Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Dispersion Managed Optical Links with Randomly Distributed Residual Dispersion Per Span for 960 Gbps WDM Transmission Read chapter Read first chapter

2013 | OriginalPaper | Chapter

112. A Study on the Design of the Efficient Adder and Multiplier Based on Normal Basis over Finite Fields

Author : Chun-Myoung Park

Published in: Future Information Communication Technology and Applications

Publisher: Springer Netherlands

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

This paper propose the method of constructing the highly efficiency adder and multiplier systems over finite fields. The addition arithmetic operation over finite field is simple comparatively because that addition arithmetic operation is analyzed by each digit modP summation independently. But in case of multiplication arithmetic operation, we generate maximum k = 2m − 2° of αk terms, therefore we decrease k into m − 1 using irreducible primitive polynomial. We propose two method of control signal generation for the purpose of performing above decrease process. One method is the combinational logic expression and the other method is universal signal generation.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Production of Nanoporous Alumina and Surface Studies by Atomic Force Microscopy
next chapter Diamond-Like Carbon Films Obtained by Ion-Plasma Magnetron Sputtering
Literature
1.
Green D (1986) Modern logic design. Addison-Wesley Company, London
2.
Hwang K (1979) Computer arithmetic principles, architecture, and design. Wiley, New York
3.
Wu H, Hasan MA, Blake IF, Geo S (2002) Finite field multiplier using redundant representation. IEEE Trans Comput 51(11):1306–1316MathSciNetCrossRef
4.
Geiselmann W, Steinwandt R (2003) A redundant representation of GF(qn) for designing arithmetic circuit. IEEE Trans Comput 52(7):848–853MATHCrossRef
5.
Reyhani-Masoleh A, Hsan MA (2003) Fast normal basis multiplication using general purpose processors. IEEE Trans. Comput 52(11):1379–1390
6.
Kaihara ME, Takagi N (2005) A hardware algorithm for modular multiplication/division. IEEE Trans Comput 54(1):12–21CrossRef
7.
Efstathiou C, Vergos HT, Nikolas D (2004) Modified modulo 2n–1 multipliers. IEEE Trans Comput 53(3):370–374CrossRef
8.
Wu CH, Wu CM, Shieh MD, Hwang YT (2004) High-speed, low-complexity systolic design of novel iterative division algorithms in GF(2m). IEEE Trans Comput 53(3):375–379
9.
Artin E (1971) Galois theory. NAPCO Graphics Arts, Inc., Wisconsin
10.
Lidi R, Niederreiter H (1986) Introduction to finite fields and their applications. Cambridge University Press, Cambridge
11.
Wang CC (1989) An algorithm to design finite field multipliers using a self-dual normal basis. IEEE Trans Comput 38(10):1457–1460
12.
Ling C, Lung J (1991) Systolic array implementation of multipliers for finite fields GF(2m). IEEE Trans Circuit Syst 38(7):796–800
13.
Fenn STJ, Benaissa M, Taylor D (1996) GF(2m) multiplication and division over dual basis. IEEE Trans Comput 45(3):319–327
Metadata
Title
A Study on the Design of the Efficient Adder and Multiplier Based on Normal Basis over Finite Fields
Author
Chun-Myoung Park
Copyright Year
2013
Publisher
Springer Netherlands
Book
Future Information Communication Technology and Applications

Print ISBN: 978-94-007-6515-3

Electronic ISBN: 978-94-007-6516-0

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-94-007-6516-0_112