CN115242930A

CN115242930A - Cipher text domain extreme prediction double-layer reversible information hiding method based on secret sharing

Info

Publication number: CN115242930A
Application number: CN202210580640.9A
Authority: CN
Inventors: 石慧; 周梓怡; 耿佳宁
Original assignee: Liaoning Normal University
Current assignee: Liaoning Normal University
Priority date: 2022-05-26
Filing date: 2022-05-26
Publication date: 2022-10-25
Anticipated expiration: 2042-05-26
Also published as: CN115242930B

Abstract

The invention discloses a cipher text domain extreme prediction double-layer reversible information hiding method based on secret sharing, which comprises the steps of firstly carrying out full bit plane decomposition on a carrier image, proposing an additive secret sharing strategy based on a bit plane to enable cipher text images to be shared by multiple parties, proposing a name-removing mechanism to process secret information, realizing lossless recovery and extraction by utilizing the sharing of other two parties under the condition that one party shares traitors, and realizing the cipher text domain double-layer information hiding strategy through extreme prediction; at a receiving end, the secret information is extracted and recovered in a lossless mode by using a contrast prediction error, a threshold value and a name-divisible mechanism, and the lossless recovery of the original image is realized through corresponding inverse transformation and special properties of additive secret sharing. The invention has the advantages of strong safety, high embedding capacity, high image quality, reversibility and the like.

Description

Cipher text domain extreme prediction double-layer reversible information hiding method based on secret sharing

Technical Field

The invention belongs to the field of multimedia information security, and particularly relates to a cipher text domain extreme prediction double-layer reversible information hiding method based on secret sharing.

Background

In recent years, the openness and the sharability of networks have promoted the rapid development of network multimedia, and 5G networks provide better network capability for multimedia information transmission and simultaneously bring great threats and challenges, such as malicious tampering, illegal copying, privacy disclosure and other problems, so that it is very important to protect the security of multimedia data, and preventing the leakage of multimedia information has become a research hotspot. The ciphertext domain Reversible information Hiding (RDHEI) can hide information while protecting Image content from being leaked, a user can decrypt the Image content according to the type of a possessed secret key and the requirement of the user, extract the hidden information and restore an original Image in a lossless mode, and the method is a cross research hotspot of information Hiding, multimedia technology and ciphertext signal processing.

The original RDHEI algorithm was to make Room After the image was encrypted, i.e. ciphertext reversible information hiding based on the VRAE (changing Room After Encryption) framework and symmetric Encryption. As early as 2008, puech et al concealed additional information in each block by segmenting the encrypted image, and finally completed information extraction and image restoration using the local standard deviation of the image pixels. However, this method has not been of interest to researchers, until 2012, zhang encrypts the original image using stream cipher and then divides the encrypted image into blocks of the same size, hiding the additional information by flipping the LSBs of some of the pixels in the block.

With the continuous improvement of data security requirements at home and abroad, ciphertext domain reversible information hiding algorithms based on symmetric Encryption and RRBE (responding from Before Encryption) framework and public key/homomorphic Encryption are generally concerned by scholars. Puteaus et al propose that the information hiding of the ciphertext domain does not need to consider the problem of image visual quality after encryption and hiding, and therefore the highest bitplane replacement of the image is adopted to embed the additional information, and therefore a higher effective load is obtained.

However, the VRAE-based framework has its own limitations, for example, some may have an error rate in data extraction or image recovery, cannot realize complete reversibility, and some may not be separable in the information extraction and image recovery processes; the algorithm based on the symmetric encryption and the RRBE framework has the problems of limited capacity and the like.

Disclosure of Invention

The invention aims to solve the problems in the prior art and provides a secret sharing-based ciphertext domain extreme prediction double-layer reversible information hiding method.

The technical solution of the invention is as follows: a secret sharing based ciphertext domain extreme prediction double-layer reversible information hiding method is sequentially carried out according to the following steps:

step 1, preprocessing an original carrier image:

step 1.1, traversing all pixels in an original carrier image with the dimension of H multiplied by W, marking the pixel point with the pixel value of 0 as 0, and marking the non-0 pixel point as 1 to obtain an LM (Levenberg-Marquard) image;

step 1.2, traversing all pixels in an original carrier image with the dimension of H multiplied by W, setting a 0-value pixel as 1, and obtaining a carrier image X with the pixel range of [1, 255 ];

step 2, encrypting the carrier image X by additive secret sharing

Step 2.1 Each pixel X of the support image X is processed according to the formula (1-4) _l (i, j) is divided into three sections: x is the number of _h High order bit part, x _m Middle-order part and x _l A lower-order bit portion in which i ∈ [1,H ]]，j∈[1，W]，α∈(0，7)，β∈(0，7)，α+β≤7；

x(i，j)＝x _h (i，j)×2 ^α +x _m (i，j)×2 ^β +x _l (i，j) (1)

x _l (i，j)＝x(i，j)-x _h (i，j)×2 ^α -x _m (i，j)×2 ^β (4)

