In 2008, Desoky proposed a method namely Noiseless Steganography or Nostega that will not produce noise while conducting message camouflaging process. One of the Nostega paradigm is Graphstega that avoids the arousal of suspicion in covert communications by concealing message as data points in a chart [1]. Since the chart as the cover in Graphstega was built by the message, it was not realistic and it would raise suspicion.

To overcome the problem, Sari [2] proposed Modified Graphstega Based on Chart Scale Modification to camouflaged the hidden message into the existing (realistic) chart. This method used Sudoku puzzle for generating shared secret. The architecture of Modified Graphstega Based on Chart Scale Modification is shown in Figure 1.

 

Figure 1 Modified Graphstega Architecture

 

For instance, the message which will be hidden is “Meet me
@7pm“, and the binary representation based on ASCII code for this message as follows:

010011010110010101100101011101000010000001101101011001010010000001000000001101110111000001101101

and the example of the chart as cover is shown in Figure 2 has taken from legal institution [3]. Assume, all fraction data has been converted to integer.

Figure 2 The cover used for the example

 

Furthermore, the scale distance s was added to the maximum value of plotted data such that the result can be represented in  bits. Finally, the scale distance s is added to each value of plotted data. The scale distance s transmitted
to the receiver by using private channel. After scale modification process, the modified scale graph is shown in Figure 3. From the scaled chart, the plotted data  code were 118, 121, 123, 124, 121, 122, 123, 124, 124, 127, 130, and 131.

Figure 3 Scale modification illustration

 

Since the maksimum data was 131 which can be represented by 8-bit in binary, then the binary string will be sliced into 8-bit slices as follows:

01001101 01100101 01100101 01110100 00100000
01101101 01100101 00100000 01000000 00110111
01110000      01101101

The process is continued by converting each group of sliced bits into decimal (called as message code) as follows: 77 101 101 116 32 109 101 32 64 55
112 109

 

Then generate a complete sudoku puzzle as shown in Figure 4

Figure 4 Complete Sudoku puzzle

 

The message code (), plotted data code , and complete Sudoku () as shown in Figure 4 is used in this step to yield modulus number () based on this equation

If  then  such that  satisfied this following equation:

If  then  was consisted of two tuple   where

And

The result of generating modulus number is shown in Table I.

 

 

 

Table 1 Result of generating modulus number (x)

118 9 77 551
121 6 101 157
123 3 101 158
124 8 116 140
121 5 32 71
122 2 109 197
123 1 101 (22,28)
124 7 32 37
124 4 64 68
127 1 55 72
130 7 112 114
131 4 109 146

 

After the sender conducted the concealing process, then the sender should transmit some information to the receiver. During the concealing process, there were informations which should be transmitted using public channel such as chart-cover and evil Sudoku puzzle. Instead of only transmitting information using public channel, there were some informations which should be transmitted using private channel such as scale distance, additional clue and modulus number.

 

Reference :

[1] Desoky, A. and Younis, M., Graphstega: graph steganography methodology, Journal of Digital Forensic Practice, Taylor & Francis, 2008, 2, page 27-36

[2] Sari, Aprianti Nanda, and Ari Moesriami Barmawi. “Modified Graphstega Based on Chart Scale Modification.” Intelligence and Security Informatics Conference (EISIC), 2016 European. IEEE, 2016.

[3] Central Bureau of Statistics Republic of Indonesia. Persentase Rumah
Tangga menurut Provinsi, Daerah Tempat Tinggal, dan Jenis Kelamin
Kepala Rumah Tangga, 2009-2013
, http://bps.go.id/linkTabelStatis/view/
id/1604, 2015