A steganographic approach based on the chaotic fractional map and in the DCT domain
aa r X i v : . [ c s . MM ] A ug A steganographic approach based on the chaotic fractional mapand in the DCT domain
A. Soria-Lorente, E. P´erez-Michel, E. Avila-DomenechTecnology Department, University of Granma, Bayamo, 85100, Granma, [email protected], [email protected] (August 30, 2019)
Abstract
A steganographic method based on the chaotic fractional map and in the DCT domain isproposed. This method embeds a secret message in some high frequency coefficients of theimage using a 128-bit private key and a chaotic fractional map which generate a permutationindicating the positions where the secret bits will be embedded. An experimental work onthe validation of the proposed method is also presented, showing performance in impercep-tibility, quality, similarity and security analysis of the steganographic system. The proposedalgorithm improved the level of imperceptibility and Cachin’s security of stego-system an-alyzed through the values of Peak Signal-to-Noise Ratio (PSNR) and the Relative Entropy(RE).
AMS Subject Classification:
Key Words and Phrases:
Steganography, chaotic fractional map, DCT domain, im-perceptibility, visual quality, security.
With the development of the technologies of information technology and communications andthe rapid growth of network bandwidth, the Internet has turned out to be a much-used channelfor transmitting much information in diverse audio, video, image, and text digital form. Thisinformation can be public or private, in case of private information; it may increase the riskto reveal this information by unauthorized external factors. Thus, there is a real necessity tosafeguard sensitive information against access and illegal manipulation. Currently, the Cryptog-raphy and Steganography offer the level of security required for private communication againsthuman interception. Cryptography provides security to the content of the message whereassteganography conceals the existence of the message itself[39]. Modern Steganography tech-niques offer such security levels. Steganography is the art and science of secret communicationto conceals sensitive information from an intermediary [4, 27]. In addition, in the steganography,the secret message is embedded inside of several cover media, such as text [16, 19, 31, 41], image[21, 25, 32, 51], video [2, 12, 28] and audio [30, 48] files. There are two main criteria by which theperformance of steganographic algorithms can be measured, embedding capacity and detectabil-ity. Therefore, new steganographic algorithms are expected to increase the image capacity and1
INTRODUCTION
In recent years, several digital steganography techniques have been proposed. All of them sharethe idea of inserting secret information into a cover media to generate a stego output. Thereare fundamentally two types of steganographic techniques: techniques in the spatial domain andin the frequency domain [36]. In the frequency domain, are used some transforms, such as thediscrete cosine transform (DCT).In [17], Sahar and Rahman developed a steganographic tool based on the Discrete CosineTransform to embed confidential information about a nuclear reactor. In particular, this tooluses the method of sequential embedding in the mean frequency of the image. On the otherhand, in [6] a new steganographic technique in JPEG images in the frequency domain is shown,which provides high embedding performance while introducing minimal changes to the covercarrier image. This algorithm uses module three of the difference between two DCT coefficientsto embed two bits of the compressed form of the secret message.Recently, in [37], the authors described a steganographic method based on DCT and theentropy threshold technique. This steganographic algorithm uses a random function to select inwhich block of the image the bits extracted from the binary sequence of a secret message will beinserted. Moreover, in another paper, Chowdhuri and others present a steganographic schemebased on a matrix weighted for a color image with a high degree of through the to a balancebetween and imperceptibility. In the paper, AC components are collected from matrices (8 ×
8) ofquantified DCT coefficients of the YCbCr channel. Then, a set of matrices (3 ×
3) are formed tohide secret data. A shared 128-bit secret key controls the gathering of AC components. Finally,the authors demonstrate experimentally that the proposed scheme provides good payload andhigh visual quality compared to existing state-of-the-art methods [13].Chaotic maps are being used in recent years to increase the security of digital steganographicsystems. In secure communications, chaotic maps have some characteristics such as; extremesensitivity to the initial conditions, the expansion of the orbits throughout the space, randombehavior, control parameters, and ergodicity. These specific properties make chaotic maps ex-cellent candidates for steganography and encryption. Hence, some applications of these mapscan be found in the literature, for example:In [20], a secure steganographic method based on the frequency domain is proposed. It allowsyou to hide a secret image in another image randomly using Chaos. The chaotic generator PeaceWise Linear Chaotic Map with disturbance was selected, it has good chaotic properties and it iseasy to implement. To obtain the pseudo-random pixel sequence in which the secret image willbe embedded in its DCT coefficients the chaotic generator was used. Experimental results showthat the proposed algorithm achieves high quality and security. Another case it is presentedin [34], the authors describe a new steganographic scheme in the frequency domain based on achaotic map. In the proposed scheme, they apply DCT on the cover image and collect the ACcoefficients in zigzag order. The process of embedding and extracting the secret message dependson a Piecewise Linear Chaotic Map [24], where its initial condition and control parameters areadopted as secret keys of the designed scheme.
