Int. j. inf. tecnol.

https://doi.org/10.1007/s41870-022-00861-9

ORIGINAL RESEARCH

Bifold-crypto-chaotic steganography for visual data security

Bharti Ahuja1 • Rajesh Doriya1

Received: 9 August 2021 / Accepted: 5 January 2022

 Bharati Vidyapeeth’s Institute of Computer Applications and Management 2022

Abstract As digital images hold sensitive information Keywords Steganography  Encryption  Discrete wavelet
from a number of areas, such as human, medical, satellite transform  Arnold map  Logistic map  Cryptography
and biometric, etc., they therefore require the utmost pro-
tection. These photos hold various vulnerability threats and
in this era of cloud and virtualization, to protect data from 1 Introduction
hackers, we need an efficient way to safeguard data that
would provide a hybrid type of algorithm to protect data ‘‘Image confidentiality could typically be accomplished
from multiple types of hackers. The approach is innovative through encryption to improve the privacy of digital
and safe in the sense that it has two-fold protections for the information during processing and storage’’ [1]. The digital
safety of a secret message or information. Secret message audio, video, photographs, and documents travel to their
is encrypted twice with Arnold and Logistic maps prior to respective owners via cyberspace. Unfortunately, people
transmission. The approach effectively blends the two may choose to participate along the way, and take this
aspects of visual data security with the integration of a material for them unethically. Steganography eliminates
chaotic mechanism in such a manner that optimal security these kinds of instances by restricting or reducing a third
can be obtained. The aim is to conceal a message or plain party’s ability to decode the information. Steganography is
text and at the same time protect it by encrypting hidden frequently used for cipher texts, therefore it is character-
keys and by means of DWT and a chaotic phenomenon. ized as a hidden method of communication or interaction
Therefore, by integrating these two approaches, the new with a covering and content is within the cover.
approach conceptualizes dual encryption. Numerous metric Steganography approaches are built on four pillars: confi-
studies, such as PSNR, MSE, correlation coefficient and dentiality, payload capacity, imperceptibility, and
SSIM, have been carried out for validation purposes. The resilience.
results demonstrate that the system performs well with There are two methodologies to steganography strate-
various grayscale images and outperforms cryptography gies having classified broadly into two domains one in the
and steganography alone in terms of security and spatial and another in the frequency; the least significant bit
reliability. (LSB) insertion process is fall under spatial domain cate-
gory. In LSB insertion process, data covering technique is
utilized by the last bit of the cover picture which could not
be identified naturally [2]. Wavelet Transform, Fourier
Transform with or without fractional order both and other
& Bharti Ahuja associated transform like Cosine Transform and Sine
bharti.salunke99@gmail.com
Transform are all characterized in frequency domain
Rajesh Doriya [3].Tremendous work has been carried out in the area of
rajeshdoriya.it@nitrr.ac.in
image encryption and steganography in the last decade
1
Department of Information Technology, National Institute of from which some very relevant and promising work is
Technology-Raipur, Raipur, Chhattisgarh, India listed below.

