Systolic array implementation of multipliers for finite fields GF(2m)

A parallel-in-parallel-out systolic array and a serial-in-serial-out systolic array are proposed for fast multiplication in finite fields GF(2^m) with the standard basis representation. Both of the architectures possess features of regularity, modularity, concurrency, and unidirectional data flow. As a consequence, they have high throughput rates and are well suited to VLSI implementation with fault-tolerant design. As compared to the related multipliers presented by C.S. Yeh et al. (see IEEE Trans. Comput., vol.C-33, p.357-360, Apr. 1984), the proposed parallel implementation makes it easier to incorporate fault-tolerant design, and the proposed serial implementation requires only one control signal instead of two