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A Modified Parallel Multiplier for Low Order Normal Elements
normal basis multiplier
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Recently, implementations of normal basis multiplication over the extended binary field GF(2^m) have received considerable attention. For efficient hardware implementation of finite field arithmetic units, the use of a normal basis is advantageous. The Massey-Omura multiplier of GF(2^m) uses a normal basis and its bit parallel version is usually implemented using m identical combinational logic blocks whose inputs are cyclically shifted from one another. In the past, it was shown that, for a class of finite fields defined by irreducible all-one polynomials, the parallel Massey-Omura multiplier had redundancy and a modified architecture of lower circuit complexity was proposed. In this article, it is shown that, not only does this type of multipliers contain redundancy in that special class of finite fields, but it also has redundancy in fields GF(2^m) defined by any irreducible polynomial. By removing the redundancy, we propose a new architecture for the normal basis parallel multiplier, which is applicable to any arbitrary finite field and has significantly lower circuit complexity compared to the original Massey-Omura normal basis parallel multiplier. The proposed multiplier structure is also modular and, hence, suitable for VLSI realization.
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