MATHEMATICAL BACKGROUND Guaranteeing the security of long-distance communication is a critical problem. This is particu-larly important in the case of storage and transmission of confidential data in a public networksuch as the Internet. The security of such data communication that is mandatory and vital tomany current applications has been a primary concern, and an ongoing issue since the Internetis open in nature and public by plan [47].It is remarkable that it is impossible to obtain the maximum embedding capacity with anacceptable level of imperceptibility at the same time. So, conciliation must be made betweenimperceptibility and embedding capacity. For different applications, the acceptable equilibriumbetween these two constraints is diverse, depending on the nature of the requirements of theapplication.Thus, in this research, the objective is to reach maximum possible level of imperceptibilityby keeping highest embedding capacity and Cachin’s security of the stego-system.In this paper, a secure and imperceptible DCT steganography method is proposed. It allowsembeds a secrete message in the first eight AC coefficients of high frequency of a cover image,taking into account a 128-bit private key and Chaos Theory. The chaotic generator FractionalChaotic Map was selected. It was used to obtain the pseudo-random position of the previouscollected AC coefficients in which the secrete message will be embedded following LSB substitu-tion. Then, the stego-image is reconstructed. Moreover, its shown an experimental comparisonof the proposed method with respect to existing state-of-the-art methods (Sahar and RahmanMethod [17], Chowdhuri et al. Method [13]., Habib et al. Method [20], and Saidi et al. Method[34]). Finally, the proposed scheme provides high imperceptibility level, strong security andgood embedding capacity compared to existing state-of-the-art methods mentioned above.In addition, the proposed algorithm is implemented in Python 3.7. For the experimentalanalysis several color images with size (512 × Let C be the cover image (gray scale or RGB images) and let K be the set of all the non-overlapping 8 × C , such that C = [ k ∈K B k . (1) MATHEMATICAL BACKGROUND B k be the two dimensional discrete cosine transform. The relationship between B k ≡ DCT and its inverse B k ≡ IDCT (Inverse Discrete Cosine Transform) is given by B ku,v = 4 − σ ( u ) σ ( v ) X ≤ i,j ≤ B ki,j cos (cid:18) πu (2 i + 1)16 (cid:19) cos (cid:18) πv (2 j + 1)16 (cid:19) , (2)to each selected block. Here 0 ≤ u, v ≤ σ ( x ) = √ − for x = 0 and σ ( x ) = 1 otherwise.In addition, the IDCT is given by B ki,j = 4 − X ≤ u,v ≤ σ ( u ) σ ( v ) B ku,v cos (cid:18) πu (2 i + 1)16 (cid:19) cos (cid:18) πv (2 j + 1)16 (cid:19) , (3) From (2) each integer block B k is transformed into a real block B k , which is scaled according tothe quantification matrix Q µ by a compression quality factor µQ µ = χ ( µ )
16 11 10 16 24 40 51 6112 12 14 19 26 58 60 5514 13 16 24 40 57 69 5614 17 22 29 51 87 80 6218 22 37 56 68 109 103 7724 35 55 64 81 104 113 9249 64 78 87 103 121 120 10172 92 95 98 112 100 103 99 (4)where χ ( µ ) = 100 − µ
