Public-key cryptosystem based on invariants of diagonalizable groups
This work addresses cryptographic security by proposing a new cryptosystem, but it appears incremental as it builds on existing group theory concepts without claiming broad breakthroughs.
The authors developed a public-key cryptosystem using invariants of diagonalizable groups and analyzed its properties across finite fields, number fields, and finite rings, while identifying necessary parameter restrictions to prevent attacks like linear algebra and Euclidean algorithm-based ones.
We develop a public key cryptosystem based on invariants of diagonalizable groups and investigate properties of such cryptosystem first over finite fields, then over number fields and finally over finite rings. We consider the security of these cryptosystem and show that it is necessary to restrict the set of parameters of the system to prevent various attacks (including linear algebra attacks and attacks based on Euclidean algorithm).