New bit parallel multiplier with low space complexity for all irreducible trinomials over GF(2 n)

Young In Cho, Nam Su Chang, Chang Han Kim, Young Ho Park, Seokhie Hong

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

Koç and Sunar proposed an architecture of the Mastrovito multiplier for the irreducible trinomial f(x)=x n+x k+1 , where k ≠ n/2 to reduce the time complexity. Also, many multipliers based on the Karatsuba-Ofman algorithm (KOA) was proposed that sacrificed time efficiency for low space complexity. In this paper, a new multiplication formula which is a variant of KOA presented. We also provide a straightforward architecture of a non-pipelined bit-parallel multiplier using the new formula. The proposed multiplier has lower space complexity than and comparable time complexity to previous Mastrovito multipliers' for all irreducible trinomials.

Original languageEnglish
Article number5999752
Pages (from-to)1903-1908
Number of pages6
JournalIEEE Transactions on Very Large Scale Integration (VLSI) Systems
Volume20
Issue number10
DOIs
Publication statusPublished - 2012 Jan 1

Keywords

  • Bit-parallel multiplier
  • finite field
  • irreducible trinomial
  • Mastrovito multiplication
  • polynomial basis

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Hardware and Architecture
  • Software

Cite this

New bit parallel multiplier with low space complexity for all irreducible trinomials over GF(2 n). / Cho, Young In; Chang, Nam Su; Kim, Chang Han; Park, Young Ho; Hong, Seokhie.

In: IEEE Transactions on Very Large Scale Integration (VLSI) Systems, Vol. 20, No. 10, 5999752, 01.01.2012, p. 1903-1908.

Research output: Contribution to journalArticle

@article{07b018f690fc4c72ba3f92585ef7cbc9,
title = "New bit parallel multiplier with low space complexity for all irreducible trinomials over GF(2 n)",
abstract = "Ko{\cc} and Sunar proposed an architecture of the Mastrovito multiplier for the irreducible trinomial f(x)=x n+x k+1 , where k ≠ n/2 to reduce the time complexity. Also, many multipliers based on the Karatsuba-Ofman algorithm (KOA) was proposed that sacrificed time efficiency for low space complexity. In this paper, a new multiplication formula which is a variant of KOA presented. We also provide a straightforward architecture of a non-pipelined bit-parallel multiplier using the new formula. The proposed multiplier has lower space complexity than and comparable time complexity to previous Mastrovito multipliers' for all irreducible trinomials.",
keywords = "Bit-parallel multiplier, finite field, irreducible trinomial, Mastrovito multiplication, polynomial basis",
author = "Cho, {Young In} and Chang, {Nam Su} and Kim, {Chang Han} and Park, {Young Ho} and Seokhie Hong",
year = "2012",
month = "1",
day = "1",
doi = "10.1109/TVLSI.2011.2162594",
language = "English",
volume = "20",
pages = "1903--1908",
journal = "IEEE Transactions on Very Large Scale Integration (VLSI) Systems",
issn = "1063-8210",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "10",

}

TY - JOUR

T1 - New bit parallel multiplier with low space complexity for all irreducible trinomials over GF(2 n)

AU - Cho, Young In

AU - Chang, Nam Su

AU - Kim, Chang Han

AU - Park, Young Ho

AU - Hong, Seokhie

PY - 2012/1/1

Y1 - 2012/1/1

N2 - Koç and Sunar proposed an architecture of the Mastrovito multiplier for the irreducible trinomial f(x)=x n+x k+1 , where k ≠ n/2 to reduce the time complexity. Also, many multipliers based on the Karatsuba-Ofman algorithm (KOA) was proposed that sacrificed time efficiency for low space complexity. In this paper, a new multiplication formula which is a variant of KOA presented. We also provide a straightforward architecture of a non-pipelined bit-parallel multiplier using the new formula. The proposed multiplier has lower space complexity than and comparable time complexity to previous Mastrovito multipliers' for all irreducible trinomials.

AB - Koç and Sunar proposed an architecture of the Mastrovito multiplier for the irreducible trinomial f(x)=x n+x k+1 , where k ≠ n/2 to reduce the time complexity. Also, many multipliers based on the Karatsuba-Ofman algorithm (KOA) was proposed that sacrificed time efficiency for low space complexity. In this paper, a new multiplication formula which is a variant of KOA presented. We also provide a straightforward architecture of a non-pipelined bit-parallel multiplier using the new formula. The proposed multiplier has lower space complexity than and comparable time complexity to previous Mastrovito multipliers' for all irreducible trinomials.

KW - Bit-parallel multiplier

KW - finite field

KW - irreducible trinomial

KW - Mastrovito multiplication

KW - polynomial basis

UR - http://www.scopus.com/inward/record.url?scp=84864777872&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84864777872&partnerID=8YFLogxK

U2 - 10.1109/TVLSI.2011.2162594

DO - 10.1109/TVLSI.2011.2162594

M3 - Article

AN - SCOPUS:84864777872

VL - 20

SP - 1903

EP - 1908

JO - IEEE Transactions on Very Large Scale Integration (VLSI) Systems

JF - IEEE Transactions on Very Large Scale Integration (VLSI) Systems

SN - 1063-8210

IS - 10

M1 - 5999752

ER -