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Nevriyanto et al. [4] introduced a procedure of image steganography is introduced using likewise fractal stream
steganography established on discrete wavelet transform cryptography to cover up Huffman based compressed
(DWT) and singular value decomposition. They utilized a Turkish writings. An assessment of Turkish newspaper
content document and changed over into a picture as feature writer content is obtained here in order to obtain not
watermark. Soni et al. [5] highlighted the importance of a only the alphabets, containing unusual Turkish characters,
discrete fractional Fourier transform (DFRFT) relative to but also punctuation marks, spaces, news lines, citations,
other transformations for steganography in computer and so on. As a consequence of the first phase, a reliable
vision. Frequency domain transformation may be per- Huffman encoding dictionary for 102 observable characters
formed either in Discrete Cosine Transform (DCT), DWT is constructed [12].
or even in DFRFT. Transform techniques have a smaller A method converting an image based steganography that
payload contrasted with spatial. However the frequency masks a hidden image into a cover image also proposed by
domain approach covers the sensitive information or Subhedar et al. The work states the advantage of decom-
message in to a specific frequency component efficiently position of bidiagonal singular value decomposition. And
but suffers with the downside of the increased computa- apart from this it also has perfect reconstruction, sparsity
tional cost. But because of the added advantages like high and stability that allow the transformation of frame let to be
security, stability and robustness in the frequency domain considered as an effective decomposition tool for the
strategies always attracts the researchers to do more work generation of transformation coefficients [13].
upon. Steganography using DWT has more benefits as it The adaptive pattern is used in one study proposed by
has higher compression ratios and therefore prevents Rustad et al. to execute the inverted LSB. Prior to
interference due to artifacts [6]. Also compression is an embedding the message, the bits of the content as well as
added advantage because its saves the space for storage and the container picture are counted, and the error ratio for
transform as done by Nasrullah et al. i.e. hidden message each bit combination is computed. For every 2-bit combi-
mining and image cover recovery was conducted together nation to reverse the LSB, eight patterns (000 to 111) are
in reversible data hiding technique for compression used in addition to the LSB of the container picture pixels.
encryption on the protected partition of the hierarchical tree Inverted LSB is used to reduce the error ratio for each
[7]. pattern. For each pair of bits, each pattern’s lower error
Methodologies relying on artificial neural network also ratios are put together. To incorporate the message, the bit
find applications in the field as the data recovery. Hu et al. combination with the lowest error ratio is chosen. Because
[8] recommended a novel steganography without embed- it is dependent on the assessment of the error ratio, the
ding imaging technique focused on deep convolutional optimal pair of bits may vary depending on the container
systems. They convert concealed data into a noise vector picture and message size. When evaluated on standardized
and use a verified neural system generator computation to and medically less varied images, the proposed technique is
create a transporter image based on a noise vector. No successful in increasing imperceptibility based on PSNR
change or insertion tasks are necessary during the picture and SSIM [14].
formation; the data put away in the picture can be recov- Another study, by Shah et al., provides an image
ered effectively. Predicated on the idea of deep learning, steganography system with changeable payload capacity
Duan et al. [9] introduces a new system of image based on Genetic Algorithm. The proposed system pro-
steganography dependent on the U-Net structure. A certi- vides both high imperceptibility and payload capacity. GA
fied deep neural system consolidates a concealing system is used to find the optimum parameter value to rearrange
and an extraction system at that point the sender utilizes a and change the hidden data. A unique method of the
concealing system to install the shrouded picture into variable chromosome is also suggested; the variable chro-
another full-size picture with no adjustment and to send it mosome is helpful in boosting the imperceptibility of the
back to another one. A novel steganography framework secret data modification steganography (SDMS) approach
relying on local reference edge detection method and [15].
exclusive disjunction property is given by Kumar Gaurav A similarity measure, sometimes known as an infor-
et al. [10]. mation measure, is a notion used to differentiate between
The primary difficulties of visual steganography are dissimilar items. It has been explored in several circum-
impalpability of the cover picture and no reconstruction of stances using mathematical, psychological, and fuzzy
the hidden information. To manage these difficulties, an methodologies. By merging intuitive human perception
altered picture steganography strategy dependent on DWT with a rule-based technique, Ashraf et al. created inter-
was also proposed. The system utilizes two unique mediate type-two fuzzy logic architecture (IT2 FLS) to
approaches in particular a mystery key calculation and estimate the proximity of neighboring pixels [16]. The LSB
blocking [11]. Another spatial and chaos based approach is used to incorporate the pixels in the picture

