Page 103 - Hardware Implementation of Finite-Field Arithmetic

86 Cha pte r T h ree

x y
ty 1 ty ty exp_2k

0 1
last 0 1 0 1 first
e

x y x y
reset Montgomery start start_mp1 reset Montgomery start start_mp2
multiplier multiplier
done mp1_done done mp2_done
z z
next_e next_y
ce ce_ty
k-bit register
k-bit register ce ce_e
initially: exp_k load load
ty
parallel_in shift update
e
load load
k-bit shift register
serial_out x
i
z
FIGURE 3.11 mod m exponentiation, LSB-fi rst algorithm.

main_component1: Montgomery_multiplier_modif port map(
x => e, y => second, clk => clk, reset=> reset, start =>
start_mp1, z => next_e, done => mp1_done
);
main_component2: Montgomery_multiplier_modif port map(
x => operand1, y => operand2, clk => clk, reset=> reset,
start => start_mp2, z => next_y, done => mp2_done
);
mp_done <= mp1_done and mp2_done;
z <= next_e;
register_e: process(clk)
begin
if clk’event and clk = ‘1’ then
if load = ‘1’ then e <= exp_k;
elsif ce_e = ‘1’ then e <= next_e;
end if;
end if;
end process register_e;
register_ty: process(clk)
begin
if clk’event and clk = ‘1’ then
if ce_ty = ‘1’ then ty <= next_y; end if;