CN115242930B - Secret sharing-based ciphertext domain extreme prediction double-layer reversible information hiding method - Google Patents

Abstract

The invention discloses a secret sharing-based ciphertext domain extreme prediction double-layer reversible information hiding method, which comprises the steps of firstly carrying out all-bit plane decomposition on a carrier image, providing an additive secret sharing strategy based on bit planes, enabling the ciphertext image to be shared in multiple ways, and simultaneously providing a renamable mechanism for processing secret information, so that under the condition that one party shares traitor, lossless recovery and extraction can be realized by utilizing the sharing of other two parties, and in addition, realizing the ciphertext domain double-layer information hiding strategy through extreme prediction; at the receiving end, the lossless recovery secret information is extracted by using a comparison prediction error, a threshold value and a divisible name mechanism, and the lossless recovery of the original image is realized through the corresponding inverse transformation and the special property of additive secret sharing. The invention has the advantages of strong safety, high embedding capacity, high image quality, reversibility and the like.

Description

Secret sharing-based ciphertext domain extreme prediction double-layer reversible information hiding method

Technical Field

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

Background

In recent years, the openness and sharing of networks promote the rapid development of network multimedia, and 5G networks provide better network capability for multimedia information transmission, and simultaneously bring great threat and challenges, such as malicious tampering, illegal copying, privacy disclosure and other problems, so that protecting multimedia data security becomes particularly important, and preventing multimedia information disclosure has become a research hotspot. The ciphertext domain reversible information hiding (Reversible Data Hiding in Encrypted Image, RDHEI) is used for hiding information while protecting image content from leakage, a user can decrypt the image content according to the owned key type and own requirements, extract hidden information and recover an original image in a lossless manner, and is a cross research hotspot of information hiding, multimedia technology and ciphertext signal processing.

The original RDHEI algorithm was to make room after image encryption, i.e., reversible information hiding based on VRAE (Vacating Room After Encryption) framework and symmetrically encrypted ciphertext. As early as 2008, puech et al have hidden additional information in each block by dividing the encrypted image, and finally utilized the local standard deviation of the image pixels to complete information extraction and image recovery. However, this method has not been paid attention to by researchers until 2012, zhang encrypts an original image using a stream cipher, then divides the encrypted image into blocks of the same size, and conceals additional information by flipping LSBs of part of pixels in the blocks.

With the continuous improvement of the data security demands at home and abroad, a ciphertext domain reversible information hiding algorithm based on symmetric encryption and RRBE (Reserving Room Before Encryption) frames and public key/homomorphic encryption is widely paid attention to by students. Puteaus et al propose that ciphertext domain information hiding does not need to consider the problem of image visual quality after encryption and hiding, so that additional information is embedded by adopting image highest bit plane substitution, and therefore, a higher effective load is obtained.

However, the VRAE framework has its own limitations, such as error rate may occur in data extraction or image recovery, complete reversibility cannot be achieved, and some are inseparable in the information extraction and image recovery processes; there are problems such as limited capacity based on symmetric encryption and RRBE framework algorithms.

Disclosure of Invention

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

The technical scheme of the invention is as follows: a ciphertext domain extreme prediction double-layer reversible information hiding method based on secret sharing sequentially comprises the following steps:

step 1, preprocessing an original carrier image:

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

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

step 2 encryption of the carrier image X with additive secret sharing

Step 2.1 Each pixel X of the Carrier image X is calculated according to the formula (1-4) _l (i, j) is divided into three parts: x is x _h Higher order bit portion, x _m Middle order bit portion and x _l Low order bit portion, where i.e. [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 determined according to the formula (5-6) _h Higher order bit portion and x _l Low order bit portion exchange:

x _h ＝x _l ×2 ^a (5)

x _l ＝x _h ÷2 ^a (6)

step 2.2 separating x according to the formula (7-9) _h Higher order bit portion, x _m Middle-order bit part, x _l Random partitioning of low order bit portions into

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

step 2.3 will

Re-randomly combining according to formula (10) to generate n shared encryption carriers share _n Wherein n is {1,2,3, …, r _max }，/>

