In this study, the author investigates the practical limitation of the recently proposed embedded cryptographic signature authentication scheme at the physical layer. By employing the log-likelihood ratio of a tag bit and its approximation, the author shows that the equivalent authentication channel observed by the secondary receiver can be viewed as a binary-input additive white Gaussian noise channel. Then, the sphere-packing lower bound can be employed to show the transmission capability for practical finite-length authentication tags. To achieve the same effective coverage area for both the primary and secondary receivers, it essentially requires efficient low-rate channel coding schemes with near sphere-packing-bound performance at the secondary receiver, which contrasts sharply with the pessimistic conclusion of Jiang et al.