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In this paper, we provide a new partially blind signature scheme which is based on n-th order characteristic sequences generated by LFSR, and then prove its security in the random oracle model (ROM). Compares with the finite field based schemes, our scheme shows advantages on the computation and storage since the reduced representation of finite field elements by LFSR. It will make those applications more efficient in hardware-limited environments, such as cellular networks, tactical networks and sensor nets.