This paper describes the arithmetic blocks based on Montgomery Multiplier (MM), which reduces complexity, gives lower power dissipation and higher operating frequency. The main objective in designing these arithmetic blocks is to use modified full adder structure and carry save adder structure that can be implemented in algorithm based MM circuit. The conventional full adder design acts as a benchmark for comparison, the second is the modified Boolean equation for full adder and third design is the design of full adder consisting of two XOR gate and a 2-to-1 Multiplexer. Besides Universal gates such as NOR gate and NAND gate, full adder circuits are used to further improve the speed of the circuit. The MM circuit is evaluated based on different parameters such as operating frequency, power dissipation and area of occupancy in FPGA board. The schematic designs of the arithmetic components along with the MM architecture are constructed using Quartus II tool, while the simulation is done using Model sim for verification of circuit functionality which has shown improvement on the full adder design with two XOR gate and one 2-to-1 Multiplexer implementation in terms of power dissipation, operating frequency and area.