Gravity Search Algorithm and Transposition Scheme
Trong-The Nguyen
1,2
, Truong-Giang Ngo
3 (B)
, Thi-Thanh-Tan Nguyen
4
, Chi-Kien Tran
5
, and Ngoc-Cuong Nguyen
6 1
School of Computer Science and Mathematics, Fujian University of Technology, Fujian, China 2
University of Management, and Technology, Haiphong, Vietnam 3
Faculty of Computer Science and Engineering, Thuyloi University, 175 Tay Son, Dong Da, Hanoi, Vietnam
Information Technology Faculty, Electric Power University, Hanoi, Vietnam 5
Hanoi University of Industry, Hanoi, Vietnam 6
Department of Cyber Security and Counter High-Tech Crime, Ministry of Public Security, Hanoi, Vietnam
Abstract. This paper suggests a new solution to conceal text messages in media by hybridizing a meta-heuristic algorithm of the Gravity search algorithm (GSA) and transposition method. Several stages are implemented, namely the concealment stage, extract stage, and evaluation metrics, whereas cover text and message text are split into blocks,and each blockcontains one letter, relying onthe fitness value of related notesboth of secret information and covermessage. Thebest positions of the letters are taken optimization by the adjusting GSA that is used to hide the confidential message. The steganography process is then carried out through the transposition process between the secret and cover message. While in the extraction stage, the fitness value of steganography message letters is found by using GSA to determine the positions that represent the secret letters. Experimental results of the proposed scheme are compared with the other in the literature which shows that the proposed approach presents robust security, provides high capacity and resistance against several steganalysis attacks.
Keywords: Gravity search algorithm·Information hiding·Transposition scheme
1 Introduction
There is no doubt that steganography has become a critical security science that is widely applied in communication and transactions in everyday life [1]. The transmis- sion of a message on the Internet, e.g., for communication or transactions has to count on some issues such as data security, copyright control. Secret communication systems for safety information and tips are needed [2]. Data hiding attempts to conceal hidden
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 J.-S. Pan et al. (eds.),Advances in Intelligent Information Hiding and Multimedia Signal Processing, Smart Innovation, Systems and Technologies 212,
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information in media such as a form that can not be seen, and the covering mask is complicated to decode [3]. The hiding information technique usually includes several subdisciplines within the field of information security, such as watermarking, digital signatures, steganography, and cryptography. Each of these methods has its function, with benefits and drawbacks. Watermarking is commonly used to safeguard the copy- right, and digital signatures are frequently used to protect digital signatures [4], while steganography and cryptography are widely used to encrypt digital messages [5]. The cryptography scrambles the letters so that it is not easily understandable. Steganography and cryptography diverge. Cryptography aims to provide encrypted communication by transforming the data into a shape that an eavesdropper can not easily comprehend.
The practice of covering text in another medium is referred to as a steganography intended to insure contact. This means unauthorized users are unable to get the privately used hidden message [6]. As stated, text steganography was considered to be the most challenging technique compared to audio and picture one due to inadequate redundant data, popular in other carriers, rendering most of its technology with inadequate capa- bility and security [7]. The right to add hidden data to protect archives, though, relies on the existence of redundant or irrelevant information inside them. The characteristics of a cover file which is altered, exploited, or updated during the embedding process will remain invisible to unauthorized users [8].
To cover text-in-text communications, including format based, random and math- ematical generations, and linguistic approaches, three major categories are employed.
Format based is the covering message that in the case of the terms and phrases will not be changed; changes will only be made to the gaps between terms, lines, or/and para- graphs using special characters, i.e., white space steganography. The cover text message is automatically generated by random and mathematical generation methods; it does not require an existing cover code. Throughout the creation process, a hidden message is used for the created cover message [9].
The linguistic approach is used to conceal a message in another message based on the cover message’s linguistic structure with the punctuation marks or the semantic terms as a way to hide the letter, letter, which has two key forms which are linguistic structure and semantic approach. The techniques have drawbacks, such as the data size depends on the number of the cover message’s punctuation marks and failed to protect the message sent when the outsider attempts to find the original message by swapping each word to the original one using the semantic algorithms [10]. One of the promising ways to solve complex problems is the metaheuristic algorithm [11].
Many metaheuristics are built on the basis of natural phenomenal inspirations such as synthetic annealing (SA) [12], genetic algorithm (GA) [13], and particle swarm opti- mization (PSO) [14]. The Gravity Search Algorithm (GSA) [15] is a recent metaheuristic algorithm which is inspired by the actual gravity phenomena. This paper introduces a new solution for text steganography through the combination of GSA and the transposi- tion process. The solution suggested seeks to solve the aforementioned inconveniences of previous approaches.
