Hiding Information

We arrived at our first data hiding method, which we called “zero hiding,” quite intuitively. If you recall, our compression algorithm removed the least important DCT coefficients. It follows, then, that we could put the bit stream we wish to hide back into these dropped coefficients without changing the image drastically. To do this though, there must be a way to distinguish a zero which resulted from a dropped coefficient and a coefficient that is zero. To do this, we ran the image through a modified compressor that, instead of dropping coefficients below the specified threshold, replaced them with either a plus or minus one, depending on the sign of the coefficient.

Figure 1: The DCT is taken and then each coefficient under the specified threshold (10) will be dropped. These are coefficients are shown in blue in the picture on the right.

Next the hiding algorithm is given a binary data stream and the threshold value. The data stream is then divided up into words. However, the maximum decimal value of the word must be less than the threshold, since values over the threshold signify an important coefficient in the picture. We then increment each word’s decimal value by one to avoid putting in zero valued coefficients, which would otherwise be indistinguishable from zero valued coefficients in the original image. We then go back to the original coefficients matrix and replace the ones with the new value of the data word, maintaining the sign throughout.

Figure 2: The dropped coefficients are replaced with words created from the data stream. The IDCT is then taken, transforming the coefficient matrix back to a picture matrix.

Data Retrieval

To recover the hidden data the recovery script is given the threshold, and subtracts one from all DCT coefficients blow that threshold and tacks their binary values together, forming the original binary data.