Hardware Implementations of Interleaved Modular Multiplications Over F256

Very-large-scale integration (VLSI) of elliptic curve cryptography (ECC) is vital for efficiently securing the digital world. This research demonstrates a description of elliptic curve cryptography (ECC), with a focus on both hardware and software approaches. An effective technique is used to create a modified interleaved modular multiplication architecture that maximizes performance while minimizing hardware use. Almost 532 and 522 slice registers are available for Spartan-6 and others with 4 unique control sets each. ECC processors must carefully balance area, time, and frequency to achieve maximum efficiency, as these factors always involve limitations. In this study, a 256-bit encryption method is used with a modified algorithm for interleaved modular multiplication (IMM) in the prime field. This method requires more resources and time, but it still operates at a satisfactory speed. In addition, a new hardware circuit methodology is introduced and implemented utilizing the Xilinx ISE software on various FPGA platforms, such as Kintex-7, Virtex-5, Virtex-6, and Spartan-6. The proposed 256-bit modular multiplication design occupies only 1478, 1497, 1478 and 1483 look-up tables (LUTs) and attains noteworthy completion with 1.9 $\mu$s, 2.09 $\mu$s, 3.83 $\mu$s, and 2.11 $\mu$s on Kintex-7, Virtex-5, Spartan-6, and Virtex-6, respectively, at maximum frequencies of 134.7 MHz, 77.9 MHz, 67.097 MHz, and 121.527 MHz individually. Taking the National Institute of Standards suggested prime fields into consideration. Rigorous simulation and verification procedures are conducted employing Modelsim and Maple’s software to ensure the accuracy and reliability of the obtained results.