2 Gravity Search Algorithm (GSA)
GSA algorithm is taken inspiration from the physical phenomenon of gravity, in which planets interact through the action of gravity [15]. The planets with large mass are a more attractive force. The planets with a small mass approach it and the planets with large mass occupy the central position, which is, the optimal position seeks, which is the search principle of the GSA algorithm. The GSA algorithm will communicate with each other, to guide planets to the optimal worlds. The mathematical model of the GSA algorithm can be expressed by a series of expressions as follows.
X
d
i (t+1)=X
d
i (t)+Vel
d
i (t+1) (1)
whereX
d
i (t), andVel
d
i(t), respectively, represent the position, velocity. The VelocityVel is calculated as follows.
Vel
d
i (t+1)=rand ·Vel
d
i (t)+a
d
i (t) (2)
wherea
d
i(t)represent acceleration, and be expressed as follows.
a
d
i(t+1)=F
d i (t)/M
d
i (t) (3)
whereF
d
i (t), andM
d
i (t),respectively, represent gravitational force, and position of the ith planet in thed—dimension during thetth iteration. The magnitude of the resultant force and the mass of inertia. The calculation mathematical of inertia mass force is expressed in the gravity inspiration as follows. The calculation of the resultant force is expressed as follows.
F
d ij(t)=
G(t)·Mi(t)·Mj(t) Rij(t)+ε
· X
d
j (t)−X
d
i (t) (4)
F
d i (t)=
N
j=1,j=i
randj·F
d
ij(t) (5)
In the formula:N is the total number of particles;F
d
ij(t)represents the gravitational force of particlejto particlei;randjis a random number of [0, 1];Rij(t)is the Euclidean distance between particleiand particlej;εis a constant with a small value;G(t)is the gravitational constant. The calculation formula is given as follows.
G(t)=G0·exp(−α·t/maxt) (6)
Among them:G0 andαare constants;tis the current number of iterations;maxt is the maximum number of iterations.The inertial mass of the particles in Eq. (4) can be obtained based on the following equations:
mi(t)=
fiti(t)−worst(t) best(t)−worst(t)
(7)
Mi(t)=mi(t)
N
j=1
mj(t) (8)
where fiti(t)represents the fitness value of the ith particle at thetth iteration. For the image multi-threshold segmentation problem for which the maximum value is obtained, best(t)and worst(t)are obtained based on following as.
best(t)=max fitj(t),j ∈ {1,2, . . . ,N} (9) worst(t)=min fitj(t),j ∈ {1,2, . . . ,N} (10)
3 A Solution to Conceal Text Messages
Steganography’s main task is to thwart the unauthorized user from knowing that some- thing is hidden even if he/she can get the stego cover. We use the invisible character structure (white space) to protect text in the text, where the secret message is hidden in the cover medium’s white space position, the results show that the method is highly confidential because it uses functional complexity to avoid unauthorized users. The lim- itation of this technique is that the binary string length must be less than or equal to the number of spaces for words. This paper proposed a rule-based steganography technique for the selection of privacy channels in the spatial domain. Steganography is commonly used in Internet communication because of its utility, where it is not encoding infor- mation but rather hiding. The presence of it that makes the hacker’s task difficult. Any characteristics in a production framework are as follows. Using the method of transpo- sition between the secret message and the cover message, that means that there is no addition, deletion, or change. By applying GSA, the best locations of the letters in the cover medium are optimized, and the method is used for combining with hiding pro- cessing in the transposition. The new scheme has high flexibility relative to test results and improves robustness.
3.1 Objective Function
The objective function is as fitness function would be drawn the relationship between the secret message and cover medium, i.e., message. LetA(i) be the ASCII code represents for that letter;S(i) be the sequence of the letter represents in the set of letters;L(i) be the location of letters and the rand is random value distribution in the range [0,1]. The relationship of each character in the cover message and secret message that uses find out the fitness value in the process of steganography by the planets of GSA, where fitness considered one of the important stages in the GSA algorithm. The objective function is expressed as follows.
Fitness(i)=
A(i)∗S(i)
iL
∗rand (11)
where Aand S are ASCII character codes and the sequence of the letter in the set of characters;Lis the location of letters, and therand is random distribution∈[0–1].
3.2 The System Design
The design of the proposed scheme consists of three phases of steganography process- ing, such as embedding, extracting process, and evaluating criterion. Figure1shows a flowchart of the design of the proposed scheme. The phases of embedding, obtaining process, and evaluating tests are expressed as follows.