50 , with 50 < µ < B k by the correspond-ing element in the quantification matrix Q µ , and then rounding to the nearest integer, i.e., thecoefficients of the quantized blocks Θ ku,v are computed by Θ ku,v = round B ku,v Q µu,v ! , ≤ u, v ≤ . (5)Next, it applies the zigzag scan to the matrix of the quantized coefficients (cid:0) Θ ku,v (cid:1) ≤ u,v ≤ , seeFigure 1, with the purpose of aligning frequency coefficients in ascending order, starting fromfrequency zero (DC coefficient) to high frequency components (AC coefficients) see [38, 50]. MATHEMATICAL BACKGROUND Θ ku,v is carried out by B ku,v = round (cid:16) Θ ku,v Q µu,v (cid:17) , ≤ u, v ≤ . (6) Chaotic maps have been used to increase the digital security of steganography. Edward Lorenzdiscovered the first chaotic system in 1963 [26]. Since then, different areas of research in engi-neering, physics and mathematics have been established. The most important specification ofchaos is its sensitivity to initial conditions. If the primary is different but very similar conditionsare chosen, the output of the system will be very different and a pseudo-random string will beproduced. In steganography, chaotic maps are used to find the insertion positions in the coverimage and the bit positions using the least significant bit method. The chaotic signals soundlike noise but are completely safe. This means that if the primary values and the map functionare given, the value of the signal can be reproduced again [18].Recently, several authors [43, 44, 46] have proposed embedding schemes based on chaoticmaps, which are nonlinear system, characterized by a pseudo random behavior and an highsensitivity to initial conditions and control, unpredictability, ergodicity, etc [29]. In this research,it is used the fractional chaotic map proposed in [9], which is defined as follows x ( n + 1) = x (0) + 1Γ( ν ) X ≤ j ≤ n Γ( n − j + ν )Γ( n − j + 1) g ( j, x ( j )) , < ν ≤ , (7)where Γ( x ) is the gamma function [3] and g ( n, x ( n )) is defined in [9]. Thus, the chaotic permu-tation of ̺ = { ̺ , . . . , ̺ n } is determined by( ̺ j ) j ∈P , where P = (cid:8)(cid:4) x ( i )10 mod. n (cid:5) , ≤ i ≤ n (cid:9) . (8) As the cover image is altered to embed the secret data, there will be changes in the coverimage pixel values. Thus, that the changes need to be analyzed since it directly affect the
MATHEMATICAL BACKGROUND (cid:18) Ξ MSE (cid:19) , where MSE = ( mnρ ) − X γ ∈ Γ kC ( γ ) − S ( γ ) k , and C and S are the cover image and the stego image respectively, of size m × n × ρ , with C , S ∈ { , , . . . , Ξ } , and Ξ = max(max( C ) , max( S )).The index set γ = ( ℓ , ℓ , ℓ ) sums over the setΓ = { , . . . , m } × { , . . . , n } × { , . . . , ρ } , where ρ = 1 for gray scale images and ρ = 3 for 24-bit color images. Usually the image quality based on the Human Visual System (HVS) is measured by the Univer-sal Image Quality Index (UIQI), which was proposed by Wang and Bovik in [45]. This measureis universal in the sense that it does not take the viewing conditions or the individual observerinto account [10]. Moreover, it does not use traditional error summation methods [49]. Thedynamic range of UIQI is between -1 and 1. For identical images its value will be 1.UIQI = 4 σ CS σ C + σ S C SC + S , where C = ( mnρ ) − X γ ∈ Γ C ( γ ) , S = ( mnρ ) − X γ ∈ Γ S ( γ ) ,σ C = ( mnρ − − X γ ∈ Γ (cid:0) C ( γ ) − C (cid:1) ,σ S = ( mnρ − − X γ ∈ Γ (cid:0) S ( γ ) − S (cid:1) ,σ CS = ( mnρ − − X γ ∈ Γ (cid:2)(cid:0) C ( γ ) − C (cid:1) (cid:0) S ( γ ) − S (cid:1)(cid:3) , MATHEMATICAL BACKGROUND Image fidelity is a measure that shows a consistent relationship with the quality perceived bythe human visual perception. Moreover, it