A ring signature scheme is a group signature scheme but with no group manager to setup a group or revoke a signer’s identity. The formation of a group is spontaneous in the way that diversion group members can be totally unaware of being conscripted to the group. It allows members of a group to sign messages on the group’s behalf such that the resulting signature does not reveal their identity (anonymity). The notion of linkable ring signature, introduced by Liu, et al. [10], also provides signer anonymity, but at the same time, allows anyone to determine whether two signatures have been issued by the same group member (linkability). In this paper, we enhance the security model of [10] for capturing new and practical attacking scenarios. We also propose two polynomial-structured linkable ring signature schemes. Both schemes are given strong security evidence by providing proofs under the random oracle model.