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with the largest similarity scores, as calculated by the of secret image is used at varying stages i.e. Arnold map at
suggested IT2 FLS similarity metric. the very beginning for fresh secret image and Logistic map
In one study, the carrier picture is chosen such that the after the steganography on the stego output to make it more
LSBs of the secret picture and the carrier image align with stable and resistant to attackers at the transmitting end.
a greater degree of compatibility, and the concealing pro- Information security is an obvious advantage of
cedure makes insignificant variations in the resulting stego steganography; the implementation of a novel encryption
picture using a genetic method. When compared to several and chaotic embedding system meets that requirement by
current approaches, we achieved 30–40% gains with pro- boosting security with Bifold Encryption. This is the new
posed approach. It is difficult to select an appropriate cover hybrid combination of cryptography, steganography with
picture and conceal the secret data to increase impercep- chaos which gives superior results compared to many other
tibility. A genetic algorithm has been used to help in the previously proposed algorithms as depicted in result
exploration of a difficult process of choosing from billions section.
and millions of options [17]. Further the article is arranged as follows; fundamental
One more research recommended reducing the physical terms are portrayed in the second section. The method-
space on different storage devices as well as the time it ologies and procedures are elaborated in the third sec-
takes to transport data via the Internet, while guaranteeing tion. The suggested algorithm is demonstrated in the fourth
that the data is encrypted and concealed from potential section. The fifth part contains the performance parameters
attackers. There are different methods: one as Lossy with that were used. The sixth part contains the findings and
data loss and another as Lossless. One such approach is a results. The final paragraph concludes with concluding
hybridized data compression methodology that increases remarks.
security by strengthening content security using the RSA
(Rivest–Shamir–Adleman) encryption method, and it may
be employed in the development of lossy and lossless 2 Fundamental knowledge
compression techniques for steganography [18]. This
approach may be suitable to reduce the data sent with each This section briefly highlights some of the basic funda-
transfer, allowing for faster transmission when utilizing mental terms that helps in comprehending the proposed
sluggish internet or taking up less space on various storage algorithm in a better way, which includes steganography,
devices. cryptography, the term crypto steganography, DWT,
An image steganography approach that uses a variety of Arnold map, and Logistic map as well.
methods to create the protection of the hidden content by
employing an image encryption approach depending on 2.1 Steganography and cryptography
binary bit-plane decomposition is suggested by Dhawan
et al. Following that, an adaptive embedding procedure Steganography in the image is a common method for
based on the Salp Swarm Optimization Algorithm (SSOA) hiding the message or content interior into a frame. It can
is developed. It is used to maximize payload capacity for be applied to many media forms such as textual content,
edge and smooth blocks by altering various settings in the audio, photos, and videos, etc. However, text content
steganographic embedding technique [19]. The SSOA steganography is the maximum difficult size of steganog-
approach is used in this case to successfully find the edge raphy due to the loss of redundancy in textual content
as well as smoothing pieces. The modified Fuzzy Neural compared to image or audio, but still needs small storage
Network with a back propagation learning approach is then and easy communication.
used to upgrade the effectiveness of the stego picture. The Cryptography is the study and exploration of ways for
photos from the stego are then transmitted to the destina- secure communication from the perspective of outsiders.
tion via the highly secure IoT protocol. To a greater extent, conventions are developed and eval-
Contribution: To add to the current steganography uated to measure the impact of adversaries and apply to
schemes and in order to refine the results in terms of many information security applications viz. data protec-
security, the DWT technique with Arnold map and the tion, data integrity, encryption, and non-refusal [20].
logistic map encryption are introduced. The suggested As seen in Fig. 1, a blend based on both cryptography
solution is a two-fold concept to mitigate the distortion of and steganography is used here. This is known as Crypto-
the cover image and too with safeguarding the secret Steganography. Figure 2 depicts a typical block diagram of
image. The first one, known as the blocking principle using the crypto steganography process as a whole for a quick
DWT, is implemented in order to guarantee the least understanding that how the two processes combine into one
variance in the cover picture. The second, i.e. the combi- to give better security highlights. DWT, Arnold, and
nation of Arnold and Logistic encryption for the protection

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Fig. 1 Crypto steganography Fig. 3 Different components of DWT coefficient

a) Scaling function of the wavelet representation is as

follows:
1 M X
1 X
N1
Wa ðj; m; nÞ ¼ pffiffiffiffiffiffiffiffi f ðx; yÞaj;m;n ðx; yÞ ð7Þ
MN x¼0 y¼0

b) Horizontal, vertical, and diagonal sub-band repre-

Fig. 2 Block diagram of crypto steganography
sentations are as follows
Logistic map are the methods that are being utilized in 1 M X
1 X
N 1

combination here for the Crypto-steganography. WbH ðj; m; nÞ ¼ pffiffiffiffiffiffiffiffi f ðx; yÞbH
j;m;n ðx; yÞ ð8Þ
MN x¼0 y¼0

