Efficient Squaring of Large Integers(<Special Section>Discrete Mathematics and Its Applications)

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概要

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• The efficient squaring algorithm is an important role in large integer arithmetic. All multiplication algorithms can be used for squaring large integers, but their performance can be greatly improved by using the standard squaring algorithm [1], [2], [8]. The standard squaring algorithm is quite well-known, but unfortunately there is an improper carry handling bug in it. Recently, Guajardo and Paar proposed a modified squar- ing algorithm [11] to fix the bug in the standard squaring algorithm. In this paper, we first point out that there is still an error-indexing bug in the Guajardo-Paar squaring algorithm. Then, we propose a new efficient squaring algorithm that not only avoids the bugs in both the standard squaring algorithm and the Guajardo-Paar squaring algorithm but also improves the performance in squaring computation. Our analyses and our simulations indicate that the proposed squaring algorithm is about 2.5 times faster in comparison with the standard multiplication algorithm in Pentium Series CPU. The performance of 1024-bit RSA cryptosystem can be saved 34.3% by using the proposed squaring algorithm to replace the standard multiplication.

• 社団法人電子情報通信学会の論文
• 2004-05-01

著者

• Laih Chi-sung

  Department Of Electrical Engineering National Cheng Kung University

• Yang Wu-chuan

  Dept. Of Electronic Engineering Nanjeon Junior College Of Technique And Commerce:department Of Elect

• HSEIH Peng-Yueh

  Department of Electrical Engineering, National Cheng Kung University

• Hseih Peng-yueh

  Department Of Electrical Engineering National Cheng Kung University

関連論文

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• New Signature Schemes Based on Factoring and Discrete Logarithms (Special Section on Cryptography and Information Security)
• Correction on "A Scalar Multiplication Algorithm with Recovery of the y-Coordinate on the Montgomery Form and Analysis of Efficiency for Elliptic Curve Cryptosystems"(Information Security)
• Efficient Squaring of Large Integers(Discrete Mathematics and Its Applications)

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