A non-redundant and efficient architecture for Karatsuba-Ofman algorithm

Nam Su Chang, Chang Han Kim, Young Ho Park, Jong In Lim

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Citations (Scopus)

Abstract

The divide-and-conquer method is efficiently used in parallel multiplier over finite field GF(2n). Leone proposed optimal stop condition for iteration of Karatsuba-Ofman algorithm (KOA). Multi-segment Karatsuba method (MSK) is proposed by Ernst et al. In this paper, we propose a Non-Redundant Karatsuba-Ofman algorithm (NRKOA) with removing redundancy operations, and design a parallel hardware architecture based on the proposed algorithm. Comparing with existing related Karatsuba architectures with the same time complexity, the proposed architecture reduces the area complexity. The proposed NRKOA multiplier has more efficient the space complexity than the previous KOA multipliers, where n is a prime. Furthermore, the space complexity of the proposed multiplier is reduced by 43% in the best case.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages288-299
Number of pages12
Volume3650 LNCS
Publication statusPublished - 2005 Dec 1
Event8th International Conference on Information Security, ISC 2005 - Singapore, Singapore
Duration: 2005 Sep 202005 Sep 23

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3650 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other8th International Conference on Information Security, ISC 2005
CountrySingapore
CitySingapore
Period05/9/2005/9/23

Fingerprint

Multiplier
Space Complexity
Hardware Architecture
Divide and conquer
Parallel Architectures
Time Complexity
Redundancy
Galois field
Architecture
Hardware
Iteration

Keywords

  • Hardware Architecture
  • Karatsuba-Ofman Algorithm
  • Non-Redundant Karatsuba-Ofman Algorithm
  • Polynomial Multiplication

ASJC Scopus subject areas

  • Computer Science(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Theoretical Computer Science

Cite this

Chang, N. S., Kim, C. H., Park, Y. H., & Lim, J. I. (2005). A non-redundant and efficient architecture for Karatsuba-Ofman algorithm. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 3650 LNCS, pp. 288-299). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3650 LNCS).

A non-redundant and efficient architecture for Karatsuba-Ofman algorithm. / Chang, Nam Su; Kim, Chang Han; Park, Young Ho; Lim, Jong In.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 3650 LNCS 2005. p. 288-299 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3650 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Chang, NS, Kim, CH, Park, YH & Lim, JI 2005, A non-redundant and efficient architecture for Karatsuba-Ofman algorithm. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 3650 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3650 LNCS, pp. 288-299, 8th International Conference on Information Security, ISC 2005, Singapore, Singapore, 05/9/20.
Chang NS, Kim CH, Park YH, Lim JI. A non-redundant and efficient architecture for Karatsuba-Ofman algorithm. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 3650 LNCS. 2005. p. 288-299. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Chang, Nam Su ; Kim, Chang Han ; Park, Young Ho ; Lim, Jong In. / A non-redundant and efficient architecture for Karatsuba-Ofman algorithm. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 3650 LNCS 2005. pp. 288-299 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
@inproceedings{50f968760148449394a3d85ee45fdeea,
title = "A non-redundant and efficient architecture for Karatsuba-Ofman algorithm",
abstract = "The divide-and-conquer method is efficiently used in parallel multiplier over finite field GF(2n). Leone proposed optimal stop condition for iteration of Karatsuba-Ofman algorithm (KOA). Multi-segment Karatsuba method (MSK) is proposed by Ernst et al. In this paper, we propose a Non-Redundant Karatsuba-Ofman algorithm (NRKOA) with removing redundancy operations, and design a parallel hardware architecture based on the proposed algorithm. Comparing with existing related Karatsuba architectures with the same time complexity, the proposed architecture reduces the area complexity. The proposed NRKOA multiplier has more efficient the space complexity than the previous KOA multipliers, where n is a prime. Furthermore, the space complexity of the proposed multiplier is reduced by 43{\%} in the best case.",
keywords = "Hardware Architecture, Karatsuba-Ofman Algorithm, Non-Redundant Karatsuba-Ofman Algorithm, Polynomial Multiplication",
author = "Chang, {Nam Su} and Kim, {Chang Han} and Park, {Young Ho} and Lim, {Jong In}",
year = "2005",
month = "12",
day = "1",
language = "English",
isbn = "354029001X",
volume = "3650 LNCS",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
pages = "288--299",
booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

}

TY - GEN

T1 - A non-redundant and efficient architecture for Karatsuba-Ofman algorithm

AU - Chang, Nam Su

AU - Kim, Chang Han

AU - Park, Young Ho

AU - Lim, Jong In

PY - 2005/12/1

Y1 - 2005/12/1

N2 - The divide-and-conquer method is efficiently used in parallel multiplier over finite field GF(2n). Leone proposed optimal stop condition for iteration of Karatsuba-Ofman algorithm (KOA). Multi-segment Karatsuba method (MSK) is proposed by Ernst et al. In this paper, we propose a Non-Redundant Karatsuba-Ofman algorithm (NRKOA) with removing redundancy operations, and design a parallel hardware architecture based on the proposed algorithm. Comparing with existing related Karatsuba architectures with the same time complexity, the proposed architecture reduces the area complexity. The proposed NRKOA multiplier has more efficient the space complexity than the previous KOA multipliers, where n is a prime. Furthermore, the space complexity of the proposed multiplier is reduced by 43% in the best case.

AB - The divide-and-conquer method is efficiently used in parallel multiplier over finite field GF(2n). Leone proposed optimal stop condition for iteration of Karatsuba-Ofman algorithm (KOA). Multi-segment Karatsuba method (MSK) is proposed by Ernst et al. In this paper, we propose a Non-Redundant Karatsuba-Ofman algorithm (NRKOA) with removing redundancy operations, and design a parallel hardware architecture based on the proposed algorithm. Comparing with existing related Karatsuba architectures with the same time complexity, the proposed architecture reduces the area complexity. The proposed NRKOA multiplier has more efficient the space complexity than the previous KOA multipliers, where n is a prime. Furthermore, the space complexity of the proposed multiplier is reduced by 43% in the best case.

KW - Hardware Architecture

KW - Karatsuba-Ofman Algorithm

KW - Non-Redundant Karatsuba-Ofman Algorithm

KW - Polynomial Multiplication

UR - http://www.scopus.com/inward/record.url?scp=33645985781&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33645985781&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:33645985781

SN - 354029001X

SN - 9783540290018

VL - 3650 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 288

EP - 299

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -