Two systolic architectures are developed for performing the product–sum computation AB + C in the finite field GF(2m) of 2melements, where A, B, and C are arbitrary elements of GF(2m). The first multiplier is a serial-in, serial-out one-dimensional systolic array, while the second multiplier is a parallel-in, parallel-out two-dimensional systolic array. The first multiplier requires a smaller number of basic cells than the second multiplier. The second multiplier heeds less average time per computation than the first multiplier if a number of computations are performed consecutively. To perform single computations both multipliers require the same computational time. In both cases the architectures are simple and regular and possess the properties of concurrency and modularity. As a consequence they are well suited for use in VLSI systems.

In this paper a parallel architecture is developed to realize a digital filter. First a systolic array is used to compute a 248-point complex number-theoretic transform (CNT). Next an algorithm is developed to realize a digital filter that uses 248-point CNT's and a generalization of the overlap-save method. This algorithm solves the conflict between long transform lengths and a wide dynamic range associated with the number-theoretic transform. Finally this algorithm is mapped to a parallel architecture. This architecture is simple, regular and expandable, and, hence, is suitable for VLSI implementation.

In this correspondence, a parallel architecture is developed to compute the linear convolution of two sequences of arbitrary lengths using the Fermat number transform (FNT). In particular, a pipeline structure is designed to compute a 128-point FNT. In this FNT, only additions and bit rotations are required.