Traditional digital signatures are often publicly verifiable, and in certain applications with privacy preservation requirements, the signer does not want the sensitive information it signed to be redelivered by a dishonest verifier. Aiming at the problem that traditional chameleon signatures (CS) cannot resist quantum computer attacks, this paper proposes a lattice-based authentication CS scheme. Based on the analysis of the lattice difficulty problem and the security vulnerability of the CS scheme, it is pointed out that it does not satisfy the third-party unforgeability and the signer rejectability, and a new lattice-based identity CS scheme is established, which is verified under the stochastic predicate machine model, and the storage and transmission efficiency of the scheme is analyzed. The results show that the newly designed identity-based CS scheme on the lattice can effectively resist quantum computer attacks, can sign messages of arbitrary length, and possesses more lightweight storage and transmission efficiency. The optimized chameleon signature scheme has better security and also provides a new solution for digital signatures to resist quantum computer attacks.