is a metric that measure the similarity between thecover image C and the stego image S after insertion of the message without any visible distortionor information loss [38]. It is defined by [23, 35, 38]IF = 1 − X γ ∈ Γ ( C ( γ ) − S ( γ )) / X γ ∈ Γ C ( γ ) , The security of a steganographic system is defined in terms of the relative entropyRE ( P C || P S ) = X P C (cid:12)(cid:12)(cid:12)(cid:12) log P C P S (cid:12)(cid:12)(cid:12)(cid:12) , where P C and P S represent the distribution of cover and stego image, respectively. This statisticalmeasure was proposed by Cachin in [11]. Moreover, a steganographic system is said to be X ε -secure if RE ( P C || P S ) ≤ ε , X perfectly secure if RE ( P C || P S ) = 0.Summing up, for the RE ( P C || P S ), the closer the value is to 0, the higher the level of security. In the box plots drawn in Figure 2, the horizontal axis represents the different methods thatare compared, and the vertical axis represents the PSNR values. The upper and lower limit ofthe rectangle are the upper and lower quartiles ( Q and Q ) of test results separately, and thedifference between the upper and lower quartile is the quartile difference IQR. The red line inthe rectangle is the median. The two black horizontal lines at Q + 1 . Q − . PROPOSED SCHEME Figure 2: Blox plot
In this work, the following notations are taken into account: X | ̟ | denote the number of elements of ̟ . X || denote the concatenation. X ∆( η ) denote the function that reorganizes the vector η of length 64 to a matrix of order8, taking into account the zigzag scan order 1. X R( x, β ) denote the function that replaces the Least Significant Bit (LSB) of x ∈ N by β ∈ { , } , see [38]. X R − ( x ) denote the function that extracts LSB of x ∈ N , see [38]. X A \ B denote the set difference of A and B . In this Section its present a DCT steganographic algorithm, which use a 128-bit private key. Inaddition, it is assumed that the sender as well as the receiver hold the same system of 128-bitprivate keys. The secret message is inserted into the cover image C and is extracted from thestego image S by the embedding and extracting algorithm, respectively. PROPOSED SCHEME The Algorithm 2 shows the step by step embedding process. Firstly, the cover image C isdivided into non-overlapping 8 × × × ω . The zigzag scanorder is used to collect the coefficients, see Figure 1. In order to increase the security of thestego system, a 128-bit private key κ is used. From this a 1024-bit sequence is generated usingBLAKE2B [7, 40]. Then, this sequence is expanded to a binary sequence κ with the same lengthof ω . Next, ω = ω (1) || ω (2) || · · · || ω ( i ) || · · · and κ = κ (1) || κ (2) || · · · || κ ( i ) || · · · are partitioned intological sequences of length 64. Then, for each ω ( i ) the secret bits collected from secrete message M = { m ℓ ∈ { , } : 1 ≤ ℓ ≤ |M|} are embedded in LSB of the value of the coefficient ofa particular position ρ i , obtaining a modified 1D-array ω ( i ) . The ρ i positions are determinedby κ ( i ) and chaotic positions generator ( ̺ i ) ≤ i ≤ given by (8), see Algorithm 1. Then, thecoefficient 1D-array ω is reconstructed by collecting all the modified ω ( i ) . After that, a new8 × ω .Applying inverse quantization (6) and IDCT (3) to all 8 × Algorithm 1
