This document discusses using Vernam cipher conjugation to increase security in Bit-Plane Complexity Segmentation (BPCS) steganography. BPCS divides an image into segments and bit-planes to hide data, but the standard pattern is not secure. The author proposes using Vernam cipher to encrypt each bit-plane before insertion. This would modify the bit-plane pattern randomly, increasing security by obscuring the stored data. An example demonstrates the BPCS process of dividing an image segment into bit-planes and calculating their complexity values. Combining Vernam cipher encryption of the bit-planes with BPCS storage in the image is described as a way to securely enhance the steganographic technique.

1. Vernam Conjugated Manipulation of Bit-Plane
Complexity Segmentation
Andysah Putera Utama Siahaan
Universitas Pembangunan Panca Budi
Jl. Jend. Gatot Subroto Km. 4,5 Sei Sikambing, 20122, Medan, Sumatera Utara, Indonesia
andiesiahaan@gmail.com
ABSTRACT
Bit-Plane Complexity Segmentation is one of the steganographic technique is often performed to conceal data. But in BPCS
method, a pattern that is used is not a classified anymore. Conjugation at the informative bit-plane is to change the bit-plane to
chiper-form bit-plane that can keep secret message. Modifying bit-plane pattern for each bit-plane is a technique for increasing
the security of the vessel image. Vernam can be used to modify the bit-plane with the predetermined blocks conjugation. Data
security would be increased by applying this method.
Keywords – Steganography, BPCS, Vernam, Cryptography
I. INTRODUCTION
Steganography is often done to send a file with a high
comfort, thereby reducing suspicion of files that are sent or
vessel image. BPCS (Bit-Plane Complexity Segmentation) is
one technique that is used to store information in an image,
which is called the image of the vessel image. This technique
uses imagery division into segments which are then each
segment will be divided into several bit-plane. However, the
possibility that data can be solved or attack so that data can be
retrieved by the irresponsible. The pattern used in BPCS is to
store data by grouping bit corresponds to the index with a 8x8
pattern forming where each sequence of eight characters will
be compiled into a binary message blocks and form each bit-
plane.
BPCS weaknesses can be seen from the preparation of the
information in 8x8 pattern. If complexity used is determined, it
is not impossible vessel information stored in the image can be
easily retrieved. Typically used complexity revolves around the
value of 0.3, and this value has become a commonly used
method of this BPCS. To anticipate unwanted things, the binary
value inserted into the vessel should be further enhanced image
security. If we know value and the data is retrieved from the
vessel image, the Vernam Cipher will play a role in protecting
the arrangement of bits of data on the bit-plane BPCS.
Vernam Cipher will make changes to the data bits to be
inserted in the vessel image. These bits will be given the
exclusive or procedure, so that the data stored in the image file
has been encrypted beforehand. This method is very
lightweight and faster to use than other methods that have to
use a lot of math calculations.
II. THEORIES
Eiji Kawaguchi and R. O. Eason introduce the BPCS
technique to be used in uncompressed color images documents.
The image of the document is divided into several segments
with a size of 8x8 pixels of each segment. In the 8-bit image of
the document, each segment has eight bit-planes representing
the pixels of each of these bits. The process of division of
segment 8x8 pixels into eight bits is called the bit slicing plane.
Representation of bit plane is PBC system (Pure Binary Code).
In BPCS, the insertion process is performed on a bit plane
system with CGC (Canonical Gray Code) because the process
of slicing bits at CGC is better than in PBC. Bit plane with PBC
representation is converted into bit-plane with CGC
representation.
The process of inserting a message is carried on the segments
that have high complexity. This is called noise-like region. In
these segments, the insertion is not only performed on the least
significant bit, but on the whole noise-like bit-planes.
Therefore, the BPCS technique, data capacity can optimumly
reach 50% of vessel image size.
For further explanation, we can see the process from original
image to bit-plane slicing on Figure 1. The image at the top-left
is the original image which has converted to 8 bits graycolor.
Each segment is divided into 8x8 pixel, where each pixel is
converted to 8 bit binary system. Every index on bit is
concatenated in a new single piece of bit-plane. So we have
eight bit-planes which are saving the information of every bit.

