Montgomery Modular Multiplication on Reconfigurable Hardware: Systolic versus Multiplexed Implementation

Algorithm 2

Montgomery modular exponentiation—square and multiply.

Require: 𝐸=∑^𝑛−1_𝑖=0𝑒_𝑖2^𝑖, 𝑒_𝑖∈{0,1}.

retun: 𝐴=𝑋^𝐸mod𝑁

𝐴=𝑅mod(𝑁)

𝑋=mont(𝑋,𝑅²mod(𝑁))

for 𝑖=𝑛−1 to 0  do

𝐴=mont(𝐴,𝐴)

if 𝑒_𝑖=1  then

   𝐴=mont(𝐴,𝑋)

 end  if

end  for

 𝐴=mont(𝐴,1)