Holomorphs of groups and their use in the Diffe-Hellman key-exchange protocol
Keywords:
Group of automorphisms, public key exchange, semidirect products of groupsAbstract
The holomorph of the group G, usually denoted by Hol(G), is the natural semidirect product Aut(G)G of G by its automorphism groupAut(G). Let λ : G → S(G), g ↦ fg : (x↦gx) the left regular representation of G. In this paper we will show that the group Hol( G) is isomorphic to the group λ(G)Aut(G). Also, we describe the public key exchange in the group λ(G)Aut(G).
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Published
2023-04-04
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