Restrictive partially blind signature, which is designed for privacy oriented information systems, allows a user to obtain a blind signature from a signer whilst the blind message must obey some certain rules. In order to reduce storage and communication costs, several public-key cryptosystems are constructed by using characteristic sequences generated by linear feedback shift register (LFSR). In this paper, we present a new partially blind signature scheme with the restrictive property, which is based on $n$-th order characteristic sequences generated by LFSR. By assuming the intractability of the discrete logarithm problem, our sequence-based schemes are provably secure in the random oracle model. We also present a practical e-cash application based on our restrictive partially blind signature. Due to the reduced representation of finite field elements and feasible sequence operations from LFSR, our scheme is time and storage efficient on both of signer and user sides. The advantages will make privacy oriented applications more practical for resource-constrained devices.