Zero-knowledge proofs

Abstract

Suppose Alice has a password and wants to log in to a website run by Bob, but she does not quite trust the computer Bob is using to verify the password. If she just sends the password to Bob then Bob’s computer will learn the whole password. To get around this problem one often sees websites that ask for the first, fourth and tenth letter of a password one time, and then maybe the first, second and fifth the second time and so on. In this way Bob’s computer only learns three letters at a time. So the password can be checked but in each iteration of checking only three letters are leaked. It clearly would be better if Bob could verify that Alice has the password in such a way that Alice never has to reveal any of the password to Bob. This is the problem this chapter will try to solve.