A NEW ARCHITECTURE FOR A PARALLEL FINITE-FIELD MULTIPLIER WITH LOW-COMPLEXITY BASED ON COMPOSITE FIELDS

In this paper a new bit-parallel structure for a multiplier with low c omplexity in Galois fields is introduced. The multiplier operates over composite fields GF((2(n))(m)), with k = nm. The Karatsuba-Ofman algo rithm is investigated and applied to the multiplication of polynomials over GF(2(n)). It is shown that this operation has a complexity of or der O(k(log23)) 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(2(k)) 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.