The upper subscript r of (1, 2,3, …, r, respectively) is in the set _max In the same order bit, the upper corner mark r is not repeatable, i.e. the same order bit is equal to r ++1 +. … +.r +. _max ；

Step 3, encrypting the secret information by using a divisible name mechanism

Step 3.1 generating a random number sequence L of equal length to the secret information matrix YD of size gxl according to equation (11) ₁ Where k is {1,2,3 …, gχl },0<x ₀ <1，3.5699456<Mu is less than or equal to 4, and x is selected ₀ And mu is stored as key K ₁ ；

x _k+1 ＝μx _k (1-x _k ) (11)

Step 3.2 converting 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 same size as the secret information matrix, namely g×l; and preserve K ₂ K in equation (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, performing bitwise exclusive OR operation, and finally converting the exclusive OR binary into decimal;

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

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

The u is the length D;

D＝D ^ω +D ^δ (13)

step 3.6D is carried out according to formula (14) ^ω And D ^δ Generating third party secret information D by bit exclusive OR ^ξ ；

Step 4 double layer embedding strategy

Step 4.1 selecting four known points f (0, 0), f (1, 0), f (0, 1), f (1, 10) as reference pixels, and adding share according to the bilinear interpolation method of formula (15) _n Expanded to 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 techniques for eshare _n Prediction is performed by overestimating predictor p ⁺ And underestimating predictor p ^- Respectively to eshare _n Extreme prediction is performed to generate

And->

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

Wherein c _q Surrounding pixels representing the predicted target pixel are used to generate a predicted value, q ε {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 value generates a right bias histogram H ⁺ Underestimating the predictive error value to generate a left-hand histogram H ^- ；

Step 4.4 performing histogram-based translation to complete double-layer embedding according to formulas (22) (23), and using the right-bias histogram H ⁺ The secret sharing after the first layer embedding is eshare' _n By means of left-hand histogram H ^- The secret sharing after the second layer embedding is eshare _n "C"; wherein s is ₁ Is embedded in the first layerSecret information s ₂ Is the secret information embedded in the second layer s ₁ Sum s ₂ Is composed of D ^ξ Average division to obtain T ⁺ And T ^- Respectively right offset histogram H ⁺ And left offset histogram H ^- Is the peak point, z ⁺ Is the zero point nearest to the peak point at the left side of the peak point of the right-offset histogram, z ^- Is the zero point closest to the peak point on the right side of the peak point of the left-shifted histogram:

step 4.5 repeating the operations of steps 4.2-4.4 until the traversal is completed with eshare _n Is included in the display panel).

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

step 5.1 the received secret-shared-image eshare is received according to formulas (17) (19) and (21) _n "under-estimating the prediction error, the prediction error value is denoted as e ^- ' i ', j ', the predicted value is noted as

Step 5.2 Using the Male (24) and

extracting second layer embedded secret information s' ₂ ；

Step 5.3 restoring the second layer pixel value reshare according to equation (25) _n ″；

Repeating steps 5.1-5.3 until all secret information of the second layer is extracted, and completely recovering reshare _n ", said reshare _n "equivalent to eshare' _n ；

Step 5.4 the reshare is performed according to formulas (16) (18) and (20) _n "overestimate prediction error, the prediction error value is denoted as e ^+′ (i ', j') the predicted value is noted as

Step 5.5 according to equation (26) and calculated

Extracting first layer embedded secret information s ₁ ′；

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

Repeating steps 5.4-5.6 until all secret information of the first layer is extracted, and completely recovering reshare' _n ，reshare′ _n Equivalent to eshare _n I.e. not embedded images;

step 5.7 recovery of secret information

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

(1) If hide D ^ω Traitor of the data hiding party using the other two shares of extracted secret information D ^ξ And D ^δ Solving for D ^ω The secret information D is recovered according to formula (28):

(2) If hide D ^δ Traitor of the data hiding party using the other two shares of extracted secret information D ^ξ And D ^ω Solving for D ^δ Recovering the secret information D according to the formula (29):

