Abstract: Through the systematic analysis,we derive the expressions that represents the relations between the amount of the utilized hardware and the bit-width of the output or the period of the generated random numbers,and prove the advantages of multi-output LFSR based UPRNG in hardware utilization in theory.Through the analysis of the transform matrix and the taps of LFSR,we propose several novel methods to improve the speed of the UPRNG.The experiments verify the expressions and the methods mentioned above in Xilinx Vertex 4 FPGA.