ChaoticPositions Input: κ ( i ) , x (0), ν . Output: ρ = { ρ , . . . , ρ } L = { , . . . , } Given x (0) and ν , get chaotic permutation ̺ = ( j ) j ∈P of L from equation (8) /*First collect the positions where the key has a bit set to one.*/ j = k = 1 for each bit in κ ( i ) do if current bit is equal to one then ρ k = ̺ j k = k + 1 end if j = j + 1 end for/*Then, pick up the positions where the key does not have a bit set to one.*/ if length( ρ ) less than 64 then Given x (0) and ν , get chaotic permutation ̺ of ̺ \ ρ from equation (8) ρ = ρ ∪ ̺ end if return ρ PROPOSED SCHEME Algorithm 2
Embedding Algorithm Input:
Cover image C , 128-bit private key κ , secret message M , x (0), ν Output:
Stego image S /* Collecting AC coefficients */ Divide C into K non-overlapping blocks of 8 × ω = ∅ ℓ = 0 for each B k ∈ C do B k ← B k : DCT( B k ) according to (2) Θ k ← B k : Quantify B k according to (5) ν k ← Θ k : Apply the zigzag scan, see Figure 1 ω ← ω ∪ { ν kj } ≤ j ≤ end for/* Key expansion using blake2b algorithm */ From κ generate 1024-bit sequence using BLAKE2B algorithm Expand the previous sequence to a binary sequence κ with the same length of ω /* Embbeding secrete bits into collected AC */ Partition ω ← ω (1) || ω (2) || · · · || ω ( i ) || · · · and κ ← κ (1) || κ (2) || · · · || κ ( i ) || · · · into a logical se-quence of length 64 for each ω ( i ) ∈ ω do ρ ← ChaoticPositions( κ ( i ) , x (0) , ν ) for each ψ ∈ ρ do ℓ ← ℓ + 1 if ω ( i ) ψ < then ¯ ω ( i ) ψ ← − R(abs( ω ( i ) ψ ) , m ℓ ); else ¯ ω ( i ) ψ ← R( ω ( i ) ψ , m ℓ ); end if end for ω ( i ) ← ¯ ω ( i ) ; Reconstruct 1D-array ω of coefficient from modified ¯ ω end for/* Grouping AC coefficients and rebuilding the stego image */ Partition ω ← ̟ (1) || ̟ (2) || · · · || ̟ ( i ) || · · · into a logical sequence of length 8 for each B k ∈ C do { ν kj } ≤ j ≤ ← ̟ ( k ) Θ k ← ∆( ν k ) B k ← Θ k : Apply the operation (6) B k ← B k : IDCT( B k ) according to (3) end for S ← B ∪ B ∪ · · · ∪ B k ∪ · · · return S PROPOSED SCHEME The detailed process of extracting the secret message from the stego image S is describedbelow. The step-by-step procedure is included in Algorithm 3. Taking as input the stego image S , this is divided into non-overlapping 8 × × × ω . The zigzag scanorder is used to collect the coefficients, see Figure 1. In order to increase the security of thestego system, a 128-bit private key κ is used. From this a 1024-bit sequence is generated usingBLAKE2B. Then, this sequence is expanded to a binary sequence κ with the same length of ω .Next, ω = ω (1) || ω (2) || · · · || ω ( i ) || · · · and κ = κ (1) || κ (2) || · · · || κ ( i ) || · · · are partitioned into logicalsequences of length 64. Then, for each ω ( i ) the LSB of the value of the coefficient of a particularposition ρ i is extracted and appended to form the final bits stream M of the secret message.The ρ i positions are determined by κ ( i ) and chaotic positions generator ( ̺ i ) ≤ i ≤ given by (8),see Algorithm 1. Algorithm 3
Extracting Algorithm Input:
Stego image S , 128-bit private key κ , x (0), ν Output:
