Tezos will use zero-knowledge proofs too. Did someone analyze their points? Can we use some of the ideas for zcash?
Quote from Tezos paper:
Zcash makes an impressive use of zero-knowledge proofs to provide full, information theoretic, anonymity, but the risk – however remote – of undetected hyperinflation in the event of a bug in the proof circuit makes some users uncomfortable.
Our initial plan is to strike a compromise and integrate Zcash’s proof circuit in the protocol, but restrict its operations to a special token issued on the Tezos blockchain. This token will be convertible 1 to 1 with Tezos tokens, but the chain will keep track of how many tokens have been converted so that undetected in action in the privacy preserving token cannot spill over onto the main token. Users who trust the security of the privacy preserving token will have full use of its functionality while those who don’t will remain protected as long as they do not make use of the privacy feature. This mechanism replicates the economic behavior of a side chain, but on a single ledger.
In the long run, the team intends to replace all operations on the blockchain with zero-knowledge proofs. Instead of downloading an entire blockchain a client will be able to download a single proof attesting that the entire blockchain has been validated starting from the genesis hash. However, to that end, they will likely make use of STARKs, zero knowledge proofs similar to SNARKs but which do not require a trusted setup.