In cloud and edge computing, senders of data often want to be anonymous, while recipients of data always expect that the data come from a reliable sender and they are not redundant. Linkable ring signature (LRS) can not only protect the anonymity of the signer, but also detect whether two different signatures are signed by the same signer. Today, most lattice-based LRS schemes only satisfy computational anonymity. To the best of our knowledge, only the lattice-based LRS scheme proposed by Torres et al. can achieve unconditional anonymity. But the efficiency of signature generation and verification of the scheme is very low, and the signature length is also relatively long. With the preimage sampling, trapdoor generation, and rejection sampling algorithms, this study proposed an efficient LRS scheme with unconditional anonymity based on the e-NTRU problem under the random oracle model. We implemented our scheme and Torres et al.’s scheme, as well as other four efficient lattice-based LRS schemes. It is shown that under the same security level, compared with Torres et al.’s scheme, the signature generation time, signature verification time, and signature size of our scheme are reduced by about 94.52%, 97.18%, and 58.03%, respectively.