Abstract
In providing secure group-oriented communication and data access control, one important task is to establish a shared key between group members. To build such protocols, various mathematical apparatus can be used. Most modern group key establishment schemes are a generalization of the Diffie–Hellman key agreement protocol. This paper presents a group key agreement protocol based on assumptions relating to isogeny of supersingular elliptic curves. The properties of isogeny graphs, as well as the abundance of hard assumptions, make it possible to build flexible protocols. The proposed scheme is decentralized and implies the presence of a trusted party (group manager). Establishing a shared key is carried out in 2 rounds, one of which is aimed at confirming the identity of the group users. Analysis of the proposed protocol security is given. In addition, performance characteristics show that there are restrictions on the size of groups due to the need to calculate the isogenies of elliptic curves.
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The reported study was funded by Ministry of Digital Development, Communications and Mass Media of the Russian Federation, project number 12/21-k (grant «Information Security»).
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Anastasia, Y. (2023). Isogeny-Based Group Key Establishment Scheme. In: Nagar, A.K., Singh Jat, D., Mishra, D.K., Joshi, A. (eds) Intelligent Sustainable Systems. Lecture Notes in Networks and Systems, vol 579. Springer, Singapore. https://doi.org/10.1007/978-981-19-7663-6_11
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