Abstract: In elliptic curve system, the operational efficiency of the finite field is essential. In this paper, for the low-end FPGA chip, we optimize finite field modular multiplication and modular inversion from both algorithms and hardware realization. The improved modular multiplication algorithm reduces a 256 bit multiplication and reduces a 128 bit multiplication in hardware implementation. Modular inversion algorithm improved without increasing the hardware resources available to reduce the number of iterations; with subtraction and subsequent correction algorithms instead of 256 bit comparator, improved design can interrupt a combination of long chain, improve resource complex with rates, and achieve a balance of size and speed.