(3) If hide D ^ξ Traitor of the data hiding party using the other two shares of extracted secret information D ^ω And D ^δ Merging and recovering the secret information D according to formula (30):

D＝D ^ω +D ^δ (30)

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

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

step 5.10, performing bit exclusive OR operation on YD 'and M' to generate decrypted secret information YD;

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

Step 5.12 merge share according to equation (32) _n Restoring the carrier image RX, wherein i e [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 RX bit plane by using formula (1-4), exchanging high and low orders by using formula (5-6), and recovering carrier image X;

step 5.14, using the LM graph, changing the pixel value of the corresponding position in X marked with 0 in the LM graph to 0, so as to fully restore the original carrier image.

The invention firstly carries out all-bit plane decomposition on the carrier image, proposes an additive secret sharing strategy based on bit planes to enable the ciphertext image to be shared in multiple ways, and simultaneously proposes a renamable mechanism to process secret information, so that under the condition that one party shares traitor, lossless recovery and extraction can be realized by utilizing the sharing of other two parties, and furthermore, a ciphertext domain double-layer information hiding strategy is realized through extreme prediction; at the receiving end, the lossless recovery secret information is extracted by using a comparison prediction error, a threshold value and a divisible name mechanism, and the lossless recovery of the original image is realized through the corresponding inverse transformation and the special property 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 invention for secret information embedding.

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

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

FIG. 4 is an interpolation extended share of an embodiment of the present invention ₁ Is a schematic diagram of (a).

Fig. 5a is a right-hand histogram of prediction error in an embodiment of the invention.

Fig. 5b is a left-hand histogram of prediction error in accordance with an embodiment of the present invention.

FIG. 6 is a schematic diagram of a dual layer embedding based on histogram shifting in accordance with 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 downsampling an interpolated image in accordance with an embodiment of the invention.

Fig. 9a is a diagram of the original carrier of an embodiment of the present invention.

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

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

Fig. 9d is a graph of interpolation effects according to an embodiment of the present invention.

Fig. 9e is a graph of the embedding effect of an embodiment of the present invention.

Fig. 9f is a graph of the effect of recovering a carrier image in accordance with an embodiment of the present invention.

Fig. 10a is a diagram of a Lena original image pixel correlation scatter plot in accordance with an embodiment of the present invention.

FIG. 10b is a ciphertext image share of an embodiment of the invention ₁ Pixel correlation scatter plots.

FIG. 10c is a ciphertext image share of an embodiment of the invention ₂ Pixel correlation scatter plots.

FIG. 10d is a ciphertext image share of an embodiment of the invention ₃ Pixel correlation scatter plots.

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

Fig. 12 is a comparison bar graph of the NIQE measurements of the original image and the restored image of 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 fig. 1 and sequentially comprises the following steps:

step 1, preprocessing an original carrier image:

step 1.1, traversing all pixels in an original carrier image with the size 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 map;

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

step 2 encryption of the carrier image X with additive secret sharing

Step 2.1 Each pixel X of the Carrier image X is calculated according to the formula (1-4) _l (i, j) is divided into three parts: x is x _h Higher order bit portion, x _m Middle order bit portion and x _l Low order bit portion, where i.e. [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 determined according to the formula (5-6) _h Higher order bit portion and x _l Low order bit portion exchange:

x _h ＝x _l ×2 ^a (5)

x _l ＝x _h ÷2 ^a (6)

in the embodiment of the present invention, the variable values are as follows α=5, β=3, and fig. 9b shows a split bit plane effect diagram of the embodiment of the present invention, where x is from left to right respectively _h Higher order bit portion, x _m Middle order bit portion and x _l A low order bit portion.