Secret message M , /* Collecting AC coefficients */ Divide S into K non-overlapping blocks of 8 × ω = ∅ ℓ = 0 for each B k ∈ S do B k ← B k : DCT( B k ) according to (2) J. Inst. Eng. India Ser. B Θ k ← B k : Quantify B k according to (5) ν k ← Θ k : Apply the zigzag scan, see Figure 1 ω ← ω ∪ { ν kj } ≤ j ≤ end for/* Key expansion using blake2b algorithm */ From κ generate 1024-bit sequence using BLAKE2B algorithm Expand the previous sequence to a binary sequence κ with the same length of ω /* Extracting secrete bits */ Partition ω ← ω (1) || ω (2) || · · · || ω ( i ) || · · · and κ ← κ (1) || κ (2) || · · · || κ ( i ) || · · · into a logical se-quence of length 64 for each ω ( i ) ∈ ω do ρ ← ChaoticPositions( κ ( i ) , x (0) , ν ) for each ψ ∈ ρ do ℓ ← ℓ + 1 m ℓ ← R − (abs( ω ( i ) ψ )) end for end for return M RESULTS AND DISCUSSION The results showed that proposed method reached higher PSNR values (75%) than the Habib etal., Sahar et al., Saidi et al. and Chowdhuri et al. methods (Figure 3), exhibiting higher PNSRvalues of 42.5 db. This indicates that obtained stego images by proposed method have higherimperceptibility level compared to the other methods. This is consistent with those results ofPSNR (30 to 50 db) found by [14].Image quality was significantly improved (75%) by the proposed method in comparison withthe other methods (Figure 4). This indicates that the cover image quality is not significantlydifferent from the stego images due to UIQI values are close to the unit. Also, it resulted inobtained stego images had a good visual quality with respect to the other methods.The proposed method enhanced notably the image fidelity (75%) compared to the othermethods (Figure 5). This means that the cover images have the similarity high level comparedto the stego images. This results are consistent with those obtained by [38] who found IFhvalues close to the unit.The ER values were slightly better in the proposed method than those obtained by the meth-ods of Habib et al., Sahar and Chowdhuri et al. However, Saidi et al. method showed smallerRE values than proposed method (Figure 6). Decreased RE values resulted in steganographicsystem that is sufficiently safe to establish a private and confidential communication betweentwo parts [11, 38].
Hab. M. Sah. M. Said. M. Chow. M. Prop. M.30.032.535.037.540.042.545.047.5 P S N R V a l u e s Hab. M. Sah. M. Said. M. Chow. M. Prop. M.30.032.535.037.540.042.545.047.5 P S N R V a l u e s Figure 3: PSNR values. The first row contains the PSNR values corresponding to the firstdataset while the another to second
RESULTS AND DISCUSSION Hab. M. Sah. M. Said. M. Chow. M. Prop. M.0.9600.9650.9700.9750.9800.9850.9900.9951.000 U I Q I V a l u e s Hab. M. Sah. M. Said. M. Chow. M. Prop. M.0.9800.9850.9900.9951.000 U I Q I V a l u e s Figure 4: UIQI values
Hab. M. Sah. M. Said. M. Chow. M. Prop. M.0.9900.9920.9940.9960.9981.000 I F V a l u e s Hab. M. Sah. M. Said. M. Chow. M. Prop. M.0.9860.9880.9900.9920.9940.9960.9981.000 I F V a l u e s Figure 5: IF values
CONCLUSIONS Hab. M. Sah. M. Said. M. Chow. M. Prop. M.0.00.10.20.30.40.5 R E V a l u e s Hab. M. Sah. M. Said. M. Chow. M. Prop. M.0.00.10.20.30.40.5 R E V a l u e s Figure 6: RE values
We have presented a steganographic algorithm embedding a secrete message in the first eightAC coefficients. Experimental analysis of two datasets for stoganographic images revealed that100% of the PSNR values of the proposed method are greater than the PSNR values of thestate-of-art analyzed, except for Saidi et al. method. The method proposed improved notablyimage quality, imperceptibility and similarity and provided high imperceptibility level and goodembedding capacity compared to existing state-of-the-art methods. We expect the presentedmethod can protect the information and establish a safe communication between parts.
