
Research Article


An Automatically Changing Feature Method based on Chaotic Encryption


Wang Li,
Gang Luo
and
Lingyun Xiang



ABSTRACT

In practical applications, in order to extract data from the
stego, some data hiding encryption methods need to identify themselves. When
performing data hiding, they embed some specific logo for selfidentification.
However, it is unavoidable to bring themselves the risk of exposure. Suppose
each hidden method has a corresponding logo S and the attacker has a logo set
Φ which consists of some hidden methods’ logos. Once he find the logo S
which matches a logo in Φ, he can easily recognize the very method. To
solve this problem, we propose a method based on synchronization to hide the
specific sign or logo. First, the sender generates a key using a public variable
parameter which is always changing from time to time. Then, we can calculate
the hidden data’s location in the cover from the key. According to the locations,
we can embed the logo into the cover. As the public parameter is changing from
time to time, each transmission of hidden data has a unique location sequence.
When the stego reaches its receiver, according to the public parameter, the
receiver could generate the key and get the hidden data’s location to extract
the secret data correctly. Experimental results verify that the data hiding
method performs well and hardly has impacts on the cover’s quality and has little
impacts on the robustness, imperceptibility and capacity of the original stegocover.
Besides, it is able to recover the key with linear time complexity when the
critical information which is used to generate the key is missing.