Fig. 1. Flowchart of the design of the proposed scheme (embedding, extracting process, and evaluating criterion)
• Embedding process—the positions that are used to hiding that are determined by adjusting GSA, as well as the process of embedding text in the text by the transposition method is achieved.
• Extracting process—the extraction process includes extract the secret message from the stego message by applying GSA.
• Evaluation criterion—comparing the cover message and stego message, if there is no difference between them, then the steganography process will be transporting a letter with another letter. Therefore, an unauthorized user can’t suspect that something is hidden in the stego message even if it uses all statistical meatuses and detection techniques or makes a comparison between them through the see or by size.
4 Experimental Results
The obtained results of the proposed scheme of (GSA) [15]are compared with the simu- lated annealing (SA)[12], genetic algorithm (GA)[13], and particle swarm optimization (PSO)[14] methods for hiding information respectively. The number of planets as agents
of the algorithms is set toNequal to 60, and the maximum number of iterations isMax- genis set to 1000; the gravitational beginning G0 and the step factorαare set to 10 and 0.1, respectively. The other parameters set for the algorithms listed as follows:c1=0.5, c2=1.5, inertia weightω=1.2, particle velocityV ∈[−5, 5], mutation ratepr is set 0.05, and cross-ratecr set to 0.6.
Figure2shows an example of the secret message, and the secret message is used for testing the proposed scheme.A secret message with size 13.9 KB that is used to be hidden into the secret message. The secret message consists of 4 words with 18 characters. Table 1listed the fitness calculated for each letter by using Eq. (8). The cover message with a size of 19.2 KB, which consists of 114 words with 683 character.
Fig. 2. An example of the secret message and the secret message
Table 1. Initialization of fitness values for the secret message
Sequence No. Characters Fitness value Sequence No. Characters Fitness value
1 A 0.436 10 Y 0.931
2 N 0.910 11 S 0.562
3 N 0.910 13 E 0.672
4 I 0.293 13 c 0.155
5 N 0.910 14 u 0.091
6 H 0.672 15 r 0.756
7 i 0.293 16 i 0.293
8 s 0.562 17 t 0.290
9 m 0.435 18 y 0.931
Several parameters are used to measure the experimental results that are listed as follows: Entropy, Energy, Variance, Squared Pearson Correlation Coefficient (SPCC), Structural Similarity Index Metric (SSIM), Signal to Noise Ratio (SNR), Average,
Euclidian distance, Chi-square [16]. Table 2 depicts the comparison of obtained val- ues between the cover message and secret message by applying calculations of several measurements.
Table 2. Comparison of obtained values between the cover message and stego message by using several measurements
Parameters of measurements Derivative rate Cover message Secret message
Entropy 0.02 4.1177 4.1175
Average 0.09 108.7754 108.7745
Energy 0.02 2.5617 2.5615
Variance 0.02 98.5799 98.5797
SNR 0.02 1.9556 1.9554
Chi-square,p 0.02 0.0977 0.0975
SSIM 0.02 0.9977 0.9975
SPCC 0.02 0.9977 0.9975
Euclidian distance 0.00 0.0001 0.0001
Figure3shows the comparison of the obtained results of the proposed scheme of GSA with the SA, GA, and PSO methods for hiding information, respectively. Subfigures:
(a) Comparison of the received error values; (b) Comparison of the converge rates. It is clearly seen that the obtained results of the proposed scheme of GSA for information hiding are better than the other methods in terms of converge rate and accuracy rate.
(a) Comparison of converge rates (b) Comparison of obtained error values
Fig. 3. A comparison of the obtained results of the proposed scheme of GSA with the SA, GA, and PSO methods forhiding information, respectively. Subfigures:a Comparison of obtained error values;bComparison of converge rates
5 Conclusion
In this paper, we presented a solution to improving the scheme of hiding messages in text messages by hybridizing the gravity search algorithm (GSA) and the transposition scheme. Several stages are implemented, namely the hiding stage, extract stage, and evaluation metrics. Both cover text and message text are split into blocks, and each block contains one character according to its fitness value of related notes both of secret information and cover message. The GSA adjusting to hide the confidential message takes optimization of the character’s best positions. The process of steganography is then carried out through the process of transposing between the message of secrecy and cover. The fitness value of steganography message letters is found while in the extraction stage by using GSA to determine the positions which represent the secret letters. In the literature, experimental findings of the proposed scheme are compared with the other show that the proposed solution offers robust protection, provides high potential, and resistance against multiple steganalysis attacks.
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