The x is expressed according to the formula (5-6) _h High order bit portion and x _l And (3) low-order bit part exchange:

x _h ＝x _l ×2 ^a (5)

x _l ＝x _h ÷2 ^a (6)

step 2.2 according to the disclosureFormula (7-9), separating x _h High order bit portion, x _m Middle-order part, x _l Low order bit portions randomly partitioned into

Wherein r is from {1,2,3, …, r _max }，r _max Is a positive integer;

step 2.3 will

Re-randomly combining according to the formula (10) to generate n shared encrypted carriers share _n Where n is the {1,2,3, …, r _max }，

The upper corner marks r are respectively in the set {1,2,3, …, r _max Get the value and mark r in the same order position can not be repeated, i.e. r in the same order position is not equal to r +1 not equal to … not equal to r _max ；

Step 3 encrypting the secret information using a mechanism for name removal

Step 3.1 generates a random number sequence L as long as the secret information matrix YD of size g × L according to the formula (11) ₁ Where k is equal to {1,2,3 …, g × l },0 < x ₀ Less than 1,3.5699456 less than or equal to 4 mu, selecting x ₀ Mu is stored as a secret key K ₁ ；

x _k+1 ＝μx _k (1-x _k ) (11)

Step 3.2 transform the range of values in the random number sequence to [0, 255] according to equation (12)]Then, converting the transformed one-dimensional random sequence into a two-dimensional matrix M with the size equal to that of the secret information matrix, namely, gxl; and store K ₂ K in the formula (14) ₂ The random key is a positive integer;

step 3.3, converting the two-dimensional matrix M and the secret information matrix YD into binary systems, then carrying out bitwise XOR operation, and finally converting the binary systems subjected to XOR into decimal systems;

step 3.4, the two-dimensional matrix subjected to the exclusive or operation is converted into a one-dimensional sequence YD' with the length of p based on S-shaped traversal, wherein p = g × l and is an even number;

step 3.5 connect LM map with one-dimensional sequence YD' = { d = { ₁ ，d ₂ ，...，d _p D is generated by connection and is split into two equal parts according to a formula (13), and the two equal parts are respectively D ^ω And D ^δ ，

The length of D for u;

D＝D ^ω +D ^δ (13)

step 3.6 preparation of D according to equation (14) ^ω And D ^δ Generating third party secret information D according to bit XOR ^ξ ；

Step 4 double-layer embedding strategy

Step 4.1 selects four known points f (0,0), f (1,0), f (0,1), f (1, 10) as reference pixels, and uses the share as a bilinear interpolation method according to formula (15) _n Extended to obtain eshare _n ，：

f(x，y)＝f(0，0)(1-x)(1-y)+f(1，0)x(1-y)+f(0，1)(1-x)y+f(1，1)xy (15)

Step 4.2 using extreme prediction technique to correct eshare _n Making a prediction using an overestimated predictor p ⁺ And underestimation predictor p ^- Respectively to eshare _n Performing extreme prediction to generate

And

and calculates a prediction error e according to the formula (16-21) ⁺ (i ', j') and e ^- (i ', j '), i ' e [0,2H ] in equation (18-23)]，j′∈[0，2W]：

Wherein, c _q Surrounding pixels representing a prediction target pixel are used to generate a prediction value，q∈{0，1，2…，q _max }，q _max The number of surrounding pixels used for prediction;

step 4.3 generating a pair of asymmetric prediction error histograms, wherein the overestimated prediction error values generate a right-biased histogram H ⁺ Generating left-hand histogram H by underestimating prediction error value ^- ；

Step 4.4 according to the formulas (22) and (23), the double-layer embedding is completed based on histogram translation, and a right-biased histogram H is utilized ⁺ Secret sharing of eshare contained after embedding of the first layer' _n Using left-hand histogram H ^- The secret sharing after the second layer embedding is eshare _n (ii) a Wherein s is ₁ Is a first layer of embedded secret information, s ₂ Is a second layer of embedded secret information, s ₁ And s ₂ Is formed by D ^ξ Is divided equally to obtain ⁺ And T ^- Respectively, a right-biased histogram H ⁺ And left-hand offset histogram H ^- Peak point of, z ⁺ Is the zero value point on the left side of the peak value point of the right-hand histogram closest to the peak value point, z ^- Is the zero value point on the right side of the peak value point of the left partial histogram closest to the peak value point:

step 4.5 repeat the operations of steps 4.2-4.4 until the traversal is completed with eshare _n All of the pixels of (1).