2.2 Discrete wavelet transform (DWT) 1 M X

1 X
N 1
WbV ðj; m; nÞ ¼ pffiffiffiffiffiffiffiffi f ðx; yÞbVj;m;n ðx; yÞ ð9Þ
MN x¼0 y¼0
It transforms picture elements to wavelets, which are fur-
ther utilized in wavelet-dependent compression and coding. 1 M X
1 X
N 1

It has the benefit over the Fourier transform in that it col- WbD ðj; m; nÞ ¼ pffiffiffiffiffiffiffiffi f ðx; yÞbD
j;m;n ðx; yÞ ð10Þ
MN x¼0 y¼0
lects frequency as well as spatial information.
The two-dimensional wavelet transform can be repre-
sented as:
LL ¼ aðx; yÞ ¼ að xÞað yÞ ð1Þ
LH ¼ bH ðx; yÞ ¼ bð xÞað yÞ ð2Þ
HL ¼ bV ðx; yÞ ¼ aðxÞbðyÞ ð3Þ
D
HH ¼ b ðx; yÞ ¼ bðxÞbðyÞ ð4Þ
Here H, V, and D represent the Horizontal, Vertical and
Diagonal decomposition direction of the wavelet.
Illustration of the scaling and wavelet structures for two-
dimension is described below, where i = {H, V, D}:
j  
aj;m;n ðx; yÞ ¼ 22 a 2j x  m; 2j y  n ð5Þ
j  
bij;m;n ðx; yÞ ¼ 22 bi 2j x  m; 2j y  n ð6Þ

Graphical representation of different components of

DWT coefficient is shown in Fig. 3; where LL = Low-
Low, HL = High-Low, LH = Low–High and HH = High-
High.
Fig. 4 Graphical representation of Arnold cat map

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Fig. 5 Crypto-chaotic embedding process

    
2.3 Arnold map xð n þ 1Þ 1 1 xð nÞ
¼ ðmod1Þ ð11Þ
yð n þ 1Þ 1 2 yð nÞ
Across The method was invented by Vladimir Arnold, who
showed its outcomes in 1967 utilizing a cat drawing [21]. Expression (11) may be converted into expression (12)
Figure 4 depicts the graphical representation of it. It is also for the estimation of fixed points as;

commonly utilized in cryptography. It is characterized as xðnÞ ¼ xðnÞ þ yðnÞðmod1Þ
[22]: ð12Þ
yðnÞ ¼ xðnÞ þ 2yðnÞðmod1Þ

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Fig. 6 Crypto-chaotic extraction process

2.4 Logistic map

Because it is a homogeneous linear equation, expression
(11) often has a specific value.
Chaotic phenomenon is an unpredictable and equally ran-
dom mechanism that occurs within the dynamic nonlinear
systems. The chaotic feature is reactive to the initial con-
dition, volatile and yet normal. Encryption makes extensive

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Fig. 9 Illustration of crypto-chaotic embedding process for test

Fig. 7 Illustration of crypto-chaotic embedding process for test images (256 9 256) under consideration
images (512 9 512) under consideration

Fig. 10 Illustration of crypto-chaotic extraction process (256 9 256)

Fig. 8 Illustration of crypto-chaotic extraction process (512 9 512) for test images under consideration
for test images under consideration
cover image with DWT. Using chaotic functions such as
use of chaotic functions. We’re making use of a logistic Arnold and Logistic makes algorithm powerful. The pro-
map here. posed approach consists of two processes: crypto chaotic
The logistic map is a typical illustration of a transition embedding and extraction. The procedure of this algorithm
from stability to chaotic activity [23]. is shown in Figs. 5 and 6. In the figure, the histograms of
It is expressed mathematically as: the cover and the stego image are the same, and the his-
ynþ1 ¼ u  yn  ð1  yn Þ ð13Þ tograms of the secret image and the reconstructed secret
image are the same as detected by histogram analysis,
It possesses a large key space for increased security. demonstrating the correctness of the proposed approach.

