The MOR cryptosystem and finite $p$-groups
This work addresses cryptographic security for specialized mathematical structures, but it is incremental as it builds on existing MOR cryptosystem concepts.
The paper investigates the MOR cryptosystem for finite p-groups, focusing on its security based on the discrete logarithm problem in automorphism groups, and reports a complete study for p'-automorphisms while identifying open problems for p-automorphisms.
The ElGamal cryptosystem is the most widely used public key cryptosystem. It uses the discrete logarithm problem as the cryptographic primitive. The MOR cryptosystem is a similar cryptosystem. It uses the discrete logarithm problem in the automorphism group as the cryptographic primitive. In this paper, we study the MOR cryptosystem for finite $p$-groups. The study is complete for $p^\prime$-automorphisms. For $p$-automorphisms there are some interesting open problems.