Small FPGA implementations for solving systems of linear equations in finite fields

Solving systems of linear equations in finite fields is among the most fundamental operations and used extensively in areas of cryptography, signal processing and clustered file system. In order to implement such systems, it is desirable to improve solving systems of linear equations. We propose FPGA implementations for Gaussian elimination in finite fields. Experimental results and comparisons show that our designs provide significant reductions in both area and clock-area product.