The secret information extraction and the carrier image recovery are sequentially carried out according to the following steps:

step 5.1, according to the formulas (17), (19) and (21), the received dense shared image eshare ″ _n Underestimating the prediction error, and recording the prediction error value as e ^-′ (i ', j'), the predicted value is recorded as

Step 5.2 Using the sum of (24) and

extracting secret information s 'embedded in second layer' ₂ ；

Step 5.3, the second layer pixel value reshare' is restored according to the formula (25) _n ；

Repeating the steps 5.1-5.3 until all secret information of the second layer is extracted and the reshare' is completely recovered _n The aforementioned reshare _n Equivalent to eshare' _n ；

Step 5.4 Pair of reshare ″, according to equations (16) (18) and (20) _n Performing overestimation on the prediction error, and recording the prediction error value as e ⁺ ' (i ', j '), and the predicted value is recorded as

Step 5.5 based on equation (26) and the calculated

Extracting first layer embedded secret information s' ₁ ；

Step 5.6 recovers the first layer secret information pixel value reshare 'according to formula (27)' _n ；

Repeating steps 5.4-5.6 until all secret information of the first layer is extracted and reshare 'is completely recovered' _n ，reshare′ _n Equivalent to eshare _n I.e. not embedding a dense image;

step 5.7 recovery of secret information

S 'extracted' ₁ And s' ₂ Respectively arranging and connecting according to the extraction sequence to obtain D ^ξ 、D ^ω 、D ^δ D is ^ω And D ^δ Combining to obtain D; sharing is distributed to different users, and only 2 users provide respective sharing together, the initial secret can be reconstructed;

(1) If hidden D ^ω Using the other two shares to extract secret information D ^ξ And D ^δ To give out D ^ω The secret information D is recovered according to equation (28):

(2) If hidden D ^δ Using the other two shares to extract secret information D ^ξ And D ^ω To give out D ^δ The secret information D is recovered according to the formula (29):

(3) If hidden D ^ξ With other two shares sharing the extracted secret information D ^ω And D ^δ Merging, and recovering the secret information D according to the formula (30):

D＝D ^ω +D ^δ (30)

step 5.8, splitting D to obtain an LM (mean squared error) graph and secret information YD ', traversing YD' according to a S-shaped traversal sequence, and converting the YD 'into a matrix YD' with the size of g multiplied by l;

step 5.9 Using the decryption Key K ₁ And K ₂ Generating a matrix M' according to the steps 3.1 and 3.2;

step 5.10 executing bitwise XOR operation on YD 'and M' to generate decrypted secret information YD;

step 5.11 extraction of all reshare' _n (2 i '-1,2j' -1) pixel points are rearranged to obtain share _n Where i' is E [1,2H]，j′∈[1，2W]；

Step 5.12 merge share according to formula (32) _n Recovering the carrier image RX, where i ∈ [1,H ∈ [ ]]，j∈[1，W]；

rx(i，j)＝share ₁ (i，j)+share ₂ (i，j)+share ₃ (i，j) (32)

Step 5.13, separating the RX bit planes by using the formula (1-4), and exchanging the high order and the low order by using the formula (5-6) to recover the carrier image X;

and 5.14, changing the pixel value of the corresponding position in the X marked as 0 in the LM picture into 0 by using the LM picture, and completely recovering the original carrier image.

The invention firstly carries out full bit plane decomposition on a carrier image, proposes an additive secret sharing strategy based on a bit plane to enable a ciphertext image to be shared by multiple parties, and simultaneously proposes a name-removing mechanism to process secret information, so that under the condition that one party shares traitors, the lossless recovery and extraction can still be realized by utilizing the sharing of other two parties, and in addition, a double-layer information hiding strategy of a ciphertext domain is realized through extreme prediction; at a receiving end, the secret information is extracted and recovered in a lossless mode by using a contrast prediction error, a threshold value and a name-divisible mechanism, and the lossless recovery of the original image is realized through corresponding inverse transformation and special properties of additive secret sharing. The invention has the advantages of strong safety, high embedding capacity, high image quality, reversibility and the like.

Drawings

FIG. 1 is a flow chart of the method of the present invention for embedding secret information.

Fig. 2 is a schematic diagram of dividing a bit plane and encrypting a carrier image according to an embodiment of the present invention.

Fig. 3 is a schematic diagram of interpolating an extended ciphertext image according to an embodiment of the present invention.

FIG. 4 is a schematic diagram of an embodiment of an interpolation extended share ₁ Schematic representation of (a).

Fig. 5a is a right-biased histogram of prediction errors according to an embodiment of the present invention.

Fig. 5b is a left-biased histogram of prediction errors according to an embodiment of the present invention.

FIG. 6 is a diagram illustrating the completion of dual-layer embedding based on histogram shifting according to an embodiment of the present invention.

Fig. 7 is a schematic diagram of extracting secret information and recovering a carrier image according to an embodiment of the present invention.

FIG. 8 is a schematic diagram of a downsampled interpolated image according to an embodiment of the present invention.

FIG. 9a is a diagram of a raw carrier according to an embodiment of the present invention.

Fig. 9b is a diagram of a split bit plane effect according to an embodiment of the present invention.

Fig. 9c is a share effect diagram according to an embodiment of the present invention.

FIG. 9d is a diagram illustrating interpolation effects according to an embodiment of the present invention.

FIG. 9e is a graph showing the effect of embedding density according to the embodiment of the present invention.

Fig. 9f is a diagram of the effect of restoring the carrier image according to the embodiment of the present invention.

FIG. 10a is a pixel correlation scatter plot of a Lena original image according to an embodiment of the present invention.

