System Level Design of Reconfigurable Server Farms Using Elliptic Curve Cryptography Processor Engines

Table 1

GF(2^𝑚) divider combinational operations.

Number	𝑅𝑚𝑅𝑚−1	𝑆𝑚𝑆𝑚−1	𝐷	𝑅	𝑆	𝑈	𝑉	Delta
1	“00”	xx	𝑋	𝑥^2𝑅	𝑆	𝑥^2𝑈	Equal	Delta + 2
2	“01”	“0x”	𝑋	𝑥𝑅	𝑥𝑆	Equal	Equal	Equal
3	“01”	“1x”	𝑋	𝑥𝑅	𝑥(𝑆−𝑥𝑅)	Equal	𝑉−𝑥𝑈	Equal
4	“10”	“00”	0	𝑥^2𝑆	𝑅	𝑥^2𝑉	𝑈	2
5	“10”	“00”	1	𝑅	𝑥^2𝑆	𝑈/𝑥^2	Equal	Delta − 2
6	“10”	“01”	0	𝑥𝑆	𝑥(𝑥𝑆−𝑅)	𝑉	𝑈−𝑥𝑉	0
7	“10”	“01”	1	𝑅	𝑥(𝑥𝑆−𝑅)	𝑈/𝑥^2	𝑉−𝑈/𝑥	Delta − 2
8	“10”	“10”	0	𝑥^2(𝑆−𝑅)	𝑅	𝑥^2(𝑉−𝑈)	𝑈	2
9	“10”	“10”	1	𝑅	𝑥^2(𝑆−𝑅)	𝑈/𝑥^2	𝑉−𝑈	Delta − 2
10	“10”	“11”	0	𝑥(𝑆−𝑅)	𝑥(𝑅−𝑥(𝑆−𝑅))	𝑉−𝑈	𝑈−𝑥(𝑉−𝑈)	0
11	“10”	“11”	1	𝑅	𝑥(𝑅−𝑥(𝑆−𝑅))	𝑈/𝑥^2	𝑉−𝑈−𝑈/𝑥	Delta − 2
12	“11”	“00”	0	𝑥^2𝑆	𝑅	𝑥^2𝑉	𝑈	2
13	“11”	“00”	1	𝑅	𝑥^2𝑆	𝑈/𝑥^2	𝑉	Delta − 2
14	“11”	“01”	0	𝑥𝑆	𝑥(𝑥𝑆−𝑅)	𝑉	𝑈−𝑥𝑉	0
15	“11”	“01”	1	𝑅	𝑥(𝑥𝑆−𝑅)	𝑈/𝑥^2	𝑉−𝑈/𝑥	Delta − 2
16	“11”	“10”	0	𝑥(𝑆−𝑅)	𝑥(𝑅−𝑥(𝑆−𝑅))	𝑉−𝑈	𝑈−𝑥(𝑉−𝑈)	0
17	“11”	“10”	1	𝑅	𝑥(𝑅−𝑥(𝑆−𝑅))	𝑈/𝑥^2	𝑉−𝑈−𝑈/𝑥	Delta − 2
18	“11”	“11”	0	𝑥^2(𝑆−𝑅)	𝑅	𝑥^2(𝑉−𝑈)	𝑈	2
19	“11”	“11”	1	𝑅	𝑥^2(𝑆−𝑅)	𝑈/𝑥^2	𝑉−𝑈	Delta − 2