Lossless information hiding method based on secret image sharing

Abstract

The invention discloses a lossless information hiding method based on secret image sharing. An information holder generates a plurality of random shadow images and secret keys according to a carrier image CI; the information holder embeds the to-be-embedded image SI into the specific shadow image CS, and the generated secret key is used for recovering the embedded image SI; the information transmitter transmits the generated shadow image to an information restorer; the information restorer collects a shadow image and recovers a carrier image CI according to the collected shadow image; if the information restorer obtains the specific shadow image CS and holds the secret key, the embedded image SI can be additionally restored. According to the method, the shared image and the embedded image can be transmitted accurately and losslessly, and meanwhile confidentiality and integrity of secret information are guaranteed.

Description

Technical Field

[0001] The invention relates to the technical field of applied cryptography, and in particular to a lossless information hiding method based on secret image sharing. Background Art

[0002] Secret image sharing is an effective method to protect image security. In the (k,n) threshold secret image sharing scheme, an image is split into n visually meaningless "shadow images" that are distributed among participants. Unlike traditional image encryption, secret image sharing requires combining at least k shadow images to restore the information of the original image, and a single or a small number of malicious participants cannot restore the secret image, thus ensuring the confidentiality of the image.

[0003] There are three types of secret image sharing schemes in the prior art: visual cryptography, polynomial-based secret image sharing, and secret image sharing based on the remainder theorem. Image steganography hides secret information in a carrier image by slightly changing the pixel values ​​of the image. At the same time, the carrier image has almost no visual changes, thus avoiding suspicion and achieving covert transmission of information. In a polynomial-based secret image sharing scheme, the secret image is shared through Lagrange interpolation technology, and the pixel values ​​of the image are used as coefficients of the Lagrange polynomial. In practical applications, in order to enhance the randomness of the shadow image in the secret image sharing scheme, some of the coefficients of the polynomial are usually filled with random numbers at the same time, but this method introduces redundant information and increases the cost of information transmission. Summary of the invention

[0004] The purpose of the present invention is to provide a lossless information hiding method based on secret image sharing, which can accurately and losslessly transmit shared images and embedded images while ensuring the confidentiality and integrity of secret information.

[0005] The objective of the present invention is achieved through the following technical solutions:

[0006] A lossless information hiding method based on secret image sharing, the method comprising:

[0007] Step 1: The information holder generates several random shadow images and keys based on the carrier image CI;

[0008] Step 2: The information holder embeds the image SI to be embedded into the specific shadow image CS, and the generated key is used to restore the embedded image SI;

[0009] Step 3, the information transmitter transmits the generated shadow image to the information restorer;

[0010] Step 4: The information restorer collects shadow images and restores the carrier image CI based on the collected shadow images; if the information restorer obtains a specific shadow image CS and holds the key, the embedded image SI can be restored in addition.

[0011] It can be seen from the technical solution provided by the present invention that the above method can accurately and losslessly transmit shared images and embedded images while ensuring the confidentiality and integrity of secret information. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0013] Figure 1 A schematic flow chart of a lossless information hiding method based on secret image sharing provided by an embodiment of the present invention;

[0014] Figure 2 This is a flow chart of the covert transmission of trade secrets over an open and insecure channel according to an example of the present invention. DETAILED DESCRIPTION

[0015] The following is a clear and complete description of the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments, which does not constitute a limitation of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0016] like Figure 1 FIG. 1 is a flow chart of a lossless information hiding method based on secret image sharing provided by an embodiment of the present invention, wherein the method comprises:

[0017] Step 1: The information holder generates several random shadow images and keys based on the carrier image CI;

[0018] In this step, the information holder uses the (k,n) threshold Lagrangian interpolation method to share the carrier image CI. The definition of the Lagrangian polynomial is as follows. All calculations related to the Lagrangian polynomial are performed on the Galois field GF(257):

[0019] f(x)=a0+a1x+a2x 2 +…+a k-1 x k-1 (mod p)

[0020] Among them, f(x) is a Lagrange polynomial; x is the independent variable of the polynomial; k is the minimum number of shadows required to reconstruct the polynomial by the (k,n) threshold Lagrange interpolation method; p is the modulus of the operation, mod p means that all the operation results are divided by p and the remainder is taken; a0 of each polynomial is a pixel value of the carrier image CI, and the other coefficients are random values. The polynomial containing the pixel value CI(x,y) is denoted as poly (x，y) ;

[0021] The shadow image is constructed by assigning Lagrangian polynomials using the id of the information transmitter. Each polynomial contains a pixel value of the carrier image CI. Therefore, a carrier image CI of size l×w will produce l×w polynomials, and each shadow image has a size of l×w;

[0022] This stage generates n shadow images, which are distributed to n information transmitters. At least k shadow images are needed to restore the carrier image CI.

