way, and since the number N can be verified in the code and by miners, there is no way that Gnosis could know its factorization, and there is no way that Gnosis could forge zerocoin proofs. This is what makes Zerocoin trustless.
What part don't you understand? I think that this is crystal clear.