Minimal degrees of invariants of (super)groups – a connection to cryptology

Abstract

We investigate questions related to the minimal degree of invariants of finitely generated diagonalizable groups. These questions were raised in connection to security of a public key cryptosystem based on invariants of diagonalizable groups. We derive results for minimal degrees of invariants of finite groups, abelian groups and algebraic groups. For algebraic groups we relate the minimal degree of the group to the minimal degrees of its tori. Finally, we investigate invariants of certain supergroups that are superanalogs of tori. It is interesting to note that a basis of these invariants is not given by monomials.

Keywords:

• Cryptosystem
• invariants
• diagonalizable group
• number field
• supergroup

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This publication was made possible by a NPRF award NPRP 6 - 1059 - 1 - 208 from the Qatar National Research Fund  (a member of The Qatar Foundation). The statements made herein are solely the responsibility of the authors.