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

2015 10th International Conference on P2P, Parallel, Grid, Cloud and Internet Computing (3PGCIC) Pub Date : 2015-11-04 DOI:10.1109/3PGCIC.2015.21

Shuanggen Liu, G. Qi, Xu An Wang

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引用次数: 5

Abstract

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.

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基于一类变形斐波那契级数的椭圆曲线标量乘法快速安全算法

将加法链与椭圆曲线相结合，可以构造出高效、安全的椭圆曲线标量乘法。本文通过对斐波那契数列的研究，提出了一类“双加法”加性链。用斐波那契和金的方法计算了任意整数k的“双加法”序列。此外，该方法的每一个周期都是基于椭圆曲线标量乘法算法的“双加法”，固定进行双点和一点相加运算，从而能够抵御简单的幂攻击。同时，与斐波那契数列的链相比，采用双点运算大大缩短了链的长度。实验结果表明，本文算法的效率比文献中已知的算法提高了4% ~ 18%，平均链长比其他无加倍加法链方法减少了38% ~ 55%。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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2015 10th International Conference on P2P, Parallel, Grid, Cloud and Internet Computing (3PGCIC)

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