What are the practical problems of using zero knowledge proofs, for instance in the field of authentication?
Currently, there are very few practical barriers to deploying zero-knowledge proofs. They've been deployed in everything from anonymous credentials to cryptocurrencies to privacy-preserving survey systems. Very fast academic systems have been developed which use zero-knowledge proofs for privacy-preserving distributed machine learning. This last example hasn't been deployed yet, but clearly is fast and scalable enough to be used in practice.