Speed and Area Optimized Parallel Higher-Radix Modular Multipliers

Modular multiplication is the fundamental and compute-intense operation in many Public-Key crypto-systems. This paper presents two modular multipliers with their efficient architectures based on Booth encoding, higher-radix, and Montgomery powering ladder approaches. Montgomery powering ladder technique enables concurrent execution of main operations in the proposed designs, while higher-radix techniques have been adopted to reduce an iteration count which formally dictates a cycle count. It is also shown that by an adopting Booth encoding logic in the designs helps to reduce their area cost with a slight degradation in the maximum achievable frequencies. The proposed designs are implemented in Verilog HDL and synthesized targeting virtex-6 FPGA platform using Xilinx ISE 14.2 Design suite. The radix-4 multiplier computes a 256-bit modular multiplication in 0.93 μs, occupies 1.6K slices, at 137.87 MHz in a cycle count of dn/2e+2, whereas the radix-8 multiplier completes the operation in 0.69 μs, occupies 3.6K slices, achieves 123.43 MHz frequency in a cycle count of dn/3e+4. The implementation results reveals that the proposed designs consumes 18% lower FPGA slices without any significant performance degradation as compared to their best contemporary designs.