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A new architecture for a parallel finite field multiplier with low complexity based on composite fields

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1 Author(s)
Paar, C. ; Dept. of Electr. & Comput. Eng., Worcester Polytech. Inst., MA

A bit parallel structure for a multiplier with low complexity in Galois fields is introduced. The multiplier operates over composite fields GF((2n)m), with k=nm. The Karatsuba-Ofman algorithm (A. Karatsuba and Y. Ofmanis, 1963) is investigated and applied to the multiplication of polynomials over GF(2n). It is shown that this operation has a complexity of order O(klog23 ) under certain constraints regarding k. A complete set of primitive field polynomials for composite fields is provided which perform module reduction with low complexity. As a result, multipliers for fields GF(2k) up to k=32 with low gate counts and low delays are listed. The architectures are highly modular and thus well suited for VLSI implementation

Published in:

Computers, IEEE Transactions on  (Volume:45 ,  Issue: 7 )

Date of Publication:

Jul 1996

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