Novel Noncommutative Cryptography Scheme Using Extra Special Group

الملخص EN

Noncommutative cryptography (NCC) is truly a fascinating area with great hope of advancing performance and security for high end applications.

It provides a high level of safety measures.

The basis of this group is established on the hidden subgroup or subfield problem (HSP).

The major focus in this manuscript is to establish the cryptographic schemes on the extra special group (ESG).

ESG is showing one of the most appropriate noncommutative platforms for the solution of an open problem.

The working principle is based on the random polynomials chosen by the communicating parties to secure key exchange, encryption-decryption, and authentication schemes.

This group supports Heisenberg, dihedral order, and quaternion group.

Further, this is enhanced from the general group elements to equivalent ring elements, known by the monomials generations for the cryptographic schemes.

In this regard, special or peculiar matrices show the potential advantages.

The projected approach is exclusively based on the typical sparse matrices, and an analysis report is presented fulfilling the central cryptographic requirements.

The order of this group is more challenging to assail like length based, automorphism, and brute-force attacks.