I just learned about Milagro through this submission and only looked at a fraction of the docs but as someone who is not a cryptographer but put some effort into understanding pairing based cryptograph, I find the documentation excellent so far.
> No, No you can't. A 4 digit pin is 14 bit security. Any system is only as secure as its weakest link.
As far as I understand it, the PIN is used to secure a secret key for a 128bit security cryptosystem against key compromise. Like password protection on ssh keys, this provides stronger security than unprotected keys but I think this PIN is actually part of an interactive proof to protect against offline attacks.
The downside of Identity Based Encryption is that you need a master secret key (aside: I think we shoud find a less loaded term like root secret key) to derive the client secrets. The DTA is a way to avoid a single authority in posession of this root secret through secret sharing. Sharing in secret sharing is not copying but splitting into shares. I'm not yet sure if it works like I think it works but I think they use secure multiparty computation to use a shared root secret to derive shares of the client secrets that the clients combine to obtain their secret. That would be really awesome and about the best we can do before more powerful cryptography (functional encryption, fully homomorphic encryption etc.) becomes practical.