A data hiding approach based on reference affected matrix

Three parts: petal matrix, calyx matrix, and stamen matrix are combined for data embedding by using the x-cross-shaped reference matrix.. The low distortion and the high capacity are two

A Data Hiding Approach Based

on Reference-Affected Matrix

Trong-The Nguyen, Jeng-Shyang Pan, Truong-Giang Ngo and Thi-Kien Dao

Abstract Data security has got many remarkable achievements However, the issues

of the lower distortion and the higher embedding capacity in the embedded secret data in media have not much been considered by scholars This paper proposes a

new data hiding approach to the embedded secrets based on the guidance of the

x-cross-shaped reference-affected matrix to solve these issues Adjacent pixels would

be found out large area with similar values which can utilize for manipulating data embedding and extracting on a difference–coordinate plan instead of the traditional pixel–coordinate plan Three parts: petal matrix, calyx matrix, and stamen matrix are combined for data embedding by using the x-cross-shaped reference matrix The experimental results compared with the previous methods in the literature shows that the proposed approach brings outstanding payload with the cover visual quality

Keywords Steganography·Data hiding·Data embedding and extracting

6.1 Introduction

Secret messages delivered to target destination need prevent from malicious attacks,

so data hiding technique is one of the accessible ways [1] Data hiding technique,

a significant subject of information security, is widely used to transfer secret mes-sages to others safely on public channels instead of highly costly and conspicuous private channels [2] Data hiding focuses on finding a secure way to embed secrets

in multimedia Pictures, known as common multimedia, can be a perfect means to

T.-T Nguyen (B) · J.-S Pan · T.-K Dao

Fujian Provincial Key Lab of Big Data Mining and Applications, Fujian University of

Technology, Fuzhou, Fujian, China

J.-S Pan

Department of Information Technology, Haiphong Private University, Haiphong, Vietnam

© Springer Nature Singapore Pte Ltd 2020

J.-S Pan et al (eds.), Advances in Intelligent Information Hiding and Multimedia

Signal Processing, Smart Innovation, Systems and Technologies 156,

https://doi.org/10.1007/978-981-13-9714-1_6

53

carry secret messages At the current stage in steganography, grayscale images are common and convenient carriers Owing to the value of every grayscale image pixel ranging from 0 to 255, so a pixel is easily represented by 8 bits in a binary system [3,4]

The low distortion and the high capacity are two aspects included the lower distor-tions of images estimate data hiding method’s performance after embedding secrets and the higher capacity of carrying secret messages Generally, a higher embedding capacity will result in higher distortions of stego-images, and vice versa Thus, how

to find a feasible way to make a trade-off is a big problem that arises from the data hiding The often steganography method used the least-significant bits (LSB) of each cover pixel’s value from a host image to carry a secret message LSB for data hiding

is the simple and achievable methods with a satisfactory capacity of carrying secret digits and the escapable view from human eyes However, they are vulnerable one under the malicious attacks based on the statistical analysis [5]

Modified LSB method (LSB to match a revisited approach) devoted to controlling the distortion of host images at a lower level with the same payload The stego-images generated under the guidance of both of the corresponding two original images’ pixels and two secret digits that performed better in visual imperceptibility apparently in comparison with traditional LSB one [6] The exploiting modification direction (EMD) [7] method in which each unit composed of n pixels of a host

image can carry one secret digit in (2n+ 1)-ary notational system during embedding processes every time and only one pixel of the unit is modified by 1 every time Therefore, it shows a larger payload and better quality of stego-images

Further, in order to improve the ability of payload, the turtle-shell methods [8,9] provided an easy way to establish a layout (like a turtle shell), so every secret digit ranging from 0 to 8 can be embedded by 2 pixels each time The regular-octagon shape [10], the other method similar to turtle-shell one, had improved the capacity of carrying secret digits This paper places an x-cross-shaped reference matrix extended

on a pixel–differencing plan to hide the secret that combined from three parts: petal matrix, calyx matrix, and stamen matrix for secret embedding, and payload with good visual quality

The remaining paper is organized as sections Section6.2presents related work Section6.3states the methodology Section6.4discusses the experimental results

A conclusion is summarized in Sect.6.5

The definition of symbols is used in this paper as follows

Cover/host image Represents the original grayscale image

Stego-image Represents the grayscale image after embedding a secret

mes-sage

i Represents the index of pixels.(p i−1, p i , p i+1): a triple of

con-secutive cover pixels

d1, d2 Represents the difference values of pixel pairs (p i−1, p i ) and

(p i+1, p i ) from a cover image, respectively.