[0023] In the specific implementation, if the calculated shadow value is 256, it is necessary to select other random numbers as coefficients from the corresponding Lagrange polynomial and recalculate all related shadow values ​​to ensure that all shadow values ​​remain within the pixel range [0,255] of the image.

[0024] Step 2: The information holder embeds the image SI to be embedded into the specific shadow image CS, and the generated key is used to restore the embedded image SI;

[0025] In this step, a specific shadow image CS is selected from the generated shadow images, and a key (Co, β, Mo, ord) is randomly generated, where Co is a coordinate value that determines the initial embedding position, which is a tuple including a horizontal coordinate and a vertical coordinate; β is the offset between the two embedding positions; Mo is the modulus of the coordinate calculation; ord is the embedding position in the polynomial;

[0026] Each pixel of the embedded image SI will be split into a pair, recorded as (p1, p2), and embedded into two adjacent pixels of the carrier image CI; where Co is the initial position of embedding, and the next embedding position is determined by p1 and β. The embedding process is:

[0027] Step 21: assign the target coordinate value coord of the current operation to the initial position, that is, coord=Co, and then perform the following operations on each pixel SI(i,j) of the embedded image SI:

[0028] Step 22, calculate p1 and p2 for each pixel, where p1 is a random integer in the range of [0,255], and p2 satisfies p1+p2=SI(i,j)mod 257, where SI(i,j) is the pixel value of the embedded image SI at the coordinate (i,j); then CI(coord) and CI(coord+1) are assigned p1 and p2 respectively, where CI(coord) is the pixel value of the carrier image CI at the coordinate value coord; if CI(coord+(p1+βmod Mo)) has been embedded, reselect p1 and re-execute step 22;

[0029] Step 23: Modify other temporary shadow images SH i The corresponding pixel value is modified to ensure that the normal restoration of the carrier image CI is not affected:

[0030]

[0031] Where j = 1 or 2, each i corresponds to a data transmitter, Si is the i-th final shadow image, Si(x, y) is the pixel value of the i-th final shadow image at the coordinate value (x, y); SHi is the i-th temporary shadow image, SHi(x, y) is the pixel value of the i-th temporary shadow image at the coordinate value (x, y); CS(x, y) is the pixel value of the specific shadow image CS at the coordinate value (x, y); idi and idCS are the ids of the i-th information transmitter and the information transmitter of the specific shadow image, respectively; if there is any S i (x, y) = 256, then reselect p1 and re-execute steps 22 and 23;

[0032] Step 24: Let coord=coord+p1+β, update the target coordinate value of the current operation, and re-execute steps 22 and 23 until all pixel values ​​of the embedded image SI are processed.

[0033] Step 3, the information transmitter transmits the generated shadow image to the information restorer;

[0034] Step 4: The information restorer collects shadow images and restores the carrier image CI based on the collected shadow images; if the information restorer obtains a specific shadow image CS and holds the key, the embedded image SI can be restored in addition.

[0035] In this step, at least k shadow images are needed to reconstruct the Lagrange polynomial, which is denoted as poly (x，y) ;

[0036] The information restorer uses the shadow value to reconstruct the polynomial according to the following formula, and extracting the coefficients of these polynomials can restore all the pixel values ​​of the carrier image CI:

[0037]

[0038] Where f'(x) is the Lagrangian polynomial restored from the shadow value; f(xi) is the i-th shadow value, xi is the i-th independent variable, corresponding to the i-th user id; p is the modulus of the operation, mod p means all the operation results are divided by p and the remainder is taken; k is the minimum number of shadows required to reconstruct the polynomial by the (k,n) threshold Lagrangian interpolation method;

[0039] If the information restorer obtains the specific shadow image CS and holds the key (Co, β, Mo, ord), the key (Co, β, Mo, ord) is used to restore the embedded image SI from the specific shadow image CS. Specifically, each pixel value of the embedded image SI is calculated through each pair of polynomials, and then the key is used to obtain the next pair of pixel values ​​until the embedded image SI is completely restored, including:

[0040] Step 41, assign the target coordinate value coord of the current operation to the initial position, that is, coord=Co, and then perform the following steps for each pixel SI(i,j) of the embedded image SI;

[0041] Step 42, extract the ordth order coefficients of the polynomials poly(coord) and poly(coord+1) reconstructed at the coordinates coord and coord+1, denoted as p1 and p2 respectively, for forming a pixel value of the embedded image SI in the next step;

[0042] Step 43: perform the inverse process of step 22 to calculate the pixel value of the embedded image SI restored at the coordinate coord, that is: SI (x，y) =p1 + p1 mod 257;

[0043] Let coord=coord+p1+β, update the target coordinate value of the current operation, and continue the operation of step 42 until the embedded image SI is completely restored.

