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Title: Fast Modular Squaring Method for Public-Key Cryptosystems
Authors: Wu, Chia-Long
Lou, Der-Chyuan
Chang, Te-Jen
Keywords: 模平方運算;公開金鑰密碼系統;演算法;查表法;移位
Modular squaring;public key cryptosystem;algorithm;Look Up Table;shift
Date: 2006
Issue Date: 2017-12-18 17:36:01 (UTC+8)
Abstract: 平方演算法在大整數的運算,扮演很重要的角色。標準的平方演算法眾所週知,但有“錯誤進位”的疑慮發生。Guajardo與Paar學者提出的平方演算法修正了這項缺點,但是又延生出“錯誤索引”的問題。在本篇論文中,我們提出一個有效的平方方法,不僅可以解決以上所述兩項問題,亦可改進Yang、Hseih與Laih三位學者所提出的演算法。對於基底b而言,xi * xj 的乘積可以事先計算並儲存之,即1*2, 1*3, …, (b-1)(b-1)可以在實際運算前,事先儲存之,進而加速平方演算法的執行效率。本文所提出的演算法與Yang、Hseih與Laih三位學者所提出的演算法相較之下,快了1.77倍,當然這個演算法比標準的平方法亦快的多。
The squaring algorithm acts an important role in large integer arithmetic. The standard squaring algorithm is quite well-known, but there is an improper carry handling bug in it. The Guajardo-Paar’s squaring algorithm fixes the carry handling bug, but generates error-indexing bug. In this paper, we propose a novel efficient squaring algorithm that not only avoids the bugs between the standard squaring algorithm and the Guajardo-Paar's squaring algorithm but also improves the performance in squaring computation for Yang-Hseih-Laih squaring algorithm. For base b, the products of xi * xj can be pre-computed on-line, that is, 1*2, 1*3, …, (b-1)(b-1) are pre-computed. Some results will be determined and stored in a look-up table before the computation and we can speed up the performance of squaring algorithm. Our proposed algorithm is about 1.77 times faster in comparison with the Yang-Hseih-Laih’s algorithm, and also faster than the standard squaring algorithm.
Relation: TANET 2006 台灣網際網路研討會論文集
Data Type: conference
Appears in Collections:[TANET 台灣網際網路研討會] 會議論文

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