References [1] Al-Jarrah, M.: Rgb-bmp steganalysis dataset. Mendeley Data, v1 (2018). DOI http://dx.doi.org/10.17632/sp4g8h7v8k.1[2] AlZain, M.A., Al-Amri, J.F.: Application of data steganographic method in video sequencesusing histogram shifting in the discrete wavelet transform. International Journal of AppliedEngineering Research (8), 6380–6387 (2018)[3] Andrews, L.C., Andrews, L.C.: Special functions of mathematics for engineers. McGraw-Hill New York (1992)[4] Aruna, M., Geeta, S., K., H.: A high capacity text steganography scheme based on lzw com-pression and color coding. Engineering Science and Technology, an International Journal , 72–79 (2017)[5] Atta, R., Ghanbari, M.: A high payload steganography mechanism based on wavelet packettransformation and neutrosophic set. J. Vis. Commun. Image R. (2018). DOI https://doi.org/10.1016/j.jvcir.2018.03.009 EFERENCES , 553–562 (2018)[10] Bayraktar, B., Bernas, T., Robinson, J., Rajwa, B.: A numerical recipe for accurate imagereconstruction from discrete orthogonal moments. Pattern Recognition , 659–669 (2007)[11] Cachin, C.: An information-theoretic model for steganography , 306–318 (1998)[12] Chen, S., Qu, Z.: Novel quantum video steganography and authentication protocol withlarge payload. International Journal of Theoretical Physics (12), 3689–3701 (2018)[13] Chowdhuri, P., Jana, B., Giri, D.: Secured steganographic scheme for highly compressedcolor image using weighted matrix through dct. International Journal of Computers andApplications pp. 1–12 (2018). DOI https://doi.org/10.1080/1206212X.2018.1505024[14] Coskun, I., Akar, F., Cetin, O.: A new digital image steganography algorithm based onvisible wavelength. Turk. J. Elec. Eng. & Comp. Sci. , 548–564 (2013)[15] Datta, B., Mukherjee, U., Kumar, S.: Lsb layer independent robust steganography usingbinary addition. Procedia Computer Science , 425–432 (2016)[16] Din, R., Bakar, R., Utama, S., Jasmis, J., Elias, S.J.: The evaluation performance ofletter-based technique on text steganography system. Bulletin of Electrical Engineeringand Informatics (1) (2019)[17] El Rahman, S.A.: A comparative analysis of image steganography based on dct algorithmand steganography tool to hide nuclear reactors confidential information. Computers &Electrical Engineering (2016). DOI http://dx.doi.org/10.1016/j.compeleceng.2016.09.001[18] Gagnani, L.P., Varjani, S.: Survey of 3d chaotic map techniques for image encryption.International Journal of Science and Research (IJSR) (12), 1000–1004 (December 2015)[19] Gutub, A., Al-Juaid, N.: Multi-bits stego-system for hiding text in multimedia imagesbased on user security priority. Journal of Computer Hardware Engineering (2), 9 (2018)[20] Habib, M., Bakhache, B., Battikh, D., El Assad, S.: Enhancement using chaos of a steganog-raphy method in dct domain. In: Digital Information and Communication Technology andits Applications (DICTAP), 2015 Fifth International Conference on, pp. 204–209. IEEE(2015) EFERENCES , 46–66 (2018)[22] Kadhim, I.J., Premaratne, P., Vial, P.J., Halloran, B.: Comprehensive survey of imagesteganography: Techniques, evaluations, and trends in future research. Neurocomputing(2018). DOI https://doi.org/10.1016/j.neucom.2018.06.075[23] Khamruia, A., Mandal, J.K.: A genetic algorithm based steganography using discrete cosinetransformation (gasdct). Procedia Technology (2013), 105–111 (2013)[24] Li, S., Chen, G., Mou, X.: On the dynamical degradation of digital piecewise linear chaoticmaps. Int J Bifurc Chaos (10), 3119–3151 (2005)[25] Liao, X., Yin, J., Guo, S., Li, X., Sangaiah, A.K.: Medical jpeg image steganography basedon preserving inter-block