Okay, here is what I think this is

- It is a straight forward combination of two forms of encryption from pairing cryptography world. Identity Based Encryption and Threshold Encryption.

- In Identity based encryption, your public key and private key is generated by an identity provider based on an identity string provided to it. This allows encrypting messages to party that hasn't yet recieved the keys. This work has been around for ages.

- Milagro proposes to distribute the trusted third party by having multiple identity providers. The public key and private key are formed from a threshold encryption/ decryption procedure.