Fast and Secure Elliptic Curve Scalar Multiplication Algorithm Based on a Kind of Deformed Fibonacci-Type Series

The efficient and secure elliptic curve scalar multiplication can be constructed by combining the addition chain and elliptic curve. In this paper, a kind of "Double-Addition" additive chain is proposed by studying the Fibonacci sequence. The "Double-Addition" sequence of arbitrary integer k is calculated by using Fibonacci and the method of gold. In addition, each cycle of this method is fixed to perform double point and a point add operations based on the "Double-Addition" of the elliptic curve scalar multiplication algorithm, so as to be able to resist the simple power attack. At the same time, the length of the chain is greatly shortened by using the double point operation compared with the chain of the Fibonacci. Experimental results showed that the efficiency of proposed algorithm in this paper has preceded by 4% to 18% over the previous ones known in the literature and in the average chain length it has attained 38% to 55% reduction compared to other doubling-free addition chain methods.