Fast elliptic curve algorithm using deformed Fibonacci-type series

Abstract

The efficient and secure scalar multiplication can be constructed by combining the addition chain and elliptic curve. In this paper, we propose an explicit algorithm which is a kind of 'double-addition' addition chain based on the Fibonacci-type sequence. The 'double-addition' sequence of arbitrary integer k is calculated by using Fibonacci and golden ratio addition chain method. 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 average chain length has attained 38% to 55% reduction compared to other doubling-free addition chain methods.