Regional secret image sharing method based on common polynomial factor

Abstract

The invention discloses a regional secret image sharing method based on a common polynomial factor, and mainly solves the problems that in the prior art, a secret image cannot be partially inquired, and excessive notification exists. According to the implementation scheme, a dealer, a share holder and a combinator initialize a system; the dealer divides the secret image into a common area and a high-level secret area, performs sharing operation on the common area and the high-level secret area, generates share images, sends the share images to share holders, generates verification information and publishes the verification information; the share holder verifies the received share image, and sends the share image to the combiners when the secret image needs to be reconstructed; the combiners verify the received share image and reconstruct the secret image. According to the method, lossless recovery of the secret image can be realized, partial query of the secret image is allowed, information leakage is avoided, the security of the system is further improved through authenticity verification of the share image, and the method can be used for information protection of the image and identity authentication of participants.

Description

Technical Field

[0001] The invention belongs to the technical field of information security, and in particular relates to a regional secret image sharing method, which can be used for image information protection and participant identity authentication. Background Art

[0002] As an information carrier, images are widely used in various fields. Due to the openness of communication networks, images can be attacked in various ways during transmission. Therefore, it is particularly important to ensure the integrity and confidentiality of images during transmission. Image secret sharing technology is one of the main technologies to ensure image security.

[0003] In common secret image sharing schemes, three parties are usually involved: dealers, share holders (participants), and combiners. First, the dealer divides the secret image into n different share images and sends them to the share holders in secret. The share holders receive and save the share images, and only when the combiner obtains at least k shares from the share holders can the secret be restored. Secret image sharing can effectively prevent the abuse of power by the secret holders. In the traditional (k,n) threshold secret image sharing scheme, all share holders have the same level of ability to retrieve images and can only access the complete secret image. When restoring the secret image, there will be a risk of over-restoring the secret image, causing excessive notification and information leakage. In practical applications, share holders have different importance and different authority levels. Some share holders can only partially obtain the secret image because of their low authority. The regional secret image sharing technology can just make up for the shortcomings of the traditional secret image sharing technology. It allows partial query of the secret image, thereby avoiding information leakage.

[0004] Patent document with application number CN201510144966.7 discloses a "secret image sharing method based on pixel mapping matrix embedding". Before sharing, the secret image is compressed by query coding, Huffman coding and data conversion to obtain shared secret data to improve the embedding ability of the secret image carrier; then a new pixel mapping matrix is ​​designed to ensure all pixels of the carrier image, hide the information of the secret image, and further improve the embedding ability; then in the embedding stage, the shared secret data is embedded into the carrier image through the above pixel mapping matrix to obtain a camouflage image to prevent pixels from crossing the boundary; finally, the secret image and the carrier image are restored through the camouflage image. Although this method realizes the sharing of secret images and embedding of carrier images, its shortcomings are that it is impossible to authenticate the identity of the share holders, and the share holders have the same authority, so it is impossible to partially query the secret image, and there is a risk of excessive notification.

[0005] The patent document with application number CN202010765499.0 discloses a "threshold variable secret image sharing method", which adjusts the threshold according to actual needs before restoring the secret image, and makes the secret image sharing system in a safe state. First, the secret image is processed to generate the secret share data corresponding to the participant; then the secret share data is embedded in the carrier image to generate a secret image for each participant; then the current threshold is announced, and the threshold can be adjusted multiple times according to actual needs before the secret image is restored; finally, it is determined whether the secret image recovery request sent by the participant is received. If so, it is determined whether the number of participants sending the request meets the threshold requirements. If so, the secret share data corresponding to the threshold is activated, and the secret image and the carrier image are restored. Although this method can realize dynamic adjustment of the recovery threshold, since each pixel is processed with the same weight, it is impossible to perform partial queries on the secret image, and there is a risk of excessive leakage of the secret image. Summary of the invention

[0006] The purpose of the present invention is to propose a regional secret image sharing method based on public polynomial factors to solve the problems that the prior art cannot perform partial queries on images and lacks identity authentication for share holders, resulting in excessive notification, information leakage and low system security.