Received: April 18, 2014;
Accepted: June 19, 2014;
Published: July 02, 2014


INTRODUCTION Data hiding techniques are mainly about researching on hiding data into cover. Avoiding being noticed by adversaries is their main purpose. Until now, it consists of Steganography, Digital Watermark, Visual Cryptography and etc. With data hiding techniques, secret communications become possible. Data hiding techniques are being applied to military, business, finance areas, such as conveying military intelligence, the privacy data of ebusiness, secret contracts between business partners and so on. Besides, data hiding techniques are utilized for identification, copyright protection, integrity authentication and so on. Nowadays, main researches on data hiding techniques can be roughly divided into three areas: Spatial domain, transform domain and file format. For spatial domain methods, LSB and LSB matching are the most commonly used algorithms. Researches on data hiding in spatial domain focus on capacity improvement, imperceptibility advancement and resistance against steganalysis (Zhang, 2011; Omoomi et al., 2011; Geetha et al., 2011; Zeki et al., 2011; Zanganeh and Ibrahim, 2011; Rajagopalan et al., 2014). For transform domain methods, though data hiding methods are more complicated, they often achieve better robustness than spatial domain ones. The QIM and adaptive embedding algorithms (Wang et al., 2002; Podilchuk and Zeng, 1998) are typical of these methods. There are also some researches (Cancellaro et al., 2011; Lian et al., 2007; Khan et al., 2011; Bouslimi et al., 2012) on techniques about reversible watermarking of encrypted media. Some (Qiao and Nahrstedt, 1998; Shi and Bhargava, 1998; Wu and Kuo, 2005; Qiu and Wang, 2012) are on encryption techniques for the compressed image and some (Chen et al., 2003; Abdulfetah et al., 2010) focus on robustness and imperceptibility. Style of file (such as XML, HTM, PDF, etc.) can be utilized in data hiding as well (Bo et al., 2009; Shahreza, 2006; Cantrell and Dampier, 2004; Liu and Tsai, 2007; Liu et al., 2008), according to the character of the file’s style. Such techniques are based on specific style of files which are different from each other.
In some cases, when extracting hiding information, we always needs a logo to mark the specific steganography algorithm. This brings great unsafety to the hiding system. For example, the software ffencode (Schroder, 2005) embeds a fixed sequence of “011001100110011001100011011011110110010001100101” into the carrier without any hiding processing. As long as an attacker calculates this specific sequence, he or she can confirm that the carrier he or she catches is encrypted by ffencode. Unfortunately, there are few researches on how to resolve such problems. Our purpose is to resolve this kind of problems. We put forward a method that can make the logo’s appearance different from time to time. Meanwhile, it makes sure that the receiver can extract the logo with 100% accuracy and recognizes the steganography tool correctly. And when the key is missing, it can recover the key with limited time cost in linear time complexity. METHODOLOGY Problem statements and analysis: To hide the specific logo, we need to encrypt it first. However, a proficient can get the logo with Chosenplaintext attack when the logo is encrypted by the same key all the time. To avoid this, we need a key that can automatically change itself. A changing mechanism is what we need. Using an automatically changing key, the key of the sender’s must synchronize with the receiver’s. When sender’s key doesn’t match the receiver’s, we need a mechanism to restore the key’s synchronization. Considering all the requirements listed above, we take system time as the changing factor of the key. The system time has 4 key important natures: Linearity, uniqueness, finiteness in a finite interval and dynamics. The uniqueness and dynamics nature of time are necessary to the key’s automatically changing. And in case of being damaged or tampered, we need an efficient way to recover the key. The finiteness and linearity nature of the time can be used to recover the key. We also need a method to hide the encrypted logo. Comparing to hiding a logo in a fixed position, it is safer to hide the logo in random positions. The chaotic system performs well in producing pseudorandom sequences. Among chaotic mappings, the skew tent mapping has excellent pseudorandomness and it obeys uniform distribution. With the skew tent mapping, we calculate the embedding locations so that it has the ability to resist statistical analysis. Merits of the method: •  Choosing different keys from time to time 
• 
Being able to figure out the missing or damaged key in linear time complexity 
• 
Resistance to statistics analysis 
Description of the method: First, P stands for plaintext, VI denotes the initial vector of 128 bits. T is the time that generated by the computer system and its precision is second. In this study, we choose the format of time as “YYYYMMDDHHMISS”. Specifically, we encrypt the time T with MD5 algorithm (128 bits) and get a sequence of hex numbers: T_{md5} = MD5(T), T_{md5} = t_{md5_0}t_{md5_1}…t_{md5_15}. S is the logo that need to be encrypted and its length is l bytes (each character is 1 byte and 1 byte = 8 bits). VI and S are divided into the following groups:
(Each vi_{i} or s_{i} is 8 bits). According to T_{md5} and VI, the system generates the secret key K in the following way:
The logo S is encrypted to M in the following way:
The M is what we need to hide into the carrier. Its length is the same with S, the length of M is also l bytes. And T^{(j)} is the jth created time and the corresponding secret key is K^{(j)} (j is an integer). T is different from time to time and the K^{(j)} is created by T^{(j)} nd VI. When i ≠ j, K^{(i)} ≠ K^{(j)}. Logistic map is often used to design random encryption system. Logistic mapping not only has low computing complexity but also has good pseudorandom performance. However, the skew tent mapping’s distribution is more uniform than logistic mapping’s (Xiang et al., 2008) and it has stronger pseudorandomness as well (Masuda and Aihara, 2001). Therefore, the chaotic sequence generated by the skew tent mapping is better for cryptographic purpose:
We set r (r is 8 bits) as follows:
To get the hidden data’s location by skew tent map, x_{0}, p, N is initiated as follow:
We embed the encrypted logo M into a cover grayscale I, M is l bytes and the length of the cover I is L bytes. Suppose there is a logo set Φ = {S_{0}, S_{1}, S_{2}ÿS_{n1}} and the l_{div} = max{length(S_{i})}+ε, ε+N and ε is agreed on by both the sender and receiver. The cover I is divided into 8l_{div} (l_{div}>l) blocks. There are g(g = ⌊L/8l_{div}⌋) pixels in each block and the block set is denoted as Block = {B_{0}, B_{1}, B_{2}ÿB8l_{div}1} The ith bit of M(b_{m_i}) is embedded into the block B_{i}. To embed the bit b_{m_i} into the block B_{i}, we set d_{i} = ⌊gxx_{i}⌋ as the embedding location of B_{i} and embed b_{m_i} into the d_{i}th pixel of B_{i} (0≤i≤8l_{div}1). Then we convert pixel’s value from decimal to binary, in the form of b_{7}b_{6}b_{5}b_{4}b_{3}b_{2}b_{1}b_{0} (0~255). To hide the bit b_{m_i}, if b_{0} = b_{m_i}, we do nothing to b_{0}, otherwise we replace b_{0} with b_{m_i}. Figure 1 shows the embedding process and the embedding algorithm is as follows:
The sender embed M into I and the original I becomes stegocarrier I_{m}. The receiver already has VI and receives T from the sender. During the extraction phase, he generates K with the T and VI. The receiver gets the sublocation sequence d_{0}d_{1}d_{2}ÿd8l_{div}1 to extract the message M_{M} which contains M. With the K, he decrypts M_{M} and gets the message S_{S} which contains logo S. Figure 2 shows the extracting process and the extracting algorithm is as follows:
 Fig. 2: 
Extracting process 
To extract the hidden logo S, the extracting algorithm needs to extract 8l_{div} bits from I_{m} and get the message M_{M} which is l_{div} bytes. It decrypts M_{M} to the form of S_{S} = S∪S_{e}, S_{e} = s_{l}s_{l+1}ÿsl_{div}1. We compare S_{S} with each logo in the set Φ. If we find that there is a logo S_{i}εΦ and S_{i} = S, then we get the correct logo. Analysis of the algorithm: Both the sender and receiver need to have the same logo set Φ. The algorithm embeds an uncertain logo that is from the logo set Φ into the cover I. Because the receiver doesn’t know which logo the sender selects, to define a fixed length l_{div} is necessary. In this study, l_{div} meets the following requirements: l_{div}≥max{l/l = length(S_{i}), S_{i}∈Φ} Adding a new logo to the set Φ needs to reset l_{div}. There is a difference between embedding and extracting: The T is generated by the system at the sender side while the receiver receives T instead of generating it. And the using of skew tent mapping makes sure that the logo bits are uniformly hidden in the cover. With a dynamic T, the hidden locations are different from time to time. In addition, when T_{c} (system time) is damaged or tampered by some attacker, we still have a chance to obtain it. Suppose we lost T_{c} and we have T_{last} which is got from the last transmission. And we received the M at the real time T_{real}. (T_{c}ε(T_{last}, T_{real}) T here is a integer). We can try each T from either T_{last} to T_{real}, or T_{real} to T_{last}. It is certain that we can deduct the correct T which is equal to T_{c}. And if the searching direction is from T_{last} to T_{real}, we need to set the time cost to Δt_{last}. And if the time interval is from T_{real} to T_{last}, we need to set the time cost as Δt_{real}. In addition, we denote the time cost to locate T_{c} as Δt and Δt≤max{Δt_{last}, Δt_{real}}. And the searching of T_{c} is in a linear way, so the time complexity to find T_{c} is O(Δt). Experiments: Let T_{c} = 20140303122212, VI = 7154A05BCC 3E552D5E5E21BA716A31EF and the images size be 512x512, 512x256 and 256x256. Each image size consists of 456 images. The images we use for experiments are all from http://sipi.usc.edu/database/. Let secret logo be m. Set m = “Hunan University is a good university”. We choose LSB embedding method for the experiments, because it is easy to operate and causes little distortion to the original images. Figure 3 shows the impacts on 1000 locations when T_{c} is changing from T_{c} = 20140303122212 to T_{s} = 201403031 22213. y is the degree of location’s difference between T_{c} and T_{s}. d_{c_i} is the ith location generated by the T_{c}, d_{s_i} is the ith location generated by T_{s}. y_{i} is the degree of difference between d_{c_i} and d_{s_i}. y_{i} = d_{c_i}d_{s_i}/8l, 8l is the bit length of S, iε{0, 1, 2…8l1}. The average degree of difference from 8l locations is:
In this experiment, we calculate the = 33.99%.
 Fig. 3:  Key sensitivity to initial value 
 Fig. 4:  Cost time for T’s recovery 
Table 1:  Average of MSE and PNSR  
Here, we count the changed locations and unchanged ones. When the ith location is changed, then z_{i} = 1, otherwise, z_{i} = 1. Then we calculate the changing rate of the locations when time changes from T to T_{s}. We set rc as the global changing rate:
Testing 456 images, we find the average rc is Figure 4 shows the time cost from different starting position when T_{c} = 22:12 is the correct solution. And from the figure, we can see that the time cost to find the exact T = T_{c} is linear. Δt = T_{x}T_{i}, the value of the Δt is determined by T_{x}. And the longer the logo is, the steeper the line is. It proved that the searching for the missing key cost is O(Δr). Generally, a logo is short, embedding it hardly causes distorsion to the cover. There are 3 kinds of image size, each size consists of 456 images. According to Table 1, we could easily find that, the of each size is very close to 0 and the has a high value that is more than 80. It verifies the fact that embedding the logo has little impacts on original algorithm’s robutness, capacity and invisibility. And we could also conclude from the Table 1 that, the larger the image size is, the less impacts caused by the embedding. DISCUSSION In this study, we analyzed the feasibility of the algorithm. In the process of embedding, we encrypt logo with a dynamic key. Then embed the encrypted logo into cover in a random way. In this way, the attacker has little chance to find the logo. When in extracting process, we need to extract an encrypted message that contains the encrypted logo. We decrypt the encrypted message and get the message which contains logo. In this way, we can use a set of data hiding algorithms which is based on logo, instead of only one. By conducting experiments on testing how sensitive the key to the chaotic mapping’s parameter, we find that the hiding location sequence’s (d_{1}d_{2}d_{3}…) changing rate is close to 100% when T changes 1 bit. When the time T_{c} for generating key is damaged, the algorithm can recover the damaged T_{c} in a linear computation complexity with limited cost. By embedding logos into more than 1300 images of different sizes, measuring by both the MSE and PSNR shows that the algorithm has little impact on the robutness, capacity and invisibility of original one. However, though the proposed algoritm can resolve the risk but there is still an efficient problem. The system time T for K’s generation is not hidden during the message’s transmission, it could be tampered easily. Though there is a way for T’s recovery, it degrades the efficiency of the algorithm to some extent.
CONCLUSION The data hiding software which relies on some fixed logo to identify themselves can perform data hiding and data extracting efficiently. However, the fixed logo may bring great risk to the data hiding algorithm, because it can be easily caught by an attacker especially when the attacker has knowledge of the algorithm. To solve this problem, this study propose a method to enable the logo to change itself automatically by adding time variable. In theory, each change of the logo is different from each other. And the method hides the logo bit by bit with a random sequence which is generated by the skew tent mapping. The random sequence is used to calculate the bit’s hiding location. In this way, the attacker can hardly extract the logo even though he has the knowledge of the data hiding algorithm. Furthermore, when the time is damaged, there is a remedy for the receiver to generate the key in limit time cost. Though the proposed method resolves the problems brought by the fixed logo, there is still room for improvements. The future study will focuse on improving the robustness of the algorithm. Besides, we need to find an efficient way to protect the system time which is exposed during the transmission. ACKNOWLEDGMENTS This study was supported by National Natural Science Foundation of China (No. 61202439, 61103215) and the Fundamental Research Funds for the Central Universities of China.

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