FIG. 10b is a diagram of a ciphertext image share according to an embodiment of the present invention ₁ A pixel correlation scatter plot.

FIG. 10c is a diagram of a ciphertext image share according to an embodiment of the present invention ₂ A pixel correlation scatter plot.

FIG. 10d is a diagram of a ciphertext image share according to an embodiment of the present invention ₃ A pixel correlation scatter plot.

Fig. 11 is a difference image of a watermark and an extracted watermark according to an embodiment of the present invention.

FIG. 12 is a NIQE measurement versus bar graph of an original image and a recovered image according to an embodiment of the present invention.

Detailed Description

The invention discloses a secret sharing-based ciphertext domain extreme prediction double-layer reversible information hiding method which is shown in figure 1 and sequentially comprises the following steps:

step 1, preprocessing an original carrier image:

step 1.1, traversing all pixels in the original carrier image with the dimension of H multiplied by W as shown in FIG. 9a, marking the pixel point with the pixel value of 0 as 0, and marking the non-0 pixel point as 1 to obtain an LM (edge weighted mean) image;

step 1.2, in order to avoid underflow (overflow cannot be generated in the invention), traversing all pixels in the original carrier image with the dimension of H multiplied by W, setting a pixel with a value of 0 as 1, and obtaining a carrier image X with a pixel range of [1, 255 ];

step 2, encrypting the carrier image X by additive secret sharing

x(i，j)＝x _h (i，j)×2 ^α +x _m (i，j)×2 ^β +x _l (i，j) (1)

x _l (i，j)＝x(i，j)-x _h (i，j)×2 ^α -x _m (i，j)×2 ^β (4)

x _h ＝x _l ×2 ^a (5)

x _l ＝x _h ÷2 ^a (6)

in the embodiment of the present invention, the variables have the following values of α =5 and β =3, and fig. 9b showsThe separation bit plane effect diagram of the embodiment of the invention is x from left to right _h High order bit part, x _m Intermediate order part and x _l A lower order bit portion.

This embodiment takes as an example a 3 × 3 pixel block having

pixel values

219, 218, 216, 217, 218, 213, 219, and 215 as shown in fig. 2.

Taking the pixel value 219 in fig. 2 as an example, the upper three bits of the 8 bits of the binary sequence of the pixel are divided into a high-order part, the lower three bits are divided into a low-order part, and the remaining two middle bits are divided into a middle-order part:

(219) ₁₀ ＝(11011011) ₂

(11011011) ₂ ＝(110) ₂ ×2 ⁵ +(11) ₂ ×2 ³ +(011) ₂ ；

the pixel value (219) ₁₀ ＝(11011011) ₂ Higher order (110) ₂ And (011) ₂ Exchange, obtain (01111110) ₂ 。

Step 2.2 according to the formula (7-9), the separated x _h High order bit part, x _m Middle-order part, x _l Low order bit portion randomly partitioned into

Wherein r is from {1,2,3, …, r _max }，r _max Is a positive integer;

the embodiment of the invention selects r E {1,2,3};

with the pixel values in FIG. 2219 as an example, (219) ₁₀ ＝(11011011) ₂ Generating 6 random factors not greater than 0.5 to rand ₁ ＝0.2145、rand ₂ ＝0.0094、rand ₃ ＝0.2624、rand ₄ ＝0.0907、rand ₅ ＝0.1796、rand ₆ =0.2034 as an example, where rand ₁ And rand ₂ For dividing the higher order part, rand ₃ And rand ₄ For dividing the medium-order part, rand ₅ And rand ₆ For splitting the low order part, as follows:

step 2.3 will

Re-randomly combining according to the formula (10) to generate n shared encrypted carriers share _n Where n is ∈ {1,2,3},

Specifically, the random combination can be performed again according to the following formula:

taking pixel 219 in FIG. 2 as an example, (219) ₁₀ ＝(11011011) ₂ Generating share ₁ 、share ₂ And share ₃ As follows:

Share three shares ₁ 、share ₂ 、share ₃ And distributed to three third party embedders.

It should be noted that the invention uses additive secret sharing to make three parts of the pixel value evenly distributed to keep the property of additive secret sharing, and the invention shares different from other schemes based on secret sharing which share the image pixel independently, sharing a plurality of pixels at one time improves the efficiency, reduces the data expansion, random segmentation and random combination, the double random superposition can further improve the security, and uses random number in the sharing process, therefore, the encryption method of the invention is a system with randomness and uncertainty, encrypts the image twice, the generated encrypted images are completely different, and the invention has a capability of resisting many potential attacks.

