Cryptosystems Using Automorphisms of Finitely Generated Free Groups

2016/03/07 by Anja Moldenhauer, Anja I. S. Moldenhauer, Moldenhauer, Anja I. S. +2
Computer Science · Mathematics · #20E05 #20E36 #94A60 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #msc:20E05 #msc:20E36 #msc:94A60

paper · pdf · doi:10.48550/arxiv.1603.02328

arxiv created 2016/03/07 · openalex publication_date 2016/03/07 · arxiv updated 2016/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper introduces a newly developed private key cryptosystem and a public key cryptosystem. In the first one, each letter is encrypted with a different key. Therefore, it is a kind of a one-time pad. The second one is inspired by the ElGamal cryptosystem. Both presented cryptosystems are based on automorphisms of free groups. Given a free group F of finite rank, the automorphism group Aut(F) can be generated by Nielsen transformations, which are the basis of a linear technique to study free groups and general infinite groups. Therefore Nielsen transformations are introduced.

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