Zero-knowledge proofs for a given statement, by definition, reveal nothing about its witness. zk-SNARKs (used by Zcash) are statistically zero-knowledge; there are no cryptographic assumptions involved.
As a slight aside, I always wondered if zero-knowledge proofs really reveal "slight" knowledge.
That is, if I ask 1 billion questions about a resource, and get true, verifiable answers, can't I find out something about it? For example, some projection onto a linear subspace or something.
