Zero-knowledge proofs are the answer to the question, “How do I prove I know something without sharing the thing I know?”

Example of How They Work

You have two people – one colorblind and one not
The colorblind person insists the balls are identical
The other person insists the balls are different colors
Q: How can the other person prove the balls are different colors without giving up which is which?
A: The other person gives the balls to the colorblind person telling them to hide them. Show one at a time to the other person. After each two shows, ask if those two were the same. Track if the person answered consistently over many iterations.

What Are They Used For

Web applications hash our passwords. When we log into the applciation, they compare the new hash of the password we entered while logging in against the hash they stored to see if we provided the correct password.
Zcash is a truly private cryptocurrency (unlike Bitcoin which is fully traceable) that uses zero-knowledge proofs