The present embodiment will be described taking as an example a pixel block of 3×3 size having pixel values 219,218, 216, 217, 218, 213, 219, 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 pixels are divided into higher order portions, the lower three bits into lower order portions, and the remaining middle two bits into middle order portions:

(219) ₁₀ ＝(11011011) ₂

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

pixel value (219) ₁₀ ＝(11011011) ₂ Higher order (110) ₂ AND (011) ₂ Exchange, get (01111110) ₂ 。

Step 2.2 separating x according to the formula (7-9) _h Higher order bit portion, x _m Middle-order bit part, x _l Random partitioning of low order bit portions into

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

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

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

step 2.3 will

Re-randomly combining according to formula (10) to generate n shared encryption carriers share _n Where n.epsilon. {1,2,3}, -is }>

The upper subscript r of (1, 2,3, …, r, respectively) is in the set _max In the same order bit, the upper corner mark r is not repeatable, i.e. the same order bit is equal to r ++1 +. … +.r +. _max ；

The re-random combination can be specifically performed 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 The following is shown:

fig. 9c is a share effect diagram of an embodiment of the present invention.

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

It should be noted that the present invention uses additive secret sharing to uniformly distribute three parts of pixel values so as to preserve the property of additive secret sharing, and the present invention shares multiple pixels at a time to improve efficiency, reduce data expansion, random segmentation and random combination, and dual random superposition can further improve security, and random numbers are used in the sharing process, so that the encryption method of the present invention is a system with randomness and uncertainty, encrypts the image twice, and the generated encrypted images are completely different, so that the present invention has a capability of resisting a plurality of potential attacks.

Tables 1 to 4 show experimental data of Lena, baboon, barbara, pepper, jetplane, boat, house, island eight gray-scale images of 256×256, respectively for the original image and the ciphertext image share ₁ 、share ₂ And share ₃ And (5) performing a correlation coefficient analysis result. As can be seen from Table 1, the correlation coefficient is about 0.9, which indicates that there is a very high correlation between adjacent pixels of the original image, any pixel easily leaks information of its surrounding pixels, and an attacker can often predict the gray value of the neighboring pixels by using the characteristic, thereby realizing the whole plaintext imageAnd (5) predicting. As can be seen from tables 2-4, the correlation coefficient is mostly lower than 0.1, indicating that the ciphertext share breaks the strong correlation of the plaintext, and therefore, the ciphertext image share has higher security. In addition, fig. 10a shows a pixel correlation scatter diagram of the Lena original image according to the embodiment of the present invention, mainly focusing on a diagonal line, which indicates that the original image has a higher correlation; FIGS. 10b-d respectively show ciphertext image share of an embodiment of the invention ₁ ，share ₂ And image share ₃ The element correlation scatter diagrams are respectively uniform, and indicate that the secret sharing correlation is low and the security is high.

TABLE 1

TABLE 2

TABLE 3 Table 3

TABLE 4 Table 4

Step 3, encrypting the secret information by using a divisible name mechanism

Step 3.1 generating a random number sequence L of equal length to the secret information matrix YD of size gxl according to equation (11) ₁ Where k is {1,2,3 …, gχl },0<x ₀ <1，3.5699456<Mu is less than or equal to 4, and x is selected ₀ And mu is stored as key K ₁ ；

x _k+1 ＝μx _k (1-x _k ) (11)

Step 3.2 converting 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 same size as the secret information matrix, namely g×l; and preserve K ₂ K in equation (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, performing bitwise exclusive OR operation, and finally converting the exclusive OR binary into decimal;

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

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

Exclusive or to obtain encrypted secret information

The method is specifically as follows:

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

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

step 3.5 comparing the LM map with the one-dimensional sequence YD' = { d ₁ ,d ₂ ,...,d _p The connection generates D and is disassembled according to the formula (13)Divided into two equal parts, respectively D ^ω And D ^δ ，

The u is the length D;

D＝D ^ω +D ^δ (13)

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

Step 3.6D is carried out according to formula (14) ^ω And D ^δ Generating third party secret information D by bit exclusive OR ^ξ ；

