New systolic array architecture for finite field division

Abstract

This paper proposes a new systolic array architecture to perform division operations over GF(2 m ) based on the modified Stein's algorithm. The systolic structure is extracted by applying a regular approach to the division algorithm. This approach starts by obtaining the dependency graph for the intended algorithm and assigning a time value to each node in the dependency graph using a scheduling function and ends by projecting several nodes of the dependency graph to a processing element to constitute the systolic array. The obtained design structure has the advantage of reducing the number of flip-flops required to store the intermediate variables of the algorithm and hence reduces the total gate counts to a large extent compared to the other related designs. The analytical results show that the proposed design outperforms the related designs in terms of area (at least 32% reduction in area) and speed (at least 60% reduction in the total computation time) and has the lowest AT complexity that ranges from 80% to 94%.

Novel bit-serial semi-systolic array structure for simultaneously computing field multiplication and squaring

“…Circles in DG represent the operations performed by the recursive Eqs. (15), (24), (25), (26), (27), (30), and (31). Fig.…”

Efficient parallel semi-systolic array structure for multiplication and squaring in GF(2<i>^m</i>)

“…There is no data dependency between the equations from (24) to (27) and thus they can be executed simultaneously.…”

“…2) allocating a time value to each node in the DG using a specific timing or scheduling function. 3) mapping several nodes of the DG to a processing element (PE) to form the systolic/semi-systolic array [20,25,26,27,28,29,30]. The DG of the unified multiplication and squaring algorithm over GFð2 m Þ can be extracted from the recursive Eqs.…”

“…The DG of the unified multiplication and squaring algorithm over GFð2 m Þ can be extracted from the recursive Eqs. 15, (24), (25), (26), (27), (30), and (31). The extracted DG based on these equations is shown in Fig.…”

“…The upper part consists of the upper l rows of the DG (rows with the light red nodes) and it computes the coefficients of C, H, G, V, U according to Eqs. (15), (24), (25), (26), (27), respectively. The lower part consists of the last row of the DG (row with the brown nodes) and it computes the coefficients of P and S according to Eqs.…”