2. Figure 1 : The Process of Bit-Plane
Conjugation is a technique to maintain bit-plane in noise-like
form. Suppose a black and white image sized 8x8 pixel P has a
white background color and foreground color black. W is a
pattern with all pixels white. Suppose a black and white image
sized 8x8 pixel P has a white background color and foreground
color black. W is a pattern with all pixels white and B is the
pattern with all black pixels. Wc and Bc is a chessboard pattern,
with a pixel on the top left of the white on black on the wc and
Bc. P * is the conjugate of the image P shown in Figure 2.
Figure 2 : Conjugation Block
The Vernam Cipher is a crypto technique by combine each
character of plaintext with repeated key characters from a key
stream. The key can be from random key or regular key by
inserting decided characters. If a truely random key stream is
used, the ciphertext will be random too. By combining Vernam
and BPCS will make the concealment powerful. Attacker will
be fooled by a set of bits obtained at the time of interception.
This make the combination of two methods work together.
Basic Vernam formula is shown by this following equation.
𝐶𝑇 𝐵𝑖𝑡𝑃𝑙𝑎𝑛𝑒 = 𝑃𝑇 𝐵𝑖𝑡𝑃𝑙𝑎𝑛𝑒 𝑥𝑜𝑟 𝐾𝑒𝑦 BitPlane (1)
Where:
CT BitPlane : Set of bits of aftercode message
PT BItPlane : Set of bits of original message
Key BitPlane : Set of bits of password
III. IMPLEMENTATION
Let's look at the next example. The following table shows
the value of light intensity which converted to pure decimal
binary code.
PBC Pixel Segmen 1
0 1 2 3 4 5 6 7
0 127 27 29 39 49 65 67 69
1 31 52 12 1 7 0 1 10
2 23 29 24 28 37 44 41 21
3 9 14 20 35 32 44 34 1
4 54 44 63 47 59 85 60 74
5 117 91 121 169 186 185 203 190
6 170 181 193 209 208 213 216 235
7 200 198 179 184 198 187 199 247
Table 1 : 8x8 pixel of Image Light Intensity
The data above is cut from image light intensity. We can see
each segment contains 64 pixels. The light intensity is
measured from 0-255 as a binary system. The PBC form must
converted to CGC to remap the subpixels in order to perfom the
message insertion. Tabel 2 and 3 show the comparison of both
form.
PBC (Pure Binary Code)
0 1 2 3 4 5 6 7
0 01111111 00011011 00011101 00100111 00110001 01000001 01000011 01000101
1 00011111 00110100 00001100 00000001 00000111 00000000 00000001 00001010
2 00010111 00011101 00011000 00011100 00100101 00101100 00101001 00010101
3 00001001 00001110 00010100 00100011 00100000 00101100 00100010 00000001
4 00110110 00101100 00111111 00101111 00111011 01010101 00111100 01001010
5 01110101 01011011 01111001 10101001 10111010 10111001 11001011 10111110
6 10101010 10110101 11000001 11010001 11010000 11010101 11011000 11101011
7 11001000 11000110 10110011 10111000 11000110 10111011 11000111 11110111
Table 2 : Pure Binary Code Segment
CGC (Canonical Gray Code)
0 1 2 3 4 5 6 7
0 01000000 00010110 00010011 00110100 00101001 01100001 01100010 01100111
1 00010000 00101110 00001010 00000001 00000100 00000000 00000001 00001111
2 00011100 00010011 00010100 00010010 00110111 00111010 00111101 00011111
3 00001101 00001001 00011110 00110010 00110000 00111010 00110011 00000001
4 00101101 00111010 00100000 00111000 00100110 01111111 00100010 01101111
5 01001111 01110110 01000101 11111101 11100111 11100101 10101110 11100001
6 11111111 11101111 10100001 10111001 10111000 10111111 10110100 10011110
7 10101100 10100101 11101010 11100100 10100101 11100110 10100100 10001100
Table 3 : Canonical Gray Code Segment

3. Figure 3 : Pure Binary Code and Canonical Gray Code Images
Figure 3 shows the difference of PBC image and CGC
image. The CGC turns the pixel by seeing the next bit of light
intensity. After the CGC values are obtained, we divide the
segment into eight bit-planes and categorize the same index of
bit position into the same bit-plane. Table 4 shows the result of
divided-bit-planes.
