Method and apparatus for embedding and extracting digital watermarking for numerical data

There is provided a method for embedding a digital watermark into and extracting a digital watermark from a numerical data set. In accordance with embodiments of the present disclosure, there is provided a method for embedding a digital watermark into a numerical data set. The method includes selecting portions of the numerical data set identified as data noise, the selected portions to be used for embedding the digital watermark into the numerical data set, the digital watermark being unique for each recipient of the numerical data. The method further includes replacing the least significant bit (LSB) of at least some of the selected portions of the numerical data set with at least portion of the digital watermark.