M (d1, d2) Represents the value with the guidance of x-cross-shaped

refer-ence matrix

pi Represents the stego-pixel of pi after carrying secret by

least-significant bit substitution method

d1, d

2 Represents the difference values of pixel pairs 

p i−1, p

i

 and



p i+1− p

i

 , respectively

pi−1, p

i+1 Represents the stego-pixel values of pi−1and pi+1after

embed-ding secret, respectively

l s Represents the length of a secret that we are going to hide

M (d

1, d

2) Represents the value of the secret we are going to embed from

the reference matrix

num Represents the number of statistics in the histogram

6.2.1 EMD Scheme

A(2n + 1)-ary notational secret data could be embedded for EMD scheme [7,11]

under a group of n cover pixels from the host image every time that achieve efficiency

embedding and secrecy with low distortions EMD’s embedding procedure included steps: First, divide a cover image into a series of nonoverlapping groups Each group

is composed of n pixels which are G = (p1, p2, , p n ) Second, convert a binary

secret message into a sequence of secret digits in (2n+ 1)-ary notational system

Every secret digit can be shown as s j ( j = 1, 2, , l), where l depends on n Apply

EMD to the group G by Eq (6.1) where “mod” represents a modulo operation.

Equation (6.2) calculates how to carry a (2n+ 1)-ary secret digit sj

= f (p1, p2, , p n ) =

 n



i=1

(p i i )



mod (2n + 1) (6.1)

D=sj − y mod (2n + 1) (6.2)

By adding or subtracting, one is used to evaluate changes for certain pivalue of

G.

p i =

⎧

⎨

⎩

p i , i f s j= ρ

p D + 1, i f s j = ρ, and D ≤ n

p (2n+1)−D − 1, i f s j = ρ, and D ≤ n

(6.3)

Demonstration, when n = 2, e.g., if the cover pixel pair is (p1, p2) = (1, 2),

ρ is 0 according to Eq (6.1) When the to-be-embedded secret digit sj = 2, the stego-pixel pair will be

p1, p 2



= (1, 3) according to Eqs (6.2) and (6.3) When the receiver wants to extract the secret, they can also utilize the function shown in

Eq (6.1) That is, the secret digit 2 can be extracted This method ensures a high

data payload (about 1.16 bpp when n= 2) and a good image quality (about 52 dB measured by peak signal-to-noise ratio, often abbreviated PSNR)

6.3 Turtle-Shell-Based Scheme

Every two pixels can carry a secret data ranging from(000)2to(111)2 each time

in the scheme of turtle shell [8] A reference matrix 256× 256 containing as many turtle shells as possible is to hide the secret data Each turtle shell is a hexagon that contains eight different distinct numbers ranging from 0 to 7, including six edge

digits and two back digits Matrix turtle shell (symbol is M) is arranged one by

one without overlapping The rule is the upper row is set to 2, and the next value difference is set to 3, and then continuously it is to 2 again Alternately, add 2 and 3 to every row to complete the entire matrix Therefore, the value difference between two adjacent numbers in the same row of the reference matrix is set to “1”, and the value difference between two adjacent numbers in the same column is set alternately to “2” and “3” Continuously, write down 0 to 7 in every row Every turtle shell contains eight numbers ranging from(000)2to(111)2, so that each cover pixel pair is expressed

as (p i , p i+1), which can carry a 3-bit digit s j Assume that the grayscale cover image I with sized of H × W is composed by I = {pi |i = 1, 2, , (H × W)}.

