Versatile multiplier architectures in GF(2k) fields using the Montgomery multiplication algorithm

Versatile digit serial multipliers for binary extension fields

“…Compared to the digit serial multipliers, the versatile bit serial multipliers [15][16][17][18][19] require less area and their critical path delays are also smaller. However, they need at least m k cycles to finish the multiplication while many digit serial multipliers need approximately dm k =we cycles.…”

“…Flexible implementations are possible with reconfigurable FPGA devices but FPGAs cannot compete with the ASIC in terms of performance, cost and power consumption. Naturally, customizable elliptic curve systems [14] and versatile multipliers [15][16][17][18][19] have been proposed in the literature but the proposed multipliers are all bit serial and there is not much work about versatile digit serial multipliers.…”

A scalable RNS Montgomery multiplier over F_2^m

“…To clarify the timing performance of this work, we introduce the following indicator shown in the last column of Table IV (8) Our work performs best among all the scalable design in terms of total computing time elapsed, with 9.09, 4.29, 5.65 speed-up improvement when the benchmark comes to [4,5,9] respectively. One can also find that the unscalable design (HybridKara [7]) performs even better than ours (about 57% above ours from the perspective of speed-up).…”

“…But it should be marked that this design is defined over fixed size field F 2 233 and over fixed special form irreducible polynomials (AOL, trinomials, pentanomials), which implies that their work will be unscalable when defined over arbitrary fields. The large LUT consumption of this design compared with [4,5,9] is due to the intrinsic property of RNS parallelism, in which 8 DMMs are employed to obtain an ultimate computational capability. But for some area or power constrained applications, it is not so critically intended.…”

“…Among alternative modular multiplication algorithms found in the literature, Montgomery's method has been extensively analyzed, since it replaces divisions with additions, multiplications and shifts [3]. Also this method can be easily tuned into different field sizes and field polynomials, putting the concept of scalable design methodology into practice [4,9]. In recent years, RNS has enjoyed renewed scientific interest due to its ability to perform fast and parallel modular arithmetic.…”