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Division (mathematics)

About: Division (mathematics) is a research topic. Over the lifetime, 12717 publications have been published within this topic receiving 87814 citations.


Papers
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Journal ArticleDOI
TL;DR: Based on MSD addition, parallel algorithms for multiplication and division are developed on the basis of symbolic substitution (SS), and the performance of the proposed optical arithmetic system is analyzed and compared with that of state-of-the-art electronic counterparts.
Abstract: The modified-signed-digit (MSD) number system offers parallel addition and subtraction of any two numbers, with carry propagation constrained only between two adjacent digits. Based on MSD addition, parallel algorithms for multiplication and division are developed in this paper. The optical implementations of these MSD arithmetic algorithms are developed on the basis of symbolic substitution (SS). The space-invariant nature of SS matches well with the parallel nature of the MSD arithmetic algorithms presented. The potential advantages of using these algorithms for optical computing include the significant increase in speed, full exploitation of parallelism, and higher system throughput compared with existing electronic arithmetic processors. The performance of the proposed optical arithmetic system is analyzed and compared with that of state-of-the-art electronic counterparts.

77 citations

Book ChapterDOI
03 Dec 2017
TL;DR: In this article, the authors propose automatic tools to detect ARX ciphers' division property at the bit level and some specific ARX Ciphers's division properties at the word level.
Abstract: Division property is a generalized integral property proposed by Todo at Eurocrypt 2015. Previous tools for automatic searching are mainly based on the Mixed Integer Linear Programming (MILP) method and trace the division property propagation at the bit level. In this paper, we propose automatic tools to detect ARX ciphers’ division property at the bit level and some specific ciphers’ division property at the word level.

76 citations

Journal ArticleDOI

76 citations

Book
01 Jan 1981

76 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20242
2023739
20221,583
2021239
2020416
2019465