To embed secret digits, the location of each pixel pair(p i , p i+1) will be determined

as M (p i , p i+1) in the reference matrix M, where p i and pi+1are the column value and row value, respectively

Our schemes work according to using three pixels every time with the guidance of the cross-shaped reference matrix under a difference–coordinate system The x-cross-shaped reference matrix combines three parts: petal matrix, calyx matrix, and stamen matrix for secret embedding, which brings a great payload with cover visual quality

6.5 Matrix Construction Procedure

A coordinate system(d1, d2), where d1and d2range from−255 to 255, represents the difference–value of pixel pairs(p i−1− pi ) and (p i+1− pi ), respectively There

is a large number of difference–values are close to 0s, due to the feature of images

that adjacent pixels have nearly similar values Therefore, when d1and d2range from

−1 to 1, a 3 × 3 is arranged as rectangle-shaped matrix called stamen matrix which

is marked in orange Every pair of(d1, d2) in the stamen matrix can carry a secret

digit ranging from(000)2to(111)2

(1, d2) = d1 + 3d2 + 4 mod 8, if d1,2 ∈ {−1, 0, 1} (6.4)

Then, settle the second part of the big matrix, when either d1or d2is equal to 0 The calyx matrix is marked in blue as shown in Fig.6.1 Equation (6.5) describes the calyx matrix

M (d1, d2) = d1 mod 4 , i f d1{−1, 0, 1}, d2 = 0

d2 mod 4, i f d1= 0, d2 /∈ {−1, 0, 1} (6.5)

The positive axis of d1ranges from 2 to 255, and the negative axis of d1ranges from−2 to −255; meanwhile, d2is set 0 The other two calyxes on the positive axis

7 6 5 4 3 2 1 0 1 2 3 4 5 6 7

2 1 0 31 30 29 28 1 28 29 30 31 0 1 2

29 28 27 26 25 24 23 2 23 24 25 26 27 28 29

23 22 21 20 19 18 17 3 17 18 19 20 21 22 23

17 16 15 14 13 12 11 0 11 12 13 14 15 16 17

11 10 9 8 7 6 5 1 5 6 7 8 9 10 11

6 5 4 3 2 1 0 2 0 1 2 3 4 5 6

6 5 4 3 2 1 0 2 0 1 2 3 4 5 6

11 10 9 8 7 6 5 1 5 6 7 8 9 10 11

17 16 15 14 13 12 11 0 11 12 13 14 15 16 17

23 22 21 20 19 18 17 3 17 18 19 20 21 22 23

29 28 27 26 25 24 23 2 23 24 25 26 27 28 29

2 1 0 31 30 29 28 1 28 29 30 31 0 1 2

7 6 5 4 3 2 1 0 1 2 3 4 5 6 7

d1

Fig 6.1 The designed scheme based on a reference-affected matrix

and on the negative axis of d2could be obtained by transposing calyxes, respectively.

Every element M (d1, d2) in these calyxes can carry secret digits from (00)2to(11)2 The major arranging area of the matrix known as petal is marked in green as shown in Fig.6.1 Every its column is set difference value as 1, and the range is from

0 to 31 and every row sets in turn difference value as 5, 6, 6, 6, and 6, and the range

is from 0 to 31 The whole matrix called x-cross-shaped reference matrix composed

of petal matrix, calyx matrix, and stamen matrix as shown in Fig.6.1

6.6 Payload Calculation

Once information hiding needs to conduct in an unreliable environment, that the total volume of secret messages will be expected as much as possible during one transmission Each cover image’s payload depends on the resolution of the host image The steps of a calculating procedure for the secret message are the following:

Step 1 Extract a triple of consecutive cover pixels (p i−1, p i , p i+1), where i =

2, 5, , (W × H − (W × H mod 3) − 1) Convert a message S to a bit

stream First, extract three bits from the secret string and embed the segment

into the host image using pi by LSB substitution method, and update ls =

l s + 3, where lsrepresents the length of the secret string which is going to

be embedded into a cover image Relative to pi is a cover pixel, and then p i

is a camouflaging pixel

Step 2 Calculate the difference values d1= pi−1− p

i and d2= pi+1− p

i, respec-tively

Step 3 Recognize M(d1, d2) belonging to which part of the x-cross-matrix: If it

belongs to the calyx area, then ls = ls+ 2; if it belongs to the stamen part,

l s = ls + 3; otherwise, ls = ls + 5, which means it belongs to the petal matrix

Step 4 Repeat from Steps 1 to 3 until all pixels in the cover image are completely

processed Return the payload length ls.