3.1 Steps of crypto-chaotic embedding

3 Proposed algorithm
Step 1: Choose the cover picture and the image to be
The key objective was to optimize the potential for securely communicated.
embedding while giving stego image the best possible Step 2: Use the DWT on the cover picture.
stability. The suggested scheme profits from DWT with Step 3: Apply Arnold cat map to the secret image.
Arnold map. In the proposed algorithm the secret image is Step 4: Perform OR operation to the resultant of step 2
encrypted with Arnold map and transform is applied to the and 3.

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Fig. 12 Comparison of PSNR of proposed scheme with different

literature

Step 5: Division into blocks of the output of step 4.

Step 6: Implement the inverse discrete wavelet trans-
form (IDWT) to get stego image.
Step 7: Employ logistic map to stego image to get the
encrypted image.

3.2 Steps of crypto-chaotic extraction

Step 1: The stego encrypted picture is largely decoded

using logistic map at the receiver’s end to obtain the stego
image.
Step 2: Employ DWT on the stego image.
Fig. 11 MSE between secret and reconstructed secret image on
various test images
Step 3: Then take off the cover image.

Table 1 PSNR, MSE, SSIM

Cover image Parameters where weight is 0.002
and correlation coefficient of
(taken baboon as secret image)
different test images (weight is PSNR(in db) MSE SSIM Correlation coefficient
0.002)
Goldhill 56.2822 0.1531 0.9986 1
Barbara 56.2821 0.1531 0.9977 1
Lena 60.4466 0.0587 0.9988 1
Peppers 56.2824 0.1531 0.9862 1
Aeroplane 56.2822 0.1531 0.9932 1
Man 56.2824 0.1531 0.9978 1
Elaine 56.2821 0.1531 0.9985 1
Cameraman 60.4455 0.0587 0.9954 1

Table 2 Comparison of PSNR

Cover images PSNR (proposed) PSNR [14] PSNR [11] PSNR [24] PSNR[12]
of proposed scheme with
different literature Barbara 56.28 NA 44.84 39.7 NA
Lena 60.44 52.49 42.87 39.91 55.98
Peppers 56.28 57.41 NA 40.29 55.98
Cameraman 60.44 57.44 NA NA 56.01

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Table 3 PSNR and SSIM

Cover image Parameters where weight is 0.0014
comparison of suggested
scheme with different literature PSNR (proposed) PSNR[13] SSIM (proposed) SSIM[13]
(weight is 0.0014)
Boat 77.4875 69.5296 0.9995 0.9999
Baboon 77.4875 69.5686 0.9999 0.9999
Lena 77.4875 69.4413 0.9989 0.9999

 
256  256
PSNR ¼ 10 log10 ð14Þ
MSE
MSE is represented, mathematically as;
X
1 M 1 X
N1
2
MSE ¼ ½f 0 ði, jÞ  f ði, jÞ ð15Þ
MN i¼0 j¼0

• ‘‘Correlation Co-efficient is a simple correlation of

neighboring pixels in horizontal, vertical and diagonal
directions for a real image’’ [26].
• The SSIM computes the relationship between an
original picture and a reconstructed image [14]. It is used to
calculate consistency based on the multiplicative variation
of three terms, such as structural, luminance and contrast.
Fig. 13 Comparison of PSNR and SSIM of proposed scheme with
different literature (weight is 0.0014)
The SSIM is described as:
SSIM ðp; qÞ ¼ lðp; qÞcðp; qÞsðp; qÞ ð16Þ
Table 4 Correlation coefficient for cover and stego image 8 2lp lq þ C1
>
>
Correlation coefficient Cover image Stego image > lðp; qÞ ¼ l2 þ l2 þ C
>
>
> p q 1
< 2rfp rq þ C2
Horizontal 0.9714 0.9714 cðp; qÞ ¼ 2
>
> rp þ r2q þ C2
Vertical 0.9745 0.9744 >
>
>
> r þ C3
Diagonal 0.9532 0.9531 : sðp; qÞ ¼ fg
rp rq þ C3

