A closer look at the multilinear cryptography using nilpotent groups

Abstract

In Kahrobaei et al. [Multilinear cryptography using nilpotent groups, Proceedings of Elementary Theory of Groups and Group Rings, and Related Topics conference. Conference held at Fairfield University and at the Graduate Center, CUNY, New York, NY, USA, November 1–2, 2018, De Gruyter, 2020, pp. 127–133] we generalized the definition of a multilinear map to arbitrary groups and introduced two multiparty key-exchange protocols using nilpotent groups. In this paper we have a closer look at the protocols and will address some incorrect cryptanalysis which has been proposed in Roman'kov [Discrete logarithm for nilpotent groups and cryptanalysis of polylinear cryptographic system, Prikl. Diskretn. Mat. Suppl. (12), (2019), pp. 154–160].

Keywords:

• Multilinear map
• nilpotent group
• key-exchange protocol

AMS Classifications:

• 20F18
• 94A60

Acknowledgments

The last two authors would like to thank the Department of Computer Science of the University of York for the excellent hospitality while part of this paper was being written.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research of the last two authors is supported by a grant of the University of Campania “Luigi Vanvitelli”, in the framework of the project GoAL (V:ALERE 2019).