A user authentication protocol based on the intractability of the 3-coloring problem

Abstract

In this note, we consider the problem of verifying the identity of an individual involved in a two party communication activity using a well-known Zero Knowledge protocol for a computationally intractable problem. This problem is the problem of coloring the vertices of a graph using three colors so that no pair of adjacent vertices receives the same color also known as 3-coloring problem. This problem is NP-complete, i.e. ít shares with a multitude of other natural combinatorial problems the property that most likely no fast (polynomial) algorithm exists for their solution. In this note, we use randomly generated 3-colorable graphs and use the knowledge of a 3-coloring of them to authenticate individuals. We exploìt the fact that one may easily generate a random 3-colorable graph with a specific 3-coloring that only he/she knows although it is a computationally intractable problem for someone who wants to impersonate the individual to discover a 3-coloring. Therefore, knowledge of a 3-coloring of a graph provides authentication of the individual possessing this knowledge. To prove this knowledge, the individual may use an adaptation of a Zero Knowledge Interactive proof protocol for 3-coloring.