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Digital Watermarking, [3] [4] [5] [6] [7] [8] [9] [11] [12] [16] [17] [18] can be summarized the technique of embedding undetectable (un-perceivable) hidden information into data objects (i.e. images, audio, video, text) mainly to protect the data from unauthorized duplication and distribution by enabling provable rights over the content. In the present paper we address the issue of rights protection in the framework of numeric data, through resilient information hiding. We're looking into the fundamental problem of watermarking numeric collections and propose resilient algorithms. To the best of our knowledge there is no work specifically addressing the problem of watermarking this type of data. The wide area of applicability of the problem ranging from numeric database content to stock market analysis data, makes it especially intriguing when considering a generic solution and particularities of its various applications. Given a range of associated numeric constraints and assumptions we provide a solution and analyze associated attacks. Our solution is resilient to a multitude of attacks, including data re-sorting, subset selection (up to 40% data loss tolerance), linear data changes etc. Finally we present and discuss a proof-of-concept implementation of our algorithm.

Watermarking Techniques for Electronic Circuit Design