Tables 1-4 show that eight gray images of Lena, babon, barbarbara, pepper, jetplane, boat, house, and Island with 256 × 256 size are used as experimental data to respectively perform sharp of original image and ciphertext image ₁ 、share ₂ And share ₃ And (5) performing correlation coefficient analysis. As can be seen from table 1, the correlation coefficient is about 0.9, which indicates that there is a high correlation between adjacent pixels in the original image, and any pixel easily leaks information of its neighboring pixels, and an attacker can often predict the gray value of the neighboring pixels by using the characteristic, thereby realizing the prediction of the entire plaintext image. As can be seen from tables 2 to 4, most of the correlation coefficients are lower than 0.1, which indicates that the ciphertext share breaks the strong correlation of the plaintext, and thus, the ciphertext share has higher security. In addition, fig. 10a shows a pixel correlation scatter diagram of Lena original image according to an embodiment of the present invention, which is mainly concentrated on diagonal lines, indicating that the correlation of the original image is high; FIGS. 10b-d respectively show ciphertext image share according to an embodiment of the present invention ₁ ，share ₂ And image share ₃ The prime correlation scatter diagrams are respectively uniform, and show that the secret sharing correlation is low and the safety is high.

TABLE 1

TABLE 2

TABLE 3

TABLE 4

Step 3 encrypting the secret information using a renameable mechanism

x _k+1 ＝μx _k (1-x _k ) (11)

in the embodiment of the present invention, g =2,l =3,p =6, and the secret information matrix is 2 × 3 in size

For example, a two-dimensional matrix of the same size

XOR to obtain the encrypted secret information

The details are as follows:

specifically, the exclusive-or two-dimensional matrix is converted into a one-dimensional sequence YD' {132, 235, 120, 48, 211, 139} with a length of 6 based on a sigmoid traversal;

The length of D for u;

D＝D ^ω +D ^δ (13)

in the embodiment of the present invention, LM = {219, 218}, YD' = {132, 235, 120, 48, 211, 139}, and p =6, and the LM map is connected to secret information as D = {219, 218, 132, 235, 120, 48, 211, 139} and split into two equal parts by length, D = {219, 218, 132, 235, 120, 48, 211, 139}, and D = ^ω = {219, 218, 132, 235} and D ^δ ＝{120，48，211，139}；

In particular, {219, 218, 132, 235} and {120, 48, 211, 139} are converted into binary and bitwise XOR-ed to generate alternative secret information D ^ξ The two shares and the generated alternative secret information are respectively embedded into three shares share ₁ 、share ₂ 、share ₃ Performing the following steps;

it should be noted that the conventional RDHEI scheme focuses on a data hiding device, and if only one encrypted image is lost or damaged, the original secret information cannot be recovered, and the named removal mechanism designed by the present invention allows traitors of one shared data hiding party to a certain extent, and can recover all secret information without loss by performing an exclusive-or operation using the secret information extracted from the other two shares, and has certain robustness, and the principle is as follows (A, B, C represents three parties, respectively):

and if one bit in the original secret information changes, the third party secret information also changes, so that the expansion characteristic is realized, and the safety is further improved.

Step 4 Dual-layer embedding strategy

Step 4.1 as shown in fig. 3, four known points f (0,0), f (1,0), f (0,1), f (1, 10) are selected as reference pixels, and the share is interpolated according to the bilinear interpolation method of formula (15) _n Extended to obtain eshare _n ，：

f(x，y)＝f(0，0)(1-x)(1-y)+f(1，0)x(1-y)+f(0，1)(1-x)y+f(1，1)xy (15)

In the embodiment of the present invention, as shown in fig. 4, for example, using 2 × 2 pixel blocks, the share is interpolated by bilinear interpolation ₁ Expanding to obtain eshare ₁ Wherein the four reference pixel values are respectively: 48. 35, 18, 32, the interpolated pixels are as follows:

it is worth noting that the image interpolation improves the correlation among pixels in the image, and meanwhile, the histogram also has obvious peak points, and the embedding capability is well improved.

And

and calculates a prediction error e according to the formula (18-23) ⁺ (i ', j') and e ^- (i ', j '), i ' e [0,2H ] in formula (18-23)]，j′∈[0，2W]：

Wherein, c _q Surrounding pixels representing the prediction target pixel are used to generate a prediction value, q ∈ {0,1,2 …, q ∈ [ ], {0,1,2 … } _max }，q _max The number of surrounding pixels used for prediction;

example q of the invention _max Taking 4, c1, c2, c3 and c4 as x (i-1,j-1), x (i-1,j), x (i-1, j + 1) and x (i, j-1) respectively;

in the embodiment of the invention, the eshare subjected to extreme prediction technology ₁ Prediction was performed with eshare in FIG. 4 ₁ (2,2) pixel value 33 pixel example, using overestimate predictor and underestimate predictor for eshare ₁ (2,2) extreme prediction to generate

And

and calculates a prediction error e ⁺ (2,2) and e ^- (2,2), as follows:

e ⁺ (2，2)＝0

e ^- (2，2)＝-15

Specifically, as shown in fig. 5, a pair of asymmetric prediction error histograms are generated using a pair of prediction error values, and fig. 5a is a right-biased histogram H ⁺ FIG. 5b is a left-hand histogram H ^- 。