Specifically, {219,218,132,235} and {120,48,211,139} are converted into binary values and then bitwise exclusive-or-ed to generate the alternative secret information D ^ξ The two parts and the generated substitutable secret information are respectively embedded into three parts of sharing share ₁ 、share ₂ 、share ₃ In (a) and (b);

it should be noted that, the conventional RDHEI scheme focuses on a data hiding device, if only one encrypted image is lost or damaged, the original secret information cannot be recovered, and the designeable mechanism designed by the invention allows traitors of one shared data hiding party in a certain range, and uses secret information extracted from the other two sharing parties to perform exclusive or operation, so that all secret information can be recovered without loss, and has certain robustness, and the principle is as follows (A, B, C respectively represents three parties):

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 double 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 share is interpolated according to equation (15) bilinear interpolation _n Expanded to 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, taking a pixel block with a size of 2×2 as an example, share is performed by using a bilinear interpolation method ₁ Enlarging to obtain eshare ₁ The four reference pixel values are respectively: 48. 35, 18, 32, the interpolated pixels are shown below, respectively:

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, so that the embedding capability is improved well.

Step 4.2 using extreme prediction techniques for eshare _n Prediction is performed by overestimating predictor p ⁺ And underestimating predictor p ^- Respectively to eshare _n Extreme prediction is performed to generate

And->

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

/>

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

inventive example q _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 an embodiment of the invention, eshare is estimated using extreme prediction techniques ₁ Prediction was performed with eshare in FIG. 4 ₁ For example, the (2, 2) pixel value is 33, and eshare is estimated by an overestimated predictor and an underestimated predictor, respectively ₁ (2, 2) extreme prediction to generate

And->

And calculates the prediction error e ⁺ (2, 2) and e ^- (2, 2) specifically as follows:

e+(2,2)＝0

e ^- (2,2)＝-15

fig. 9d is a graph of interpolation effects according to an embodiment of the present invention.

Step 4.3 generating a pair of asymmetric prediction error histograms wherein the overestimated prediction error value generates a right bias histogram H ⁺ Underestimating the predictive error value to generate a left-hand histogram H ^- ；

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-hand deviation histogram H ⁺ FIG. 5b is a left-hand histogram H ^- 。

Step 4.4 performing histogram-based translation to complete double-layer embedding according to formulas (22) (23), and using the right-bias histogram H ⁺ The secret sharing after the first layer embedding is eshare' _n By means of left-hand histogram H ^- The secret sharing after the second layer embedding is eshare _n "C"; wherein s is ₁ Is the secret information embedded in the first layer s ₂ Is the secret information embedded in the second layer s ₁ Sum s ₂ Is composed of D ^ξ Average division to obtain T ⁺ And T ^- Respectively right offset histogram H ⁺ And left offset histogram H ^- Is the peak point, z ⁺ Is the zero point nearest to the peak point at the left side of the peak point of the right-offset histogram, z ^- Is the zero point closest to the peak point on the right side of the peak point of the left-shifted histogram:

in the embodiment of the present invention, eshare is taken as an example of the pixel with the pixel value of 33 in the second row and the second column in fig. 6 ₁ ' is the secret sharing after first embedding, eshare ₁ "is the secret sharing after the second embedding, s ₁ =1 is the first bit of secret information embedding, s ₂ Is the second bit embedded by secret information, T ⁺ ＝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

Step 4.5 repeating the operations of steps 4.2-4.4 until the traversal is completed with eshare _n Is included in the display panel).

Fig. 9e is a schematic diagram of the embedding effect according to the embodiment of the present invention.

Specifically, firstly embedding 1bit secret information in a right-leaning prediction error histogram (the number of pixels on the right side of a peak value is more than the number of pixels on the left side of the peak value), comparing a prediction error value with a threshold value, and if the prediction error value is equal to the threshold value, modifying the pixel value to be embedded in 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, subtracting one from the pixel value, otherwise, keeping the pixel value unchanged; similarly, embedding 1bit of secret information in a left-leaning prediction error histogram (the number of pixels on the left side of a peak value is more than the number of pixels on the right side of the peak value), comparing a prediction error value with a threshold value, and if the prediction error value is equal to the threshold value, modifying the pixel value to be embedded in the secret information; if the prediction error value is greater than the threshold and less than the nearest zero point to the right of the peak, then the pixel value is incremented by one, otherwise, the pixel value is unchanged. And repeating the process until the secret information is completely embedded, and obtaining the ciphertext image containing the secret.

