Low-Complexity Bit-Parallel Multiplier over GF(2^m) Using Dual Basis Representation

Recently, cryptographic applications based on finitefields have attracted much attention. The most demanding finitefield arithmetic operation is multiplication. This investigationproposes a new multiplication algorithm over GF(2^m) using thedual basis representation. Based on the proposed algorithm, aparallel-in parallel-out systolic multiplier is presented. Thearchitecture is optimized in order to minimize the silicon covered area(transistor count). The experimental results reveal that the proposedbit-parallel multiplier saves about 65% space complexity and 33% timecomplexity as compared to the traditional multipliers for a generalpolynomial and dual basis of GF(2^m).