*Scribed by Madhur Tulsiani*

** Summary **

In this lecture we begin the construction and analysis of a zero-knowledge protocol for the 3-coloring problem. Via reductions, this extends to a protocol for any problem in NP. We will only be able to establish a weak form of zero knowledge, called “computational zero knowledge” in which the output of the simulator and the interaction in the protocol are computationally indistinguishable (instead of identical). It is considered unlikely that NP-complete problem can have zero-knowledge protocols of the strong type we defined in the previous lectures.

As a first step, we will introduce the notion of a *commitment scheme* and provide a construction based on any one-way permutation.