The invention adopts the extreme prediction method to embed secret data, and can obtain larger embedding rate for a plurality of natural images. Table 5 shows a comparison of the embedded capacity of the experiments of the examples of the present invention with the relevant methods, and it can be seen that the present invention has a capacity greater than the relevant methods by about 7 times that of the other methods.

TABLE 5

It is worth noting that the invention only moves the side with the least number of pixels, vacates embedding space for secret information, and adopts a bidirectional embedding strategy to fully utilize redundant information in the image. Compared with the traditional method for embedding the secret information by using the prediction error histogram, which needs to move pixels at two sides of the peak value and vacate an embedding space for the secret information, the method has the advantages of less quantity of the moved pixels, less influence on the image and better performance in a capacity distortion control task.

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

step 5.1 the received secret-shared-image eshare is received according to formulas (17) (19) and (21) _n "under-estimating the prediction error, the prediction error value is denoted as e ^- ' i ', j ', the predicted value is noted as

Specifically, as shown in FIG. 7, eshare is shown in the figure ₁ For example, "(2, 2), the prediction error value is calculated: e, e ^- ′(2,2)＝-16；

Step 5.2 Using the Male (24) and

extracting second layer embedded secret information s' ₂ ；/>

Specifically, as shown in FIG. 7, eshare is shown in the figure ₁ For example, "(2, 2)" the secret-containing image is traversed by S according to the reverse order of the embedding order, S is extracted first ₂ If the current pixel value minus the underestimated predicted value is equal to the threshold value, the secret information is 0, if the current pixel value minus the underestimated predicted value is equal to the threshold value plus 1, the secret information is 1, otherwise, any information is not hidden:

thus, no secret information is hidden in the second layer embedding within the current pixel.

Step 5.3 restoring the second layer pixel value reshare according to equation (25) _n ″；

As shown in FIG. 7, in which eshare ₁ For example, "(2, 2), the second layer pixel values are restored:

reshare ₁ ″(2,2)＝32

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

Step 5.4 the reshare is performed according to formulas (16) (18) and (20) _n "overestimate prediction error, the prediction error value is denoted as e ^+′ (i ', j') the predicted value is noted as

As shown in FIG. 7, in which there is a reshare ₁ For example, "(2, 2)" calculates the prediction error value:. E ^+′ (2,2)＝-1；

Step 5.5 according to equation (26) and calculated

Extracting first layer embedded secret information s ₁ ′；

As shown in FIG. 7, in reshare ₁ For example, (2, 2) is taken as an example, if the current pixel value minus the overestimated predicted value is equal to the threshold value, the secret information is 0, and if the overestimated predicted value is equal to the threshold value plus one, the secret information is 1.

s ₁ ′＝1

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

As shown in FIG. 7, in reshare ₁ ' As an example, (2, 2), restore to free of secretsEshare for secret information ₁ Pixel values of (2):

reshare ₁ ′(2,2)＝32+1

repeating steps 5.4-5.6 until all secret information of the first layer is extracted, and completely recovering reshare' _n ，reshare _n ' equivalent to eshare _n I.e., not embedded image, fig. 9f is a restoration carrier image effect diagram of an embodiment of the present invention;

step 5.7 recovery of secret information

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

(1) If hide D ^ω Traitor of the data hiding party using the other two shares of extracted secret information D ^ξ And D ^δ Solving for D ^ω The secret information D is recovered according to formula (28):

specifically, eshare 'is extracted' ₂ ' and eshare ₃ Hidden secret information in the EShare is solved by exclusive OR operation ₁ "secret information D hidden in ^ω :

And then combined into D, D= {219,218,132,235,120,48,211,139};

(2) If hide D ^δ Traitor of the data hiding party using the other two shares of extracted secret information D ^ξ And D ^ω Solving for D ^δ Recovering the secret information D according to the formula (29):

specifically, eshare is extracted ₁ "and eshare ₃ "secret information in eshare 'is solved by exclusive or operation' ₂ ' hidden secret information D ^δ :