Our scheme embeds a 3-bit sub-secret string to the LSB pixel of pi, and we also embed

a ls-bit sub-secret string to the pair of difference values (d1, d2) The binary value s

is converted to its corresponding decimal value sd The length lsof to-be-embedded

secret data s depends, on where the pair (d1, d2) locates on the flow-shaped reference

matrix

A secret message is embedded in a binary system into a host image During the procedure of embedding a secret, our scheme is efficient due to the embedding time less than 25 s with more than 2.6 bit per pixel (bpp)

Step 1 Extract a triple of consecutive cover pixels (p i−1, p i , p i+1), where i =

2, 5, , (W × H − (W × H mod 3) − 1).

Step 2 Embed three bits of secret message into the LSB of p ito generate a

stego-image pixel p i Then, compute d1= pi−1− p

i , d2= pi+1− p

i

Step 3 If the decimal secret s d is equal to M (d1, d2), then keep d1, d2unchanged;

otherwise, embed sdas the following rules:

Case 1 M (d1, d2) belongs to the petal matrix, which means this pair

of (d1, d2) can carry five digits of secret message ranging from (00000)2 to (11111)2 While the sub-secret sd is unequal to

M (d1, d2), find the paird1, d

2

 which has the shortest distance with(d1, d2) and is equal to sub-secret s d with the guidance of matrix x-cross Change (d1, d2) to d1, d

2

 later, according to

d1 = p

i−1 − p

i , d2 = p

i+1 − p

i, to generate the stego-pixels:

p i−1 and pi+1

Case 2 M(d1, d2) belongs to the stamen matrix, which means this pair

of(d1, d2) can carry three digits of secret message ranging from (000)2to(111)2 While the sub-secret sd is unequal to M (d1, d2),

find the pair

d1, d 2



that is equal to sub-secret sd with the guid-ance of matrix x-cross Change(d1, d2) tod1, d

2

 later, according

to d1=p

i−1 − p

i , d2 = p

i+1− p

i, to generate the stego-pixels:

p i−1 and pi+1

Case 3 M (d1, d2) belongs to the calyx matrix, which means this pair of

(d1, d2) can carry two digits of secret message ranging from (00)2

to(11)2 While sub-secret sd is unequal to M (d1, d2), find the pair



d1, d 2



that is equal to sub-secret sdwith the guidance of matrix x-cross Change(d1, d2) tod1, d

2



later, according to d1= p

i−1−p

i,

d2 = p

i+1 − p

i , to generate the stego-pixels: pi−1 and p i+1

So far, the triple of consecutive stego-pixels

p i−1, p

i , p

i+1

 are generated

Step 4 Repeat Steps 1–4 until all secret messages are embedded We obtain the

stego-image finally

For example: Once embedding a secret digit “3” by the x-cross-shaped refer-ence matrix, and a secret digit “7” by LSB substitution under the triple cover pix-els(p i−1, p i , p i+1) = (79, 74, 82), the LSB substitution procedure changes the

central pixel from 74 (1001010)2 to 79 (1001111)2 such that

p i−1, p

i , p i+1

=

(79, 79, 82) Then compute (d1, d2) = (0, 3), and find M(0, 4) is 3, so that



d1, d

2



= (0, 4), and finally change the stego-vector p i−1, p

i , p

i+1



=

(79, 79, 83) If we want to embed a secret digit “2” by the x-cross-shaped reference

matrix, the procedure flowchart of calculating the length of the secret message 4, and

a secret digit “5” by LSB substitution under the triple cover pixels(p i−1, p i , p i+1) = (77, 74, 77), the embedding procedure first hasp i−1, p

i , p i+1

= (77, 77, 77),

next compute(d1, d2) = (0, 0), and lastd1, d

2



= (−1, 1) Therefore, the triple

stego-pixels are

pi−1, p

i , p

i+1



= (78, 77, 76) If embedding a secret digit “14”

the x-cross-shaped reference, and a secret digit “7” by LSB substitution under the triple cover pixels(p i−1, p i , p i+1) = (49, 45, 50), apply LSB procedure to change



p i−1, p

i , p i+1

= (49, 47, 50) and compute (d1, d2) = (2, 3), so thatd1, d

2



=

(3, 4) At last, the triple stego-pixels arepi−1, p

i , p

i+1



= (50, 47, 51).

