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

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