Is there a decentralized zk-SNARK (zero-knowledge Succinct Non-Interactive ARgument of Knowledge)? Normally, in zk-SNARK, we need to generate two public keys: one for prover and one for verifier. However, the input parameter of this generator algorithm must be secret, meaning that it must be hidden for both prover and verifier. 

And because of this, the process of those public generation is done by a trusted third party. 

Since using a trusted third party is not desirable for decentralized blockchain, I am looking for a decentralized approach of those public key generation. Is there ? or it's impossible to have a decentralized zk-SNARK ?

P.S. More information about zk-SNARK is found here: https://media.consensys.net/introduction-to-zksnarks-with-examples-3283b554fc3b
Here's Zcash's multi-party parameter calculation code, which...


  ... used a multi-party computation protocol with the property that the resulting parameters are secure unless all of the participants were dishonest or compromised during the ceremony.


By the way, you might find Bulletproofs more interesting which is newer and doesn't require a trusted setup.