Table 5 Correlation coefficient for stego and stego encrypted image 5 Results and discussion
Correlation coefficient Stego image Stego encrypted image
The ‘‘cover image’’ is utilized as a carrier in the proposed
Horizontal 0.9714 - 0.4037 work; the secret picture is an image that should be sent
Vertical 0.9744 0.0010 through the ‘‘cover image’’ as illustrated in Figs. 7 and 8.
Diagonal 0.9531 - 0.0054 The DWT technique is for hiding a picture in a ‘‘cover
image’’ while the Arnold map is used to encrypt a secret
image. Stego-image combines the cover and the hidden
image. In the stego picture, a logistic function is used to
4 Performance parameters encrypt it once more for more security.
Figure 7 illustrates the Crypto-Chaotic Embedding
Some prominent measures, such as SSIM, PSNR, MSE, Process for test images under consideration. Here goldhill
correlation co-efficient, and, would be assessed to ensure image of the size 512 9 512 is taken as cover image and
system performance. baboon image of the size 512 9 512 is considered as the
• PSNR refers to the proportion between the highest secret image or as the message which is to be protected.
possible signal value and the noise [24], 25. To obtain a DWT is applied to the cover image and Arnold cat map is
robust system, the mean square error should be as little as applied to the secret image, then by OR operation, the
feasible, and the PSNR result should be high. The equation above two outputs are combined together. Further this
of the PSNR is represented as: combination is then divided into blocks. Thereafter IDWT

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Fig. 14 Illustration of
correlation co-efficient for cover
and stego image

Fig. 15 Correlation co-efficient

for stego and stego encrypted
image

is implemented to get the stego picture. Finally Logistic the message which is to be protected. The process is similar
map is implemented to stego picture to get the encrypted to as explained earlier for goldhill and baboon images.
image. Figure 10 illustrates the crypto-chaotic extraction pro-
Figure 8 illustrates the Crypto-Chaotic Extraction Pro- cess for another test image of 256 9 256 sizes under
cess for test images under consideration i.e. goldhill and consideration i.e. rice and cameraman. Here also the pro-
baboon. On receiving end primarily, the stego encrypted cess is similar to as explained earlier for goldhill and
image is decrypted by logistic map to get the stego image. baboon images.
Then DWT is applied to stego image. Thereafter the cover A set of experiments were conducted from under diverse
image is taken off and at the last Arnold map is applied to carrier images over 30 in numbers to determine the effi-
get the reconstructed secret image baboon. ciency of the suggested scheme. However for illustration
Figure 9 also illustrates the crypto-chaotic embedding only 6 are considered here. Reference images are selected
process for another test image of 256 9 256 sizes under from SIPI image database [27]. Here two type of dimen-
consideration. Here rice image is taken as cover image and sions for reference images are used, 256 9 256 and
cameraman image is considered as the secret image or as 512 9 512. Following the application of the suggested
technique, the following measurements, such as MSE,

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SSIM and correlation co-efficient and PSNR, are employed Funding No funding available.
to examine picture quality. The result of MSE between
Data availability No.
secret and reconstructed secret image is shown in Fig. 11
for various test images which is 0 for all also having the Declarations
PSNR to be infinite suggesting the faithful reconstruction
of the message. Conflict of interest The author declared that they have no conflict of
interest.
Outcomes of different performance metrics such as
correlation coefficient, SSIM, PSNR, MSE, and on various Ethical approval NA.
test images on 0.002 weight is depicted in Table 1. It is
important to note that all results displayed here are having Consent to participate Yes.
baboon as secret image. Further the comparison of PSNR
Consent for publication Yes.
of proposed scheme with different literature is shown in
Table 2 where baboon is taken as secret image. Graphical
comparison illustration of Table 2 is also illustrated in References
Fig. 12.
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