Efficient linkable ring signatures and threshold signatures from linear feedback shift register

For many practical usages or resource-limited environments, it is often desirable to speed up the cryptographic systems without any security lost. Linkable ring signature is a kind of signatures which can simultaneously provide the properties of anonymity, spontaneity as well as linkability. Threshold signature is a useful tool for decentralizing the power to sign a message by distributed computing. The paper presents linkable ring signatures and threshold signatures using n-th order characteristic sequences generated by a linear feedback shift register (LPSR). Our schemes enjoy the following attractive features: (i) main computation operations are performed in GF(q); and (ii) security properties rely on the difficulty of solving the state based discrete logarithm problem(S-DLP) and on state based decisional Diffie-Hellman(S-DDH) assumption. Since the complexity of breaking S-DLP(S-DDHP, resp.) is computationally equivalent to that of solving traditional DLP(DDHP, resp.) in GF(qⁿ), the proposed schemes successfully enhance the security of the system and meanwhile maintain low computational costs. All these make our schemes more flexible.