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

  • Chun-Myoung Park
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 235)


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.


Normal basis Addition algorithm Multiplication algorithm Adder Multiplier Finite fields modP 


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of Computer EngineeringThe Korea National University of TransportationChungju-siKorea

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