A General Approach to Authenticated Key Establishment Based on Homomorphic Secret Sharing

Abstract

This paper addresses the problem of establishing a secure communication channels between parties in a multiparty environment. Most of well-known key establishment protocols used in practice are based on Diffie–Hellman problems and require significant computational costs. Therefore, key pre-distribution protocols are preferred for resource-constrained devices. In this paper, we consider protocols of this type based on secret sharing and propose a general approach using the homomorphic property of secret sharing schemes. Examples of such protocols are given and their security properties are analyzed. We also prove some interesting side results there are no perfectly secure two party key agreement and joint multiparty threshold decreasing protocols in a public channels setting. Finally, we rise a problem whose solution will allow for lightweight and secure connections between any devices.