Strong Designated Verifier Signature (SDVS) allows only the designated verifier to authenticate the validity of the signature, effectively addressing the issue of sensitive messages being retransmitted by dishonest verifiers. Specifically, SDVS, with its unforgeability, non-transferability, and privacy of signer identity, has been widely applied in areas such as electronic contracts. This paper conducts a cryptographic analysis of a lattice-based strong designated verifier signature scheme applicable to data integrity auditing in cloud computing environments. The analysis reveals two significant security flaws in the scheme: errors in the public and private key computations of the signer and the designated verifier; and the lack of signer identity privacy, meaning that any third party can verify the validity of the signature.