Efficient Large Integer Squarers on FPGA

This paper presents an optimised high throughput architecture for integer squaring on FPGAs. The approach reduces the number of DSP blocks required compared to a standard multiplier. Previous work has proposed the tiling method for double precision squaring, using the least number of DSP blocks so far. However that approach incurs a large overhead in terms of look-up table (LUT) consumption and has a complex and irregular structure that is not suitable for higher word size. The architecture proposed in this paper can reduce DSP block usage by an equivalent amount to the tiling method while incurring a much lower LUT overhead: 21.8% fewer LUTs for a 53-bit squarer. The architecture is mapped to a Xilinx Virtex 6 FPGA and evaluated for a wide range of operand word sizes, demonstrating its scalability and efficiency.