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In this paper, a novel concept "authentication set" is used to analyze the security of the authentication schemes in detail. Several novel concepts on the authentication set are defined, which are called "cover authentication set", "attack authentication set", "watermark-based authentication set" or "signature-based authentication set", "verified authentication set" and "malicious-attack authentication set". According to the relation among the aforementioned sets, the security of the authentication schemes is exploited. Furthermore, a conclusion is drawn according to the analysis result. At the same time the principle that guides the design of the more secure authentication schemes is presented. Finally, as an example, a novel authentication design method based on multi-feature watermarks is proposed according to the design principle. The experimental results prove the validity of the design method and the significance of the guide principle.