Step 4.4 according to the formulas (22) and (23), the double-layer embedding is completed based on histogram translation, and a right-biased histogram H is utilized ⁺ Secret sharing of eshare contained after embedding of the first layer' _n Using left-hand histogram H ^- The secret sharing after the second layer embedding is eshare _n (ii) a Wherein s is ₁ Is a first layer of embedded secret information, s ₂ Is a second layer of embedded secret information, s ₁ And s ₂ Is formed by D ^ξ Is divided equally to obtain ⁺ And T ^- Respectively, a right-biased histogram H ⁺ And left-hand histogram H ^- Peak point of, z ⁺ Is the zero value point on the left side of the peak value point of the right-hand histogram closest to the peak value point, z ^- Is the zero value point on the right side of the peak value point of the left partial histogram closest to the peak value point:

in the embodiment of the invention, the pixel with the pixel value of 33 in the second row and the second column in FIG. 6 is taken as an example, eshare' ₁ Is a secret share after the first embedding, eshare ₁ Is secret sharing after the second embedding, s ₁ =1 is the first bit, s, in which the secret information is embedded ₂ Is the second bit, T, in which secret information is embedded ⁺ ＝T ^- ＝0，z ⁺ ＝-17，z ^- ＝17：

e ⁺ (2，2)＝0

eshare′ ₁ (2，2)＝33-1

e ^- (2，2)＝-15

eshare″ ₁ (2，2)＝32

FIG. 9e is a schematic diagram illustrating the embedding effect of the embodiment of the present invention.

Specifically, 1bit of secret information is embedded into a right-leaning prediction error histogram (the number of pixels on the right side of a peak value is more than that of pixels on the left side of the peak value), a prediction error value is compared with a threshold value, and if the prediction error value is equal to the threshold value, a pixel value is modified to be embedded into the secret information; if the prediction error value is smaller than the threshold value and larger than the nearest zero point on the left side of the peak value, the pixel value is reduced by one, and in other cases, the pixel value is unchanged; similarly, 1bit of secret information is embedded into a left inclination prediction error histogram (the number of pixels on the left side of the peak value is more than that of pixels on the right side of the peak value), the prediction error value is compared with a threshold value, and if the prediction error value is equal to the threshold value, the pixel value is modified and the secret information is embedded; if the prediction error value is larger than the threshold value and smaller than the nearest zero point on the right side of the peak value, the pixel value is added with one, and otherwise, the pixel value is unchanged. Repeating the process until the secret information is completely embedded to obtain the ciphertext image containing the secret.

The invention adopts an extreme prediction method to embed the secret data, and can obtain larger embedding rate for a plurality of natural images. Table 5 shows the embedded capacity of the experiment of the embodiment of the present invention compared with the related method, and it can be seen that the present invention has a larger capacity than the related method, about 7 times more than the other methods in capacity.

TABLE 5

It is worth noting that the present invention only shifts the side with the least number of pixels, frees up embedding space for secret information, and employs a bi-directional embedding strategy to take full advantage of redundant information in the image. Compared with the traditional method for embedding the secret information by the prediction error histogram, which needs to move the pixels at two sides of the peak value and vacates an embedding space for the secret information, the method has the advantages of less moving pixel amount, less influence on the image and better performance in a capacity distortion control task.

The secret information extraction and the carrier image recovery of the embodiment of the invention are sequentially carried out according to the following steps:

step 5.1 is to receive the dense shared image eshare ″' according to the formulas (17), (19) and (21) _n Underestimating the prediction error, and recording the prediction error value as e ^-′ (i ', j'), the predicted value is recorded as

Specifically, as shown in FIG. 7, the figure shows eshare ″) ₁ (2,2) as an example, the prediction error value is calculated: e.g. of the type ^- ′(2，2)＝-16；

Step 5.2 Using the sum of (24) and

extracting second layer embedded secret information s' ₂ ；

Specifically, as shown in FIG. 7, eshare ″', which is shown in the figure ₁ (2,2) for example, S is extracted first by traversing the dense image according to the reverse order of the embedding order, the reverse S ₂ If the current pixel value minus the underestimation prediction value is equal to the threshold value, the secret information is 0, if the current pixel value minus the underestimation prediction value is equal to the threshold value plus 1, the secret information is 1, otherwise, no information is hidden:

thus, the secret information is not hidden in the second layer of embedding within the current pixel.

Specifically, as shown in FIG. 7, eshare ″ ₁ (2,2) for example, the second layer pixel values are restored:

reshare″ ₁ (2，2)＝32

repeating the steps 5.1-5.3 until all secret information of the second layer is extracted and the reshare' is completely recovered _n ，reshare″ _n Equivalent to eshare' _n ；

Step 5.4 Pair of reshare ″, according to equations (16) (18) and (20) _n Performing overestimation on the prediction error, and recording the prediction error value as e ^+′ (i ', j'), the predicted value is recorded as

Specifically, as shown in FIG. 7, the residual ″' in the figure ₁ (2,2) as an example, the prediction error value is calculated: e.g. of the type ^+′ (2，2)＝-1；

Step 5.5 based on equation (26) and calculated

Extracting first layer embedded secret information s' ₁ ；

Specifically, as shown in FIG. 7, the term "reshare ₁ (2,2) for example, if the current pixel value minus the overestimated prediction value is equal to the threshold, the secret information is 0, if it is, the secret information is 0Equal to the threshold plus one, the secret information is 1.

