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This paper studies the problem of achieving watermark semifragility in watermark-based authentication systems through a composite hypothesis testing approach. Embedding a semifragile watermark serves to distinguish legitimate distortions caused by signal-processing manipulations from illegitimate ones caused by malicious tampering. This leads us to consider authentication verification as a composite hypothesis testing problem with the watermark as side information. Based on the hypothesis testing model, we investigate effective embedding strategies to assist the watermark verifier to make correct decisions. Our results demonstrate that quantization-based watermarking is more appropriate than spread-spectrum-based methods to achieve the semifragility tradeoff between two error probabilities. This observation is confirmed by a case study of an additive Gaussian white noise channel with a Gaussian source using two figures of merit: 1) relative entropy of the two hypothesis distributions and 2) the receiver operating characteristic. Finally, we focus on common signal-processing distortions, such as JPEG compression and image filtering, and investigate the discrimination statistic and optimal decision regions to distinguish legitimate and illegitimate distortions. The results of this paper show that our approach provides insights for authentication watermarking and allows for better control of semifragility in specific applications.