Edwards curve addition and doubling formula analysis for effective parallel decomposition

Abstract

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. The objective is to give the reader an overview on efficient addition and doubling formulas of Edwards curves together with analysis and effective parallel decomposition of these formulas. Practical analysis is provided with implementation consideration.