s′ ₁ ＝1

Specifically, as shown in FIG. 7, reshare 'is used' ₁ (2,2) for example, recovery of eshare without secret information ₁ Pixel value of (a):

reshare′ ₁ (2，2)＝32+1

repeating steps 5.4-5.6 until all secret information of the first layer is extracted and reshare 'is completely recovered' _n ，reshare′ _n Equivalent to eshare _n I.e. non-embedded image, fig. 9f is a diagram of the effect of recovering the carrier image according to the embodiment of the present invention;

step 5.7 recovery of secret information

specifically, eshare ″' is extracted ₂ And eshare ₃ The hidden secret information in the table is decoded by XOR operation to obtain eshare ₁ In the hidden secret information

Recombining D, D = {219, 218, 132, 235, 120, 48, 211, 139};

specifically, eshare ″' is extracted ₁ And eshare ₃ In the secret information, the eshare decoded by XOR operation ₂ In the hidden secret information

Recombining into secret information D: d = {219, 218, 132, 235, 120, 48, 211, 139};

D＝D ^ω +D ^δ (30)

specifically, directly set {219, 218, 132, 235} + {120, 48, 211, 139} = {219, 218, 132, 235, 120, 48, 211, 139};

it is worth noting that the invention creates an anonymous mechanism for secret information, which is capable of resisting collusion analysis, and in case of traitor with one data hiding party, the secret information can be completely recovered by using the secret information extracted from other two shares, thereby improving the security and reliability of the invention. Fig. 11 shows a difference image of the watermark and the extracted watermark according to the embodiment of the present invention, and BER =0, which indicates that the present invention can implement lossless extraction.

in particular, the amount of the solvent to be used,

Specifically, as shown in FIG. 8, reshare 'is taken' _n (1，1)、reshare′ _n (1，3)、reshare′ _n (3，1)、reshare′ _n (3，3)；

rx(i，j)＝share ₁ (i，j)+share ₂ (i，j)+share ₃ (i，j) (32)

By using the special property of additive secret sharing, the carrier image can be directly and quickly recovered by directly adding the distributed n shares without separating bit planes and recovering high, middle and low order parts,

specifically, pixel value (126) ₁₀ ＝(01111110) ₂ Higher order (011) ₂ And (110) ₂ Exchange to give (11011011) ₂ ；

x _h ＝(110) ₂ ×2 ⁵

x _l ＝(011) ₂ ÷2 ⁵

FIG. 12 shows a NIQE measurement versus bar graph of an original image and a restored image, which are identical, indicating that lossless restoration can be achieved by the present invention.

It should be noted that since data embedding and image encryption are independent, data extraction and image reconstruction are separable.

The invention provides an additive secret sharing mechanism, a name-removing mechanism, an extreme prediction mechanism and a ciphertext domain double-layer reversible embedding strategy, and has the advantages of high safety, large capacity and high image quality. Since each step of the encryption and embedding process is reversible, the present invention can fully recover the embedded data and the original image without data distortion.

Table 6 shows comparison of the encryption and decryption theoretical time complexity of the secret sharing and the related methods, and in general, the encryption and decryption computation complexity of the present invention is O (n), which is lower than that of other related documents, indicating that the encryption scheme proposed by the present invention has higher efficiency. Table 7 shows the actual run-time comparison, and it can be seen that even though the dual-layer embedding strategy is implemented, the average time for embedding 1bit is 0.000002, which is lower than that of other related references, indicating that the embedding efficiency of the present invention is high.

TABLE 6

TABLE 7

Reference documents:

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[2]Chen Y C，Hung T H，Hsieh S H，et al.A new reversible data hiding in encrypted image based on multi-secret sharing and lightweight cryptographic a lgorithms[J].IEEE Transactions on Information Forensics and Security，14(12)：3332-3343，2019.

[3]S.Xiang and X.Luo，″Reversible Data Hiding in Homomorphic Encrypted Domain by Mirroring Ciphertext Group，″in IEEE Transactiohs on Circuits an d Systems for Video Technology，vol.28，no.11，pp.3099-3110，Nov.2018.

[4]Z.Tang，S.Xu，D.Ye，J.Wang，X.Zhang，C.Yu，Real-time reversible d atahiding with shifting block histogram of pixel differences in encrypted image，J.Real-Time Image Process，16(3)，709-724，2019.

[5]L.Xiong，Z.Xu，Y.-Q.Shi，An integer wavelet transform based scheme f or reversible data hiding in encrypted images，Multidimens.Syst.Signal Proces s，29(3)，1191-1202，2018.

[6]S.Agrawal，M.Kumar，Mean value based reversible data hiding in encryp ted images，Optik-Int.J.Light Electron Opt，130，922-934，2017.

[7]M.Li，Y.Li，Histogram shifting in encrypted images with public key cryp tosystem for reversible data hiding，Signal Process，130，190-196，2017

[8]S.Xiang，X.Luo，“Reversible data hiding in homomorphic encrypted dom ain by mirroring ciphertext group，”IEEE Trans.Circuits Syst.Video Technol.，vol.28，pp.3099-3110，Nov.2018.

