Nonlinear Phenomena in Complex Systems, 2024, Vol.27, No.3, pp.301

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2024, Vol.27, No.3, pp.301 - 310

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

N. N. Shenets

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.

Key words: authenticated key exchange, secret sharing, key pre-distribution

DOI: https://doi.org/10.5281/zenodo.13960663

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