Fast Continuous Scalar Multiplication Algorithms on Twisted Edwards Elliptic Curve

In this paper, we research the operation rules and scalar multiplication of Twisted Edwards elliptic curve. Based on the properties of point addition and double point operations, we propose the fast continuous double point algorithm, continuous point addition algorithm and continuous double point-point addition algorithm on Twisted Edwards elliptic curve. These algorithms reduce the amount of operations significantly by reducing the inverse operations. For comparison purposes, the top-level operations of the new algorithm use the non-adjacent form(NAF) and double base number system(DBNS) scalar multiplication algorithms. In contrast, it effectively improves the computational efficiency of the Twisted Edwards elliptic curve scalar multiplication algorithm, in which it is more than 50% faster than the underlying operation using Horner's rule, continuous multiplier algorithm, and about 10% to 35% or more faster than the base operation using the 4-NNAF algorithm.