Page 344 - Hardware Implementation of Finite-Field Arithmetic

324 App endix B

LUTs Slices Total time
97 49 9

B.2.4 mod p Multiplication
The double, add, and reduce algorithm, with stored-carry encoding
(Eq 3.10), is used. The package storing the parameter values is the
following:

package dar_csa_multiplier_parameters is
constant k: integer := 32;
--logk is the number of bits of k-1
constant logk: integer := 5;
constant m: std_logic_vector(k+1 downto 0) :=
“00” & X”fffffe7d”;
--minus_m = 2**(k+2) - m
constant minus_m: std_logic_vector(k+1 downto 0) :=
“11” & X”00000183”;
end dar_csa_multiplier_parameters;

Some kind of synchronization of the final operations should be
introduced.

FFs LUTs Slices Period Cycles Total time
109 322 167 6.1 64 390.4

B.2.5 mod p Division
The plus-minus algorithm is used. The following values are previously
computed:

34
minus_p = 2 k + 2 − p = 2 − (2 − 387) = 3.2 + 387 = [300000183]
32
32
16
two_p = 2p = 2[FFFFFE7D] = [1FFFFFCFA]
16 16
In this case, p mod 4 = 1 (the least significant bits of p are 01) so
−1
that Eq. (4.28) is used for computing w4 mod p. The parameter
values are the following:
constant K: natural := 32;
constant P: std_logic_vector(K downto 0)
:= ‘0’&X”fffffe7d”;
--LOGK+1 bits for representing integers between -k and k
constant LOGK: natural := 6;
constant MINUS_P: std_logic_vector(K+1 downto 0)
:= (‘1’ & not P) + ‘1’;
constant TWO_P: std_logic_vector(K+1 downto 0) := P & ‘0’;