Fast Binary Multiplication Method forModular Exponentiation

Abstract

本論文結合二元乘法、符號元表示法、以及補數表示法三種運算技術提出新的快速模指數演算法。對於大部份的公開金鑰密碼系統而言，模指數運算是相當耗時且佔記憶體的運算。而當我們利用本論文所提出的演算法時，我們可以將整體模指數運算複雜度由11k/8有效降至13k/12，其中k為指數E的長度。

This paper proposes a new fast technique to fast evaluate modular exponentiation which combines a binary exponentiation method, a complement representation method, and a signed-digit representation method. Because modular exponentiation is one of the most time-consuming operations for many cryptosystems, we adopt the proposed method to reduce the computational complexity from 11k/8 to 13k/12, where k is the bit-length of the exponent E. We can therefore efficiently speed up the overall performance of the modular exponentiation.