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An AB2 operation is known as an efficient basic operation for public key cryptosystems over GF(2m), and various systolic arrays for performing AB2 operations have already been proposed using a standard basis representation. However, these circuits have certain shortcomings for cryptographic application due to their high circuit complexity and long latency. Therefore, further research on an efficient AB2 multiplication circuit is still needed. Accordingly, the authors present a new AB2 algorithm and its systolic realisations in GF(2m). First, a new algorithm is proposed based on the MSB-first scheme using a standard basis representation. Thereafter, bit-parallel and bit-serial systolic power multipliers are derived that exhibit a lower hardware complexity and smaller latency than conventional approaches. In addition, since the proposed architectures incorporate simplicity, regularity, modularity, and pipelinability, they are well suited to VLSI implementation and can be easily applied as a basic architecture for computing an inverse/division operation and in crypto-processor chip design.