Booth memoryless modular multiplier with signed-digit number representation

We present new Booth modular multipliers with a signed-digit number representation. The proposed Booth algorithm can recode the multiplier in which every two-digit has an element of the set {-2, -1, 0, 1, 2}. In a serial modular multiplier, the proposed Booth modular multipliers compared to earlier ones offer savings up 50 percent in the execution time. In a parallel multiplier, it can be up to 18.76 percent in the implementation area for modulus m = 255.