[0007] To achieve the above object, the technical solution adopted by the present invention includes the following steps:

[0008] (1) Initialize the system including the dealer, the share holder, and the combiner, and determine their common parameters as (t, k, n), n ≥ k ≥ t, where n is the number of share holders, k is the minimum number of shares required to reconstruct the image, and the n share holders are divided into t necessary share holders and nt non-essential share holders according to their rights;

[0009] (2) The dealer generates a share image and publishes a verification message h:

[0010] (2a) The dealer selects a color image of size M×N as the secret image S, where M is the image height and N is the image width;

[0011] (2b) The dealer selects n mutually prime modular polynomials r1(x),…,r t (x),r t+1 (x),…,r i (x),…,r n (x), r1(x),…,r t (x) is sent to t necessary share holders respectively, r t+1 (x),…,r i (x),…,r n(x) is sent to nt non-essential share holders respectively, and a verification polynomial g(x) is selected and made public, where r i (x) is the i-th modular polynomial;

[0012] (2c) The dealer determines the high-level secret area A of the secret image S, uses A to generate two noise images Z1 and Z2 of the same size, and applies two mapping functions to the pixels of Z1 and Z2 respectively. Generate advanced regional polynomials s1(x), s2(x);

[0013] (2d) The dealer generates random polynomials α1(x), α2(x), and uses α1(x), α2(x) and s1(x), s2(x) to generate two high-level secret polynomials f1(x), f2(x);

[0014] (2e) The dealer uses polynomials f1(x), f2(x), r1(x),…,r i (x),…,r n (x) Generates the advanced regional share polynomial m1(x),…,m i (x),…m n (x), and then for the advanced regional share polynomial m i (x) Using the mapping function The inverse operation generates the pixel values ​​of the share image, where m i (x) is the i-th advanced regional share polynomial;

[0015] (2f) Repeat steps (2d) to (2e) for all pixel values ​​of the noise images Z1 and Z2 to obtain the shares A1, ..., A of n high-level secret areas. i ,...,A n ;

[0016] (2g) The dealer determines the common region R of the secret image S using two mapping functions Generate a common local polynomial s(x), and then use s(x) and a random polynomial α(x) to generate a common secret polynomial f(x);

[0017] (2h) Using f(x), g(x), r1(x),…,r i (x),…,r n (x) Generates the common area share polynomial q1(x),…,q i (x),…q n (x), where: q i (x) = f(x) mod (r i (x)·g(x)) is the i-th common area share polynomial, 1≤i≤n;

[0018] (2i) Repeat steps (2g) to (2h) until each common area share polynomial q i (x) satisfies x 24 ,x 25 The coefficient of the polynomial q is 0. i (x) Using the mapping function The inverse operation of generates the pixel values ​​of the share image;

[0019] (2j) Repeat steps (2g) to (2i) for all pixel values ​​in the common region rR to obtain the shares R1,…,R i ,...,R n ;

[0020] (2k) Dealer combines A1,…,A i ,...,A n and R1,…,R i ,...,R n The shared images of the secret image will be obtained as SHARE1,…,SHARE t Send them to the necessary share holders respectively, and SHARE t+1 ,…,SHARE i ,…,SHARE n Send them to non-essential share holders respectively, and use the common secret polynomial f(x) and the verification polynomial g(x) to calculate the dealer's two verification coefficients a and b, and then use a and b to calculate the dealer's verification message h, and publish h among the share holders and combiners;

[0021] (3) Shareholders receive the share image SHARE′ i Extract the common region R′ i , for R′ i The pixels use the mapping function Generator polynomial q′ i (x), using the polynomial q′ i (x) and the verification polynomial g(x) calculate the two verification coefficients a′, b′ of the shareholder, and then use a′, b′ to calculate the verification message h′ of the shareholder, and determine whether h′=h holds:

[0022] If so, the share holder accepts the share image and executes step (4);

[0023] Otherwise, the share holder rejects the share image and broadcasts it to the dealer and other share holders;

[0024] (4) The combiner collects the shared images SHARE″1,…,SHARE″ t ,…,SHARE″i ,…,SHARE″ k , where SHARE″ i Represents the share image obtained by the combiner from the i-th share holder, and extracts the common area R″ i , for R″ i The pixels use the mapping function The generating polynomial q″ i (x), using the polynomial q″ i (x) and the verification polynomial g(x), calculate the combiner's two verification coefficients a″ and b″, then use a″, b″ to calculate the combiner's verification message h″, and determine whether h″=h:

[0025] If it is satisfied, the combiner accepts this share image and reconstructs the secret image;

[0026] Otherwise, the Assembler rejects the share image and broadcasts a notification to the distributor and share holders.

[0027] Compared with the prior art, the present invention has the following advantages:

[0028] Firstly, the present invention ensures the legitimacy of the identities of dealers, share owners and assemblers and the authenticity of share images by having dealers generate, share holders and assemblers calculate and verify messages, thereby preventing dishonest behavior and improving the security of the system.

