Abstract: Cryptographic calculation exploits limited field arithmetic and, specifically, multiplication. Lightweight and quick usage of such arithmetic is fundamental for some delicate applications. This brief proposed a low-complexity systolic Montgomery multiplication over GF (2^m). Our many-sided quality examination demonstrates that the area complexity in quality of the proposed design is decreased contrasted with the past work. This has likewise been affirmed through our application-specific integrated circuit area and time proportional estimations and usage. Consequently, the proposed design seems, by all accounts, to be extremely appropriate for high throughput low-complexity cryptographic applications. This Proposed configuration will be actualized by Verilog HDL and mimicked by Modelsim Tool. The Proposed Montgomery Multiplier is Synthesis by Xilinx and FPGA Spartan 3 XC 3S 200 TQ 144.

Keywords: Galois Field (GF), VLSI, Application Specific Integrated circuits(ASIC) Karatsuba-Of man (KO).