[0044] It is worth noting that the contents not described in detail in the embodiments of the present invention belong to the prior art known to professional and technical personnel in the field.

[0045] The following is an example of the method described in the embodiment of the present invention. This example is in the scenario of commercial secret transmission, such as Figure 2 The figure shows a flow chart of covert transmission of trade secrets in an open and insecure channel according to an example of the present invention, involving stages 1, 2, 3 and optional 4. The sender of the trade secret acts as the information holder, multiple company employees act as information transmitters, and the receiver of the trade secret acts as the information restorer.

[0046] Specifically, the sender performs phase 1 carrier image CI sharing, using a less important image to generate n carrier shadow images; the sender continues to perform phase 2 secret image embedding, embeds the important secret image into a random shadow image, generates a specific shadow image CS, and modifies other shadow images to ensure the normal recovery of the carrier image CI; the n shadow images are distributed to different employees, each holding a shadow image for transmission, to ensure the reliability and fault tolerance of secret transmission; the receiver performs phase 3 carrier image recovery, if the authorization of no less than k (k≤n) transmission employees is obtained, and no less than k shadow images are obtained, the recovery of the carrier image CI can be completed;

[0047] If the recipient successfully obtains the specific shadow image CS and holds the key, stage 4 secret image recovery can be performed to recover the secret image SI containing the trade secret from the specific shadow image CS.

[0048] If part of the transmission channel is unreliable, resulting in a small amount of shadow images being lost or damaged, the carrier image can still be restored by using no less than k but not all n shadow images, thus ensuring the reliability and fault tolerance of the transmission of trade secrets. If the transmission of trade secrets is discovered by the rival company, since the embedding of the secret image SI does not affect the recovery of the carrier image CI, and all shadow images are in the form of random noise, the rival company can be induced to focus its decryption efforts on the carrier image CI rather than the real trade secret SI.

[0049] This scheme ensures the behavioral security of secret image transmission, hides the transmission of secret images in the transmission of carrier images, conceals the transmission process of the secret image itself, and further ensures the confidentiality of trade secrets; at the same time, the less important carrier image requires no less than k shadow images to recover, and this scheme also ensures that a small number of malicious transmission users cannot obtain all the carrier image ciphertexts, making it more difficult for rival companies to steal trade secrets.

[0050] In summary, the method described in the embodiment of the present invention makes full use of the redundancy of the shadow image in the traditional secret image sharing scheme, embeds another secret image into one of the shadows, and ensures that the restoration of the two images does not affect each other; at the same time, the method performs well in terms of the peak signal-to-noise ratio (PSNR) between the reconstructed image and the original image, the entropy of the shadow image, and the information embedding rate, and greatly increases the amount of information transmitted compared to the basic secret image sharing method.

[0051] In addition, a person skilled in the art can understand that all or part of the steps in the above-mentioned embodiment method can be implemented by instructing related hardware through a program, and the corresponding program can be stored in a computer-readable storage medium. The above-mentioned storage medium can be a read-only memory, a disk or an optical disk, etc.

[0052] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by any technician familiar with the technical field within the technical scope disclosed in the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims. The information disclosed in the background technology section of this article is only intended to deepen the understanding of the overall background technology of the present invention, and should not be regarded as an admission or in any form that the information constitutes prior art known to those skilled in the art.

Claims

1. A lossless information hiding method based on secret image sharing, characterized in that: The method comprises: Step 1: The information holder generates several random shadow images and keys based on the carrier image CI; Step 2: The information holder embeds the image SI to be embedded into the specific shadow image CS, and the generated key is used to restore the embedded image SI; Step 3, the information transmitter transmits the generated shadow image to the information restorer; Step 4: The information restorer collects shadow images and restores the carrier image CI based on the collected shadow images; if the information restorer obtains a specific shadow image CS and holds the key, the embedded image SI can be restored in addition.