[9]X.Wu，J.Weng，and W.Yan，“Adopting secret sharing for reversible data hiding in encrypted images，”Signal Process.，vol.143，pp.269-281，2018.

[10]Y Ke，M.Zhang，J.Liu，T.Su，and X.Yang，“Fully Homomorphic Encry ption Encapsulated Difference Expansion for Reversible DataHiding in Encrypte d Domain，”IEEE Transactions on Circuits and Systems for Video Technology，vol.30，pp.2353-2365，2020.

Claims

1. a secret sharing based ciphertext domain extreme prediction double-layer reversible information hiding method is characterized by comprising the following steps in sequence:

step 1, preprocessing an original carrier image:

step 2, encrypting the carrier image X by additive secret sharing

Step 2.1 Each pixel X of the support image X is processed according to the formula (1-4) _l (i, j) is divided into three sections: x is the number of _h High order bit part, x _m Intermediate order part and x _l A lower-order bit portion in which i ∈ [1,H ]]，j∈[1，W]，α∈(0，7)，β∈(0，7)，α+β≤7；

x(i，j)＝x _h (i，j)×2 ^α +x _m (i，j)×2 ^β +x _l (i，j) (1)

x _l (i，j)＝x(i，j)-x _h (i，j)×2 ^α -x _m (i，j)×2 ^β (4)

x _h ＝x _l ×2 ^a (5)

x _l ＝x _h ÷2 ^a (6)

step 2.2 according to the formula (7-9), the separated x _h High order bit part, x _m Middle-order part, x _l Low order bit portions randomly partitioned into

Wherein r ∈ {1,2,3, …, r _max }，r _max Is a positive integer;

step 2.3 will

Step 3 encrypting the secret information using a mechanism for name removal

x _k+1 ＝μx _k (1-x _k ) (11)

Step 3.2 transform the range of values in the random number sequence to [0, 255] according to equation (12)]Then, the transformed one-dimensional random sequence is converted into a two-dimensional matrix M with the size equal to that of the secret information matrix, namely, gxl; and store K ₂ K in the formula (14) ₂ The random key is a positive integer;

step 3.5 connect LM map with one-dimensional sequence YD' = { d = { ₁ ，d ₂ ，...，d _p Connecting to generate D and splitting the D into two equal parts according to a formula (13), wherein D is the number of D ^ω And D ^δ ，

The length of D for u;

D＝D ^ω +D ^δ (13)

Step 4 Dual-layer embedding strategy

f(x，y)＝f(0，0)(1-x)(1-y)+f(1，0)x(1-y)+f(0，1)(1-x)y+f(1，1)xy (15)

And

Step 4.4 according to the formulas (22) and (23), the double-layer embedding is completed based on histogram translation, and a right-biased histogram H is utilized ⁺ Secret sharing of eshare contained after embedding of the first layer' _n Using left-hand histogram H ^- The secret sharing after the second layer embedding is eshare _n (ii) a Wherein s is ₁ Is the first layer of embedded secret information, s ₂ Is a second layer of embedded secret information, s ₁ And s ₂ Is formed by D ^ξ Is divided equally to obtain ⁺ And T ^- Respectively, a right-biased histogram H ⁺ And left-hand histogram H ^- Peak point of, z ⁺ Is the zero value point on the left side of the peak value point of the right-hand histogram closest to the peak value point, z ^- Is the zero value point on the right side of the peak value point of the left partial histogram closest to the peak value point:

2. The secret sharing based ciphertext domain extreme prediction double-layer reversible information hiding method according to claim 1, wherein the secret information extraction and the carrier image recovery are sequentially performed according to the following steps:

step 5.1, according to the formulas (17), (19) and (21), the received dense shared image eshare ″ _n Underestimating the prediction error, and recording the prediction error value as e ^-′ (i ', j'), and the predicted value is recorded as

Step 5.2 Using the sum of (24) and

extracting secret information s 'embedded in second layer' ₂ ；

Step 5.5 based on equation (26) and the calculated

Extracting first layer embedded secret information s' ₁ ；

step 5.7 recovery of secret information

S 'extracted' ₁ And s' ₂ Respectively arranging and connecting according to the extraction sequence to obtain D ^ξ 、D ^ω 、D ^δ D, mixing ^ω And D ^δ Combining to obtain D; sharing is distributed to different users, and only 2 users provide respective sharing together, the initial secret can be reconstructed;

(1) If hidden D ^ω Using the other two shares to extract secret information D ^ξ And D ^δ Is solved to obtain D ^ω The secret information D is recovered according to equation (28):

D＝D ^ω +D ^δ (30)

rx(i，j)＝share ₁ (i，j)+share ₂ (i，j)+share ₃ (i，j) (32)

Step 5.13, separating the RX bit plane by using a formula (1-4), exchanging high and low orders by using a formula (5-6), and recovering a carrier image X;