Zero Knowledge (ZK) proofs are disruptive technology for anonymous payments in crypto currency.

Here are some links to applications of zero-knowledge proofs in crypto currency.

1. ZCash is now live. It is slow and expensive yet promised for a great future.
2. ZCash was built from erlier ZeroCoin system. An older lecture about ZeroCoin by Matthew Green.
3. ZK proofs: how to prove equality of plaintexts [by Jonathan Bootle, UCL].
4. ZK proofs allow to build so called confidential transactions (CT).
   • Confidential transactions by bitcoin/blockstream developers:
     white paper and some introduction.
   • An improvement called CCT by Denis Lukianov (see also his slides).
5. ZK proofs are potentially not necessary to build an anonymous crypto currency.
   A major alternative is CryptoNote protocol and Monero which uses ring signatures and not Zero-Knowledge proofs, and which does not yet achieve perfect anonymity, for example it does not (or does not yet) protect the transaction amounts (see Table 1 here).

In my opinion wide adoption of truly anonymous crypto currency is unlikely. On the other side, bitcoin anonymity is very poor. A middle ground needs to be found.