Page 340 - Hardware Implementation of Finite-Field Arithmetic

320 App endix B

using a block RAM component available within the unisim library of
Xilinx. For another semiconductor or programmable device vendor,
the table model should be modified. The package storing the
parameter values includes the Frobenius coefficients:

constant f1: polynomial :=
(
x”43”, x”bb”, x”65”, x”4b”, x”06”, x”a3”, x”a6”, x”80”,
x”d3”,x”24”, x”16”, x”28”, x”33”, x”47”, x”d8”, x”84”,
x”01”
);
constant f2: polynomial :=
(
x”bb”, x”4b”, x”a3”, x”80”, x”24”, x”28”, x”47”, x”84”,
x”43”,x”65”, x”06”, x”a6”, x”d3”, x”16”, x”33”, x”d8”,
x”01”
);
constant f4: polynomial :=
(
x”4b”, x”80”, x”28”, x”84”, x”65”, x”a6”, x”16”, x”d8”,
x”bb”,x”a3”, x”24”, x”47”, x”43”, x”06”, x”d3”, x”33”,
x”01”
);
constant f8: polynomial :=
(
x”80”, x”84”, x”a6”, x”d8”, x”a3”, x”47”, x”06”, x”33”,
x”4b”,x”28”, x”65”, x”16”, x”bb”, x”24”, x”43”, x”d3”,
x”01”
);

B.1.2 FPGA Implementations
Combinational circuits have been used for implementing the 16-bit to
8-bit mod 239 reducer, the mod 239 adder-subtractor, and the mod
239 multiplier (Table B.1):

Operation LUTs Slices Total time
Reducer 63 37 17.1
Adder-subtractor 25 13 9
Multiplier 31 18 15
TABLE B.1 Cost and Delay of mod 239 Operators

As quoted above the mod 239 inverter is a table storing the
238 inverses.