Bit Plane 1 9 0,080357143
0 1 2 3 4 5 6 7
0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0
3 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0
5 0 0 0 1 1 1 1 1
6 1 1 1 1 1 1 1 1
7 1 1 1 1 1 1 1 1
Bit Plane 2 33 0,294642857
0 1 2 3 4 5 6 7
0 1 0 0 0 0 1 1 1
1 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0
3 0 0 0 0 0 0 0 0
4 0 0 0 0 0 1 0 1
5 1 1 1 1 1 1 0 1
6 1 1 0 0 0 0 0 0
7 0 0 1 1 0 1 0 0
Bit Plane 3 34 0,303571429
0 1 2 3 4 5 6 7
0 0 0 0 1 1 1 1 1
1 0 1 0 0 0 0 0 0
2 0 0 0 0 1 1 1 0
3 0 0 0 1 1 1 1 0
4 1 1 1 1 1 1 1 1
5 0 1 0 1 1 1 1 1
6 1 1 1 1 1 1 1 0
7 1 1 1 1 1 1 1 0
Bit Plane 4 48 0,428571429
0 1 2 3 4 5 6 7
0 0 1 1 1 0 0 0 0
1 1 0 0 0 0 0 0 0
2 1 1 1 1 1 1 1 1
3 0 0 1 1 1 1 1 0
4 0 1 0 1 0 1 0 0
5 0 1 0 1 0 0 0 0
6 1 0 0 1 1 1 1 1
7 0 0 0 0 0 0 0 0
Bit Plane 5 61 0,544642857
0 1 2 3 4 5 6 7
0 0 0 0 0 1 0 0 0
1 0 1 1 0 0 0 0 1
2 1 0 0 0 0 1 1 1
3 1 1 1 0 0 1 0 0
4 1 1 0 1 0 1 0 1
5 1 0 0 1 0 0 1 0
6 1 1 0 1 1 1 0 1
7 1 0 1 0 0 0 0 1
Bit Plane 6 52 0,464285714
0 1 2 3 4 5 6 7
0 0 1 0 1 0 0 0 1
1 0 1 0 0 1 0 0 1
2 1 0 1 0 1 0 1 1
3 1 0 1 0 0 0 0 0
4 1 0 0 0 1 1 0 1
5 1 1 1 1 1 1 1 0
6 1 1 0 0 0 1 1 1
7 1 1 0 1 1 1 1 1
Bit Plane 7 57 0,508928571
0 1 2 3 4 5 6 7
0 0 1 1 0 0 0 1 1
1 0 1 1 0 0 0 0 1
2 0 1 0 1 1 1 0 1
3 0 0 1 1 0 1 1 0
4 0 1 0 0 1 1 1 1
5 1 1 0 0 1 0 1 0
6 1 1 0 0 0 1 0 1
7 0 0 1 0 0 1 0 0
Bit Plane 8 56 0,5
0 1 2 3 4 5 6 7
0 0 0 1 0 1 1 0 1
1 0 0 0 1 0 0 1 1
2 0 1 0 0 1 0 1 1
3 1 1 0 0 0 0 1 1
4 1 0 0 0 0 1 0 1
5 1 0 1 1 1 1 0 1
6 1 1 1 1 0 1 0 0
7 0 1 0 0 1 0 0 0
Table 4 : Bit-Planes

4. Each bit-plane is calculated to obtain the value of
complexity. The complexity is counted from how many times
the bit change from 0 to 1 and from 1 to 0. The maximal bit
change value of 8x8 block is 112. The formula to calculate the
complexity is shown on equation 2.