6.8 Secret Extraction Procedure

First, select the triple of consecutive stego-pixels

p i−1, p

i , p

i+1

 , from a

stego-image The secret data can be obtained from the three least-significant bits of p i

Second, compute d1 = p

i−1− p

i and d2 = p

i+1− p

i Based on the location indication

of the two values

d1, d 2



on the x-cross-shaped reference matrix, M

d1, d 2



is the secret data Whole secret message could be archived by repeating to process the secret extraction procedure Assume

pi−1, p

i , p

i+1

 from a stego-image is (83, 79,

79) According to the extraction procedure, we can extract secret “7” (111)2 from p i

and “3” (11)2 from

d1, d 2

 , respectively What about the triples

p i−1, p

i , p

i+1



=

(78, 77, 76)? Secret data “5” (101)2 and “2” (101)2 can be extracted from p

i and



d1, d

2



, respectively Let us look at what the secret message will be extracted from the

pi−1, p

i , p

i+1



= (51, 47, 50), which are “7” (111)2 from p

i = 47 and “14” from

d1, d

2



= (4, 3).

6.9 Experimental Result

Two measuring parameters are used in the experiment to quantify the performance

of the proposed method included: the embedding capacity (EC) and peak signal-to-noise ratio (PSNR) EC is the number of secret data embedded in a test image, and PSNR is a kind of objective criteria for the evaluation of the image (greater PSNR

is the better quality of the image)

PSNR= 10 log10

2552

M S E

(6.6)

H × W

H



i=1

W



j=1



p i , j − p

i , j



(6.7)

where H and W represent the height and width of the cover image, respectively, pi , j represents the original cover pixels, and p i, jrepresents the camouflage image pixels, respectively The process of embedding payload and image quality is as follows: First, divide each test image into 4 × 4 nonoverlapping blocks Second, calculate the block standard deviations Third, use the histogram to present the relationship between the standard deviation and the number of blocks

Table6.1shows a comparison of the experimental results of embedding secret information into two categories of the image Apparently, the smooth regions are more suitable for embedding secret information due to the smaller difference between the pixel values

Figure6.2shows the calculation of the block standard deviations for images that use six 512× 512 grayscale test images The category of smooth images has the block standard deviations that are mostly around 0s The category of complex images has variances block standard deviations are hardly around over 0

Table6.2shows the comparison of results of the experiments of the proposed scheme with the turtle-shaped scheme [8] and the regular-octagon scheme [10] Obvi-ously, the performance of the proposed scheme provides outstandingly the results Figure6.3compares the original image of bridge with its camouflage one that has low PSNR of 38.1356(dB) Though the image ofbridge is classified as a complex image, with human being’s eyes is difficult to recognize the difference between the original image and the stego-image

Table 6.1 Smooth images and complex images PSNR and payload

Fig 6.2 Calculation of the block standard deviations for smooth and complex images

Table 6.2 Comparison of the proposed scheme with the turtle-shaped scheme and the

regular-octagon scheme

[ 10 ]

Fig 6.3 Original image and stego-image based on bridge

Figure 6.4 shows the histograms of six 512 × 512 grayscale test images for identifying image types The experimental results of embedding payload and image quality demonstrate that the proposed method is a competitor of embedding secret data scheme

In this paper, we proposed a new scheme of embedding secrets information to solve the issues of low distortion and high embedding capacity in the embedded secret data in media The guidance of the x-cross-shaped reference-affected matrix was applied for embedding capacity in transferring more secret messages Adjacent pixels

in a large area of the matrix with similar values can utilize for manipulating data

in a large area of the matrix with similar values can utilize... standard deviations for images that use six 512× 512 grayscale test images The category of smooth images has the block standard deviations that are mostly around 0s The category of complex images...

Table6.1shows a comparison of the experimental results of embedding secret information into two categories