Page 192 - Hardware Implementation of Finite-Field Arithmetic

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Operations over GF (2 )—Polynomial Bases 173

An executable Ada file LSBfirst.adb, including Algorithm 7.3, is
available at www.arithmetic-circuits.org. It can be observed that
Algorithm 7.3 is the binary version of the LSE-first multiplier given in
Algorithm 5.7. It is also important to note that in the MSB- and LSB-
first multiplication schemes, several coefficients could be processed
at each step.
A VHDL model for the LSB-first multiplication algorithm is
given in the file interleaved_mult.vhd available at www.arithmetic-
circuits.org. The datapath corresponding to Algorithm 7.3 is shown
in Fig. 7.2.
The entity declaration of the LSB-first multiplier given in the file
interleaved_mult.vhd is

entity interleaved_mult is
port (
A, B: in std_logic_vector (M-1 downto 0);
clk, reset, start: in std_logic;
Z: out std_logic_vector (M-1 downto 0);
done: out std_logic
);
end interleaved_mult;

B (m – 1 : 0) A (m – 1 : 0)
new_a (m – 1 : 0)
1 0 inic

inic
m-bit shift register m-bit register
shift_right
a (m – 1 : 0)

a m–2 f m–1 a i –1 f i a 0 f 1 f 0
b i
c m–1 a m–1 c i a i c 0 a 0 a m–1
a m–1 a m–1 a m–1
. . . . . . . . . . . .

new_c m–1 new_c i new_c 0 new_a m–1 new_a i new_a 1 new_a 0
new_c (m – 1 : 0)
inic
m-bit register
ce_c
c (m – 1 : 0)
Z (m – 1 : 0)

FIGURE 7.2 Interleaved LSB-fi rst multiplier datapath.