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A new security strategy based on Galois linear feedback shift register structure is proposed in this paper. To make the VLFSR's details unpredictable from the key stream out, a novel circular variable polynomial and independent feedback loop is presented and designed. Through the cryptanalysis, the mutual authentication requirements between Reader and Tag is met, as well as increases the security capability, while maintains low cost and low power consumption. Furthermore, the authentication protocol is implemented in HJTC 0.25μm 2P5M EEPROM process, only extra 3370 gates is needed for the proposed authentication protocol, and the power consumption is as low as 35.5 μW.