Browse > Article
http://dx.doi.org/10.7236/JIIBC.2014.14.2.121

Shift-and-Add Multiplication Algorithm for Decimal System  

Lee, Sang-Un (Dept. of Multimedia Eng., Gangneung-Wonju National University)
Publication Information
The Journal of the Institute of Internet, Broadcasting and Communication / v.14, no.2, 2014 , pp. 121-126 More about this Journal
Abstract
The problem of finding the fastest algorithm for multiplication of two large n-digit decimal numbers remains unsolved in the field of mathematics and computer science. To this problem so far two algorithms - Karatsuba and Toom-kook - have been proposed to shorten the number of multiplication. In the complete opposite of shorten the number of multiplication method, this paper therefore proposes an efficient multiplication algorithm using additions completely. The proposed algorithm totally applies shift-and-add algorithm of binary system to large digits of decimal number multiplication for example of RSA-100 this problem can't perform using computer. This algorithm performs multiplication purely with additions of complexity of $O(n^2)$.
Keywords
Multiplication; Long (grade-school) multiplication; Shift-and-add; Karatsuba multiplication; Toom-kook multiplication;
Citations & Related Records
연도 인용수 순위
  • Reference
1 A. Mandal and R. Syal, "Tripartite Modular Multiplication using Toom-Kook Multiplication," International Journal of Advanced Research in Computer Science and Electronics Engineering, Vol. 1, No. 2, pp. 100-104, 2012.
2 Wikipedia, "List of Unsolved Problems in Computer Science," http://en.wikipedia.org/wiki/List_of_unsolved_problems_in_computer_science, Wikimedia Foundation Inc., 2012.
3 Wikipedia, "Multiplication Algorithm," http://en.wikipedia.org/wiki/Multiplication_algorithm, Wikimedia Foundation Inc., 2012.
4 A. Karatsuba and Y. Ofman, "Multiplication of Multidigit Numbers on Automata," Soviet Physics-Doklady, Vol. 7, pp. 595-596, 1963.
5 R. P. Brent and P. Zimmermann, "Modern Computer Arithmetic, Version 0.5," Cambridge Monographs on Computational and Applied Mathematics, Cambridge University Press, 2010.
6 A. Eigenwilling and K. Mehlhorn, "Multiplication of Long Integers (Faster than Long Multiplication)," Max Planck Institute for Informatics, Saarbrucken, Germany, http://www.mpi-inf.mpg.de/-mehlhorn/ftp/chapter2A-en.pdf, 2005.