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.
The scalar multiplication techniques used in Elliptic curve cryptography (ECC) are having the scope for gaining the computation efficiency. This is possible through the reduction of precomputed operations. Finding the more efficient technique compares to the most recent or efficient one is a research gap for all schemes. The manuscript presents an application oriented work for Telemedicine using ECC. It is based on robust application on reduced computational complexity. The methodology we apply for the same is Scalar Multiplication without precomputation on Radix-8. Introduced software and the hardware performance are reporting a big advantage over all the related proposed techniques. The reason to cover this problem is to provide a path on a fascinating area of ECC on a smaller key size be applicable for all applications on a same level of security strengths. The smaller length key gives the higher speed and shorter clock cycle to initiate the operation.
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