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http://dx.doi.org/10.9708/jksci.2013.18.2.009

Design of High-Speed Parallel Multiplier with All Coefficients 1's of Primitive Polynomial over Finite Fields GF(2m)  

Seong, Hyeon-Kyeong (School of Computer Information & Communication Eng., Sangji University)
Publication Information
Journal of the Korea Society of Computer and Information / v.18, no.2, 2013 , pp. 9-17 More about this Journal
Abstract
In this paper, we propose a new multiplication algorithm for two polynomials using primitive polynomial with all 1 of coefficient on finite fields GF($2^m$), and design the multiplier with high-speed parallel input-output module structure using the presented multiplication algorithm. The proposed multiplier is designed $m^2$ same basic cells that have a 2-input XOR gate and a 2-input AND gate. Since the basic cell have no a latch circuit, the multiplicative circuit is very simple and is short the delay time $D_A+D_X$ per cell unit. The proposed multiplier is easy to extend the circuit with large m having regularity and modularity by cell array, and is suitable to the implementation of VLSI circuit.
Keywords
Finite fields; GF($2^m$); Parallel multiplier; Primitive polynomials; Cell array;
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