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The Elliptic Curve Cryptosystem is an emerging alternative for traditional Public-Key Cryptosystem like RSA, DSA and DH. It provides the highest strength-per-bit of any cryptosystem known today with smaller key sizes resulting in faster computations, lower power consumption and memory. It also provides a methodology for obtaining high-speed, efficient and scalable implementation of protocols for authentication. All Elliptic curve based systems rely on solving discrete logarithm problem on Elliptic curve over finite field. Book also provides an introduction into elliptic curves in Edwards form also called Edwards curves. Deep and 'low-level' description is omitted due to complexity and document shortage. References are provided for further details and testimonials. These elliptic curves are used in this work to replace currently used, NIST approved, elliptic curves within two protocols mentioned above to improve security and performance increase. Also cryptographic impact is demonstrated. Parallel computation and performance analysis of multiprocessor architecture is discussed as an outcome of the work.