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

(3) If hide D ^ξ Traitor of the data hiding party using the other two shares of extracted secret information D ^ω And D ^δ Merging and recovering the secret information D according to formula (30):

D＝D ^ω +D ^δ (30)

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

it is worth noting that the invention creates a divisible name mechanism of secret information, has the capability of resisting collusion analysis, can still utilize the secret information extracted from other two shares to completely recover the secret information under the condition of one data hiding side traitor, and improves the safety and reliability of the invention. Fig. 11 shows a difference image of a watermark and an extracted watermark according to an embodiment of the present invention, where ber=0, indicating that lossless extraction can be achieved according to the present invention.

Step 5.8, splitting the D to obtain an LM diagram and secret information YD ', traversing the YD ' according to an S-shaped traversing sequence, and converting the LM diagram and the secret information into a matrix YD ' with the size of g multiplied by l;

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

step 5.10, performing bit exclusive OR operation on YD 'and M' to generate decrypted secret information YD;

in particular, the method comprises the steps of,

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

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

Step 5.12 merge share according to equation (32) _n Restoring the carrier image RX, wherein i e [1, H]，j∈[1,W]；

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

By utilizing the special property of additive secret sharing, the carrier image can be directly and quickly restored without separating bit planes and restoring high, middle and low order parts,

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

specifically, the pixel value (126) ₁₀ ＝(01111110) ₂ Higher order of (011) ₂ AND (110) ₂ Exchange, get (11011011) ₂ ；

x _h ＝(110) ₂ ×2 ⁵

x _l ＝(011) ₂ ÷2 ⁵

Step 5.14, using the LM graph, changing the pixel value of the corresponding position in X marked with 0 in the LM graph to 0, so as to fully restore the original carrier image.

FIG. 12 shows a comparison bar graph of NIQE measurements for the original image and the restored image, identical to each other, showing that the present invention can achieve lossless restoration.

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

The invention provides an additive secret sharing mechanism, a divisible name mechanism, an extreme prediction mechanism and a ciphertext domain double-layer reversible embedding strategy, which has 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 that the encryption and decryption theoretical time complexity of the secret sharing and related method is compared, and in general, the encryption and decryption calculation complexity of the invention is O (n), which is lower than that of other related documents, and the encryption scheme provided by the invention has higher efficiency. The actual run time comparison is given in table 7, and it can be seen that even though the present invention implements a dual layer embedding strategy, the average time of embedding 1bit is 0.000002, which is lower than other related references, indicating that the present invention has high embedding efficiency.

TABLE 6

TABLE 7

Reference is made to:

[1]Manikandan V M,Zhang Y D.An adaptive pixel mapping based approach for reversible data hiding in encrypted images[J].Signal Processing:Image C ommunication,116690,2022.

[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 Transactions 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 (2)

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

step 1, preprocessing an original carrier image:

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

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

step 2 encryption of the carrier image X with additive secret sharing

Step 2.1 Each pixel X of the Carrier image X is determined according to formulas (1) - (4) _l (i, j) is divided into three parts: x is x _h Higher order bit portion, x _m Middle order bit portion and x _l Low order bit portion, where i.e. [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 determined according to formulas (5) - (6) _h Higher order bit portion and x _l Low order bit portion exchange:

x _h ＝x _l ×2 ^a (5)

x _l ＝x _h ÷2 ^a (6)

step 2.2 isolating x according to formulas (7) - (9) _h Higher order bit portion, x _m Middle-order bit part, x _l Random partitioning of low order bit portions into

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

step 2.3 will

Re-randomly combining according to formula (10) to generate n shared encryption carriers share _n Wherein n is {1,2,3, …, r _max }，/>

The upper subscript r of (1, 2,3, …, r, respectively) is in the set _max In the same order bit, the upper corner mark r is not repeatable, i.e. the same order bit is equal to r ++1 +. … +.r +. _max ；

