Authentication of videos and images based on the content is becoming an important problem in information security. Unfortunately, previous studies lack the consideration of Kerckhoffs's principle in order to achieve this (i.e., a cryptosystem should be secure even if everything about the system, except the key, is public knowledge). In this paper, a solution to the problem of finding a relationship between a frame's index and its content is proposed based on the creative utilization of a robust manifold feature. The proposed solution is based on a novel semi-fragile watermarking scheme for H.264/AVC video content authentication. At first, the input I-frame is partitioned for feature extraction and watermark embedding. This is followed by the temporal feature extraction using the Isometric Mapping algorithm. The frame index is included in the feature to produce the temporal watermark. In order to improve security, the spatial watermark will be encrypted together with the temporal watermark. Finally, the resultant watermark is embedded into the Discrete Cosine Transform coefficients in the diagonal positions. At the receiver side, after watermark extraction and decryption, temporal tampering is detected through a mismatch between the frame index extracted from the temporal watermark and the observed frame index. Next, the feature is regenerate through temporal feature regeneration, and compared with the extracted feature. It is judged through the comparison whether the extracted temporal watermark is similar to that of the original watermarked video. Additionally, for spatial authentication, the tampered areas are located via the comparison between extracted and regenerated spatial features. Experimental results show that the proposed method is sensitive to intentional malicious attacks and modifications, whereas it is robust to legitimate manipulations, such as certain level of lossy compression, channel noise, Gaussian filtering and brightness adjustment. Through a comparison between the extracted frame index and the current frame index, the temporal tempering is identified. With the proposed scheme, a solution to the Kerckhoffs's principle problem is specified.