𝛼 =
𝑘
𝑛
Where:
𝛼 : Complexity
k : Total bit change
n : Maximum change of 8x8 bit-plane
Table 5 shows the complexity of all bit-planes. We have to set
the limitation between informative and noise-like region. The
limit is called treshold. Basically, the standard value of treshold
is 0.3 but we can modify as needed. The modification is often
performed to avoid the informative area or to add the noise-like
area. The n value is set to maximum that is 112.
Bit-Plane Bit Change Complexity
1 9 0,080357142857
2 33 0,294642857143
3 34 0,303571428571
4 48 0,428571428571
5 61 0,544642857143
6 52 0,464285714286
7 57 0,508928571429
8 56 0,500000000000
Table 5 : The Complexity of Bit-Planes
From table 5, bit-plane number 1 and 2 are informative regions.
These bit-planes cannot be inserted by message because the
value of complexity is below the treshold. So the insertion is
skipped to the next bit-plane.
Assume we want to hide word “ANDYSAH!”. The word
consists of eight characters. It has eight bit-planes. Tabel 6 and
7 shows the original message and the bit-plane.
Char Dec. Biner
A 65 1000001
N 78 1001110
D 68 1000100
Y 89 1011001
S 83 1010011
A 65 1000001
H 72 1001000
! 33 100001
Table 6 : The Original Message
Bit Plane Message
0 1 2 3 4 5 6 7
0 0 1 0 0 0 0 0 1
1 0 1 0 0 1 1 1 0
2 0 1 0 0 0 1 0 0
3 0 1 0 1 1 0 0 1
4 0 1 0 1 0 0 1 1
5 0 1 0 0 0 0 0 1
6 0 1 0 0 1 0 0 0
7 0 0 1 0 0 0 0 1
Table 7 : The Bit-Plane of Message
The Vernam algorithm needs repeated key to make the cipher
text. Now we can see an example for the key. The key is
“SDM21”. The word is repeated until the length of bit-plane is
covered.
Char Dec. Biner
S 83 01010011
D 68 01000100
M 77 01001101
2 50 00110010
1 49 00110001
S 83 01010011
D 68 01000100
M 77 01001101
Table 8 : The Repeated Key
The key itself is converted to bit-plane model as shown on table
9. The bit-plane of key is called conjugation block. BPCS uses
conjugation block to converted informative region to noise-like
region. But now we replace the conjugation block with our own
block which can be set as we wish.
Bit Plane Message
0 1 2 3 4 5 6 7
0 0 1 0 1 0 0 1 1
1 0 1 0 0 0 1 0 0
2 0 1 0 0 1 1 0 1
3 0 0 1 1 0 0 1 0
4 0 0 1 1 0 0 0 1
5 0 1 0 1 0 0 1 1
6 0 1 0 0 0 1 0 0
7 0 1 0 0 1 1 0 1
Table 9 : The Bit-Plane of Key
The bit-plane of message and key must be transformed by
performing the exclusive or (xor). The result from both bit-
planes will be the cipher bit-plane. After all the bit-planes is
encrypted, the bit-planes are restored to its original position and
reconverted to pure binary code before finally rewritten to the
new image.
(2)

5. Cipher Bit-Plane
0 1 2 3 4 5 6 7
0 0 0 0 1 0 0 1 0
1 0 0 0 0 1 0 1 0
2 0 0 0 0 1 0 0 1
3 0 1 1 0 1 0 1 1
4 0 1 1 0 0 0 1 0
5 0 0 0 1 0 0 1 0
6 0 0 0 0 1 1 0 0
7 0 1 1 0 1 1 0 0
Table 10 : The Bit-Plane of Cipher
Table 10 shows the bit-plane after encrypted and table 11 shows
the bit-plane after conversion. We can see that the message is
turned to encrypted message.
Char Dec. Biner
18 00010010
10 00001010
9 00001001
k 107 01101011
b 98 01100010
18 00010010
12
00001100
l 108 01101100
Table 11 : The Cipher Message
V. CONCLUSION
From the calculations above, we can see BPCS can be
combined with encryption. But this encryption method is very
light but powerful. The calculation does not have to use
difficult mathematical operation. The way is just only to remap
the bit-plane by doing the exclusive or with the conjugation. All
we have to do is to find the correct key to produce the
informativeless region.
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