2. The lossless information hiding method based on secret image sharing according to claim 1 is characterized in that: In step 1, the information holder uses the (k, n) threshold Lagrangian interpolation method to share the carrier image CI. The definition of the Lagrangian polynomial is as follows. All calculations related to the Lagrangian polynomial are performed on the Galois field GF(257): f(x)=a0+a1x+a2x 2 +…+a k-1 x k-1 (mod p) Where f(x) is a Lagrange polynomial; x is the independent variable of the polynomial; k is the minimum number of shadows required to reconstruct the polynomial using the (k, n) threshold Lagrange interpolation method; p is the modulus of the operation, mod p means that all operation results are divided by p to take the remainder; a0 of each polynomial is a pixel value of the carrier image CI, and the other coefficients are random values. The polynomial containing the pixel value CI(x, y) is denoted as poly(x, y); The shadow image is constructed by assigning Lagrangian polynomials using the id of the information transmitter. Each polynomial contains a pixel value of the carrier image CI. Therefore, a carrier image CI of size l×w will produce l×w polynomials, and each shadow image has a size of l×w; This stage generates n shadow images, which are distributed to n information transmitters. At least k shadow images are needed to restore the carrier image CI.

3. The lossless information hiding method based on secret image sharing according to claim 1 is characterized in that: In step 2, A specific shadow image CS is selected from the generated shadow images, and a key (Co, β, Mo, ord) is randomly generated, where Co is a coordinate value that determines the initial position of embedding, and is a two-tuple including a horizontal coordinate and a vertical coordinate; β is the offset between two embedding positions; Mo is the modulus of the coordinate calculation; ord is the embedding position in the polynomial; Each pixel of the embedded image SI will be split into a pair, recorded as (p1, p2), and embedded into two adjacent pixels of the carrier image CI; where Co is the initial position of embedding, and the next embedding position is determined by p1 and β. The embedding process is: Step 21: assign the target coordinate value coord of the current operation to the initial position, that is, coord=Co, and then perform the following operations on each pixel SI(i, j) of the embedded image SI: Step 22, calculate p1 and p2 for each pixel, where p1 is a random integer in the range of [0, 255], and p2 satisfies p1+p2=SI(i, j) mod 257, where SI(i, j) is the pixel value of the embedded image SI at the coordinate (i, j); then CI(coord) and CI(coord+1) are assigned to p1 and p2 respectively, where CI(coord) is the pixel value of the carrier image CI at the coordinate value coord; if CI(coord+(p1+β mod Mo)) has been embedded, reselect p1 and re-execute step 22; Step 23: Modify other temporary shadow images SH i The corresponding pixel value is modified to ensure that the normal restoration of the carrier image CI is not affected: Where j = 1 or 2, each i corresponds to a data transmitter, S i is the i-th final shadow image, S i (x, y) is the pixel value of the i-th final shadow image at the coordinate value (x, y); SH i is the i-th temporary shadow image, SH i (x, y) is the pixel value of the i-th temporary shadow image at the coordinate value (x, y); CS(x, y) is the pixel value of the specific shadow image CS at the coordinate value (x, y); id i and id CS are the ids of the i-th information transmitter and the information transmitter of a specific shadow image respectively; if there is any S i (x, y) = 256, then reselect p1 and re-execute steps 22 and 23; Step 24: Let coord=coord+p1+β, update the target coordinate value of the current operation, and re-execute steps 22 and 23 until all pixel values ​​of the embedded image SI are processed.

4. The lossless information hiding method based on secret image sharing according to claim 3 is characterized in that: In step 4, at least k shadow images are needed to reconstruct the Lagrangian polynomial, which is denoted as poly (x，y) ; The information restorer uses the shadow value to reconstruct the polynomial according to the following formula, and extracting the coefficients of these polynomials can restore all the pixel values ​​of the carrier image CI: Where f'(x) is the Lagrange polynomial restored from the shadow value; f(x i ) is the i-th shadow value, x i is the ith independent variable, corresponding to the ith user id; p is the modulus of the operation, mod p means that all operation results are divided by p to get the remainder; k is the minimum number of shadows required to reconstruct the polynomial using the (k, n) threshold Lagrangian interpolation method; If the information restorer obtains the specific shadow image CS and holds the key (Co, β, Mo, ord), the key (Co, β, Mo, ord) is used to restore the embedded image SI from the specific shadow image CS. Specifically, each pixel value of the embedded image SI is calculated by each pair of polynomials, and then the key is used to obtain the next pair of pixel values ​​until the embedded image SI is completely restored, including: Step 41, assign the target coordinate value coord of the current operation to the initial position, that is, coord=Co, and then perform the following steps for each pixel SI(i, j) of the embedded image SI; Step 42, extract the ordth order coefficients of the polynomials poly(coord) and poly(coord+1) reconstructed at the coordinates coord and coord+1, denoted as p1 and p2 respectively, for forming a pixel value of the embedded image SI in the next step; Step 43, perform the inverse process of step 22, and calculate the restored embedded image SI pixel value at the coordinate coord, that is: SI (x, y) = p1 + p1 mod 257; Let coord=coord+p1+β, update the target coordinate value of the current operation, and continue the operation of step 42 until the embedded image SI is completely restored.

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