Two Binary Number Coding Systems

　

PBC and CGC are related by Exclusive OR operation as follows.

                  

　

The following pictures illustrate the difference of the views of one bmp picture. The left side is in PBC, and the right in CGC. However, here in CGC case, the pixel values are "regarded" as ordinary PBC for PC monitor display.

　

　

PBC CGC

　

　

In BPCS-Steganography, embedding operation is executed after the vessel image has been transformed from PBC to CGC. This is because CGC is better than PBC for obtaining "better looking (i.e. blocking-less)" stego images. The reason is as follows.

　

Let  an "n-th (n=1,2,3,...) least plane" be the n-th Least Significant bit-plane. For example, the 3rd least plane in PBC above is the b2 bit-plane.

　

"Embedding a file-block (i.e. 8 consecutive Bytes) into a certain 8x8 square area on an n-th least PBC plane actually means that it changes the colors of several pixels in that square area by the value 2n-1 quite "uniformly." In this case the "blocking effect" emerges on the stego image.

  <Example>

If a bit in the 3rd least PBC plane is changed from "0" to "1", it actually changes 0 (=0000) ->4 (=0100),  1 (=0001) ->5 (=0101),  2 (=0010) ->6 (=0110),  3 (=0011) ->7 (=0111), and 8 (=1000) ->12 (=1100), .... The amount of the change is always 4. This will cause a blocking effect. The case "1" is changed to "0", 4(=0100) ->0 (=0000), 5 (=0101) -> 1 (=0001), 6 (=0110) -> 2 (=0010) , 7 (=0111) -> 3 (=0011), and so on. The value change is always -4. This will also cause a blocky area on the stego image.

 

While in the CGC embedding, the color change "differs pixel by pixel." The value change ranges from 1 to 2n-1. This will not produce blocky areas so much.

  <Example>

For "0" to "1" case, the change occurs 0 (=0000) ->7 (=0100),  1 (=0001) ->6 (=0101),  2 (=0011) ->5 (=0111),  3 (=0010) ->4 (=0110), and 12 (=1010)->11 (=1110), ... . It is similar for "1" to "0" case. The amount of the change differs case by case. This will not cause blocking effect so remarkably.

　

Consequently, we conclude that CGC is better than PBC.

　

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(Updated on April 5, 2017, by Eiji Kawaguchi)