Based upon the Kerckhoffs' principle, illegal users can get to know the embedding and detection algorithms except for a secret key. Then, it is possible to access to a host signal which may be selected from frequency components of a digital content for embedding watermark signal. Especially for a fingerprinting scheme which embeds user's information as a watermark, the selected components can be easily found by the observation of differently watermarked copies of a same content. In this scenario, it is reported that some non-linear collusion attacks will be able to remove/modify the embedded signal. In this paper, we study the security analysis of our previously proposed spread-spectrum (SS) fingerprinting scheme[1], [2] under the Kerckhoffs' principle, and reveal its drawback when an SS sequence is embedded in a color image. If non-linear collusion attacks are performed only to the components selected for embedding, the traceability is greatly degraded while the pirated copy keeps high quality after the attacks. We also propose a simple countermeasure to enhance the robustness against non-linear collusion attacks as well as possible signal processing attacks for the underlying watermarking method.