Watermarking technologies have been envisioned as a potential means for establishing ownership on digital media objects. However, achievable robustness and false-positive rates of the state-of-the-art watermarking techniques raise doubts about applicability of watermarking to ownership problem. With this perspective, we address the security weaknesses common to most watermarking techniques and assess the role of watermarking in construction of ownership assertion systems. We identify the requirements of a watermarking based ownership assertion system. Also, we provide a basic functional outline of a practical version of such a system and identify its potential vulnerabilities. To mitigate these vulnerabilities, we aim at reducing the false positive rate of the watermark detection scheme. For this purpose, we propose embedding multiple watermarks as opposed to single watermark embedding while constraining the embedding distortion. The crux of the proposed method lies in watermark generation which deploys a family of one-way functions. We incorporate the multiple watermark embedding idea with the additive watermarking technique  and present results to illustrate the potential of this approach in reducing the false-positive rate of the watermark detection scheme.