dependencies. Computers & Electrical Engineering , 320–329(2018)[26] Lorenz, E.N.: The essence of chaos. University of Washington Press (1995)[27] Majumder, A., Changder, S.: A novel approach for text steganography: Generating textsummary using reflection symmetry[28] Manisha, S., Sharmila, T.S.: A two-level secure data hiding algorithm for video steganog-raphy. Multidimensional Systems and Signal Processing pp. 1–14 (2018). DOI https://doi.org/10.1007/s11045-018-0568 { $ \ $ } , 435–449 (2016)[30] Mishra, S., Yadav, V.K., Trivedi, M.C., Shrimali, T.: Audio steganography techniques:A survey. In: Advances in Computer and Computational Sciences, pp. 581–589. Springer(2018). DOI https://doi.org/10.1007/978-981-10-3773-3 { $ \ $ } (2018). DOI https://doi.org/10.1016/j.aej.2017.09.005[33] Sahu, A.K., Swain, G.: A novel n-rightmost bit replacement image steganography technique.3D Research (1), 2 (2019)[34] Saidi, M., Hermassi, H., Rhouma, R., Belghith, S.: A new adaptive image steganog-raphy scheme based on dct and chaotic map. Multimed Tools Appl DOI 10.1007/s11042-016-3722-6[35] Sengupta, M., Mandal, P., Das, T., Dey, A.: A novel hash based technique for thermalimage authentication. Procedia Technology , 147–156 (2013) EFERENCES (1), 45–50 (2018)[37] Singh, P., Singh, S., Rani, S.: Efficient steganography algorithm based on dct and entropythresholding technique. International Journals of Advanced Research in Computer Scienceand Software Engineering (1), 45?50 (2018)[38] Soria-Lorente, A., Berres, S.: A secure steganographic algorithm based on frequency domainfor the transmission of hidden information. Security and Communication Networks , 1–14 (2017). DOI https://doi.org/10.1155/2017/5397082[39] Subhedar, S., Mankar, H.: Current status and key issues in image steganography: A survey.Computer Science Review (2014). DOI http://dx.doi.org/10.1016/j.cosrev.2014.09.001[40] Sugier, J.: Implementation efficiency of blake2 cryptographic algorithm in contemporarypopular-grade fpga devices. In: International Conference on Reliability and Statistics inTransportation and Communication, pp. 456–465. Springer (2017)[41] Vaishakh, K., Pravalika, A., Abhishek, D., Meghana, N., Prasad, G.: A semantic ap-proach to text steganography in sanskrit using numerical encoding. In: Recent Find-ings in Intelligent Computing Techniques, pp. 181–192. Springer (2019). DOI https://doi.org/10.1007/978-981-10-8639-7 { $ \ $ } , 142–151 (2017)[43] Valandar, M.Y., Barani, M.J., Ayubi, P., Aghazadeh, M.: An integer wavelet transformimage steganography method based on 3d sine chaotic map. Multimedia Tools and Appli-cations pp. 1–19 (2018)[44] Walia, G.S., Makhija, S., Singh, K., Sharma, K.: Robust stego-key directed lsb substitutionscheme based upon cuckoo search and chaotic map. Optik , 106–124 (2018)[45] Wang, Z., Bovik, A.: A universal image quality index. IEEE Signal Processing Letters (3),81–84. (2002)[46] Yadav, G.S., Ojha, A.: Chaotic system-based secure data hiding scheme with high embed-ding capacity. Computers & Electrical Engineering (2018). DOI https://doi.org/10.1016/j.compeleceng.2018.02.022[47] Yahya, A.: Steganography Techniques for Digital Images. Springer (2018). DOI https://doi.org/10.1007/978-3-319-78597-4[48] Zhang, S., Khan, I., Ullah, Y.: Audio steganography by additional channel. In: RecentDevelopments in Intelligent Computing, Communication and Devices, pp. 633–642. Springer(2019). DOI https://doi.org/10.1007/978-981-10-8944-2 { $ \ $ } (9), 703–709 (2009) EFERENCES , 1540–1558 (2012)[51] Zou, W., Zhuang, Z., Jiao, S., Zhang, L., Kpalma, K.: Image steganography based ondigital holography and saliency map. Optical Engineering58