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Abstract
In 1991, the first public key protocol involving automaton groups has been proposed. In this paper, we give a survey about algorithmic problems around automaton groups which may have potential applications in cryptography. We then present a new public key protocol based on the conjugacy search problem in some families of automaton groups. At the end, we offer open problems that could be of interest to group theorists and computer scientists in this direction.
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Acknowledgments
The authors thank Prof. Slava Grigorchuk for helpful discussions.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Additional information
Funding
The second author is partially supported by project SERICS (PE00000014) under the MUR National Recovery and Resilience Plan funded by the European Union - NextGenerationEU, and partially by the ‘National Group for Algebraic and Geometric Structures, and their Applications’ (GNSAGA - INdAM)