Step 3, encrypting the secret information by using a divisible name mechanism

Step 3.1 generating a random number sequence L of equal length to the secret information matrix YD of size gxl according to equation (11) ₁ Where k is {1,2,3 …, gxl },0 < x ₀ 1,3.5699456 is more than or equal to mu and less than or equal to 4, and x is selected ₀ And mu is stored as key K ₁ ；

x _k+1 ＝μx _k (1-x _k ) (11)

Step 3.2 converting 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 same size as the secret information matrix, namelyg×l; and preserve K ₂ K in equation (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, performing bitwise exclusive OR operation, and finally converting the exclusive OR binary into decimal;

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

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

The u is the length D;

D＝D ^ω +D ^δ (13)

step 3.6D is carried out according to formula (14) ^ω And D ^δ Generating third party secret information D by bit exclusive OR ^ξ ；

Step 4 double layer embedding strategy

Step 4.1 selecting four known points f (0, 0), f (1, 0), f (0, 1), f (1, 10) as reference pixels, and adding share according to the bilinear interpolation method of formula (15) _n Expanded to 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 techniques for eshare _n Prediction is performed by overestimating predictor p ⁺ And underestimating predictor p ^- Respectively to eshare _n Extreme prediction is performed to generate

And->

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

Wherein c _q Surrounding pixels representing the predicted target pixel are used to generate a predicted value, q ε {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 value generates a right bias histogram H ⁺ Underestimating the predictive error value to generate a left-hand histogram H ^- ；

Step 4.4 pressPerforming histogram translation based double-layer embedding according to formulas (22) and (23), and using right-bias histogram H ⁺ The secret sharing after the first layer embedding is eshare' _n By means of left-hand histogram H ^- The secret sharing after the second layer embedding is eshare _n The method comprises the steps of carrying out a first treatment on the surface of the Wherein s is ₁ Is the secret information embedded in the first layer s ₂ Is the secret information embedded in the second layer s ₁ Sum s ₂ Is composed of D ^ξ Average division to obtain T ⁺ And T ^- Respectively right offset histogram H ⁺ And left offset histogram H ^- Is the peak point, z ⁺ Is the zero point nearest to the peak point at the left side of the peak point of the right-offset histogram, z ^- Is the zero point closest to the peak point on the right side of the peak point of the left-shifted histogram:

step 4.5 repeating the operations of steps 4.2-4.4 until the traversal is completed with eshare _n Is included in the display panel).

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

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

Step 5.2 Using equations (24) and

extraction ofSecond layer embedded secret information s' ₂ ；

Step 5.3 restoring the second layer pixel value reshare according to equation (25) _n ；

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

Step 5.4 for reshare' according to equations (16) (18) and (20) _n Overestimating the prediction error, the prediction error value is denoted as e ^+′ (i ', j') the predicted value is noted as

Step 5.5 according to equation (26) and calculated

Extracting first layer embedded secret information s' ₁ ；

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

Repeating steps 5.4-5.6 until all secret information of the first layer is extracted, and completely recovering reshare' _n ，reshare′ _n Equivalent to eshare _n I.e. not embedded images;

step 5.7 recovery of secret information

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

(1) If hide D ^ω Traitor of the data hiding party using the other two shares of extracted secret information D ^ξ And D ^δ Solving for D ^ω The secret information D is recovered according to formula (28):

(2) If hide D ^δ Traitor of the data hiding party using the other two shares of extracted secret information D ^ξ And D ^ω Solving for D ^δ The secret information D is recovered according to formula (29):

(3) If hide D ^ξ Traitor of the data hiding party using the other two shares of extracted secret information D ^ω And D ^δ Merging and recovering the secret information D according to formula (30):

D＝D ^ω +D ^δ (30)

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

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

step 5.10, performing bit exclusive OR 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' e [1,2H ]]，j′∈[1，2W]；

Step 5.12 merge share according to equation (32) _n Restoring the carrier image RX, wherein i e [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 using formulas (1) - (4), and exchanging the high and low orders using formulas (5) - (6), recovering carrier image X;

step 5.14, using the LM graph, changing the pixel value of the corresponding position in X marked with 0 in the LM graph to 0, so as to fully restore the original carrier image.

Images