Page 247 - Hardware Implementation of Finite-Field Arithmetic

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Operations over GF (2 )—Polynomial Bases 227

m FFs LUTs Slices Period Cycles Total time
8 23 30 16 3.1 8 25
16 42 50 29 3.5 16 56
32 76 84 47 3.6 32 115
64 142 148 80 5.9 64 378
128 273 276 147 6.3 128 806
163 344 347 184 7.4 163 1,206
233 484 489 255 7.5 233 1,748

TABLE 7.8 Cost and Delay of Sequential Montgomery Multiplier
7.7.7 Classic Squaring
The circuits were generated for specific polynomials and are fully
combinational (see Table 7.9).

m LUTs Slices Total time
8 8 5 2
16 17 9 2
32 47 24 3
64 170 87 3
128 339 173 4
163 165 86 3
233 153 99 3
TABLE 7.9 Cost and Delay of Classic Squarers

7.7.8 LSB-First Squarer, Second Version
The circuits are for specific polynomials and are sequential
implementations that produce a bit of result per cycle. The cost and
delay of several LSB-first squarers are shown in Table 7.10. The results
show that for a specific polynomial a fully combinational circuit uses
fewer resources and is faster.

m FFs LUTs Slices Period Cycles Total time
8 28 31 18 3.1 4 12
16 49 57 31 3.1 8 25
32 92 109 59 3.5 16 56
64 175 207 111 4.3 32 138
128 369 402 243 4.9 64 314
163 464 510 306 5.3 82 435
233 659 723 436 6.0 117 702

TABLE 7.10 Cost and Delay of LSB-First Squarer