On Security and Performance in ECC Noncommutative Cryptography and Signcryption

Abstract

The thesis addresses the security and performance dvancement for the Discrete Logarithmic Problem DLP in the following primitives of cryptography such as: Elliptic Curve Cryptography ECC Edwards and twisted Edwards Curves Noncommutative Cryptography NCC multilayer key generation for ECC using signcryption and proxy re- newline ryptographic approach. newlineThese entire primitive formulates into the following five objectives The first objective claims Radix-16 scalar multiplication without pre-computations for ECC. newlineUsing the designed hardware support the proposed claim shows the more appropriateness for reduced instruction set computing and is a particular suite for low memory devices with resistance to the simple side channel attack and safe-error fault attack. This is in theoretically computing 6.25 percent faster than the recently proposed Radix-8 scalar conversion technique without pre-computed operations. The performance from the hardware perspective also improves newlineby 8.33 percent. newline newlineThe second objective works on the architecture of prime Edwards curves and extended Twisted Edwards curves on 4-processors and 8-processors. The proposed scalar multiplication results for both the curves are available on the reduced clock cycles and in a reduced newlinemultiplication processing costs. newline newlineThe third objective pertains on Noncommutative Cryptography NCC which is truly a fascinating area with great hope of advancing performance and security for high end newlineapplications. It provides a high level of safety measures. The basis of this group is established on the Hidden subgroup or subfield problem HSP. A proposed scheme is based on the extra special group ESG for finding the solution of an open problem for the most appropriate Noncommutative platform. This ESG supports at Heisenberg Dihedral order and Quaternion group. The working principle is made possible on the random polynomials chosen by the communicating parties for secure key-exchange encryption-decryption and authentication schemes on NCC.