[0029] Secondly, the present invention realizes lossless recovery of secret images by adopting polynomial rings, and by setting the permissions of share holders, the combiner can make partial queries on the secret images, avoiding the risks of excessive notification and information leakage, and further improving the security of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 is a schematic flow chart of the present invention;

[0031] Figure 2 It is a sub-flow chart of the distributor generating a share image in the present invention. DETAILED DESCRIPTION

[0032] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0033] Reference Figure 1 , the implementation steps of this example are as follows:

[0034] Step 1: System initialization.

[0035] The initialization system includes three parties: dealers, share holders, and combiners. Their public parameters are determined as (t, k, n), n ≥ k ≥ t, where n is the number of share holders, k is the minimum number of share images required to reconstruct the image, and the n share holders are divided into t necessary share holders and nt non-essential share holders according to their authority.

[0036] In this example, the combiner is one of the share holders or a trusted third party. The complete secret image S can only be restored if the combiner collects k share images and includes the share images of all t necessary share holders during the reconstruction phase. Otherwise, only the ordinary area R of the secret image can be restored, and the advanced secret area A cannot be restored. If the number of share images collected by the combiner is less than k, all areas of the secret image cannot be restored.

[0037] Step 2: The dealer generates a share image and sends it to each share holder, generates a verification message h and makes it public.

[0038] Reference Figure 2 , the specific implementation of this step is as follows:

[0039] (2.1) The dealer selects a color image of size M×N as the secret image S, where M is the image height and N is the image width. In this example, the secret image S is the image to be protected and is kept secret by the dealer;

[0040] (2.2) Dealer selection finite field GF(2), polynomial ring and the function deg(·), from the polynomial ring Choose two mutually prime modular polynomials r1(x),…,r t (x),r t+1 (x),…,r i (x),…,r n (x) and verification polynomial g(x), and the selected polynomial must satisfy deg(r i (x))=24, deg(g(x))=2, g(x) and r i (x) are relatively prime, where GF(2) represents a finite field with only two elements, 0 and 1. represents the polynomial ring consisting of polynomials whose coefficients are in the finite field GF(2), x represents the variable in the polynomial, deg(·) represents the function of finding the highest degree of the polynomial, r i (x) is the i-th modular polynomial;

[0041] (2.3) The dealer sets r1(x),…,r t (x) is sent to t necessary share holders respectively, r t+1 (x),…,r i(x),…,r n (x) is sent to nt non-essential share holders, publicly verifying the polynomial g(x), in this example, modulo the polynomial r i (x) is kept secret by the i-th shareholder;

[0042] (2.4) The dealer determines that the size of the high-level secret area A of the secret image S is m×n, and uses [x, y] to represent the position coordinates of the pixel, where m is the height of the high-level secret area, n is the width of the high-level secret area, 1≤m≤M, 1≤n≤N;

[0043] (2.5) The dealer selects a noise image of the same size as the high-level secret area A as the first noise image Z1, and uses A and Z1 to generate the second noise image Z2:

[0044]

[0045] Where Z2[x,y] represents the pixel value of the xth row and yth column of the second noise image, [x,y] represents the pixel value of the xth row and yth column of the high-level secret area, and Z1[x,y] represents the pixel value of the xth row and yth column of the first noise image. Represents XOR operation;

[0046] In this example, the pixels of the image are represented as binary and then an XOR operation is performed. Since the selected secret image is a color image, there are three pixel channels of red (r), green (g), and blue (b), represented as (r, g, b). The specific operation is as follows: Assuming that the pixel value of the high-level secret area A is (123, 234, 70), the binary representation is (01111011, 11101010, 01000110), and the pixel value of the first noise image Z1 is (155, 150, 177), the binary representation is (10011011, 10010110, 10110001), then after the XOR operation, the pixel value of the second noise image Z2 is (11100000, 01111100, 11110111), and the pixel value is (224, 124, 247);

[0047] (2.6) The dealer chooses two polynomial rings In the selected two polynomial rings Generate mapping function They are respectively expressed as follows:

[0048]

[0049]

[0050] in, represents the polynomial ring consisting of the highest 8th degree polynomials whose coefficients are in the finite field GF(2),

[0051] represents the polynomial ring consisting of polynomials of degree 23 or higher whose coefficients are in the finite field GF(2),

[0052] [0,255] represents the range of pixel values, a i Indicates the i-th bit of the pixel value, b i Indicates the i-th bit of the red channel of the pixel value, c i Indicates the i-th bit of the green channel of the pixel value, d i Indicates the i-th bit of the blue channel of the pixel value, x i represents the i-th term of the polynomial expansion;

[0053] (2.7) Dealer uses mapping function Generate two advanced area polynomials s1(x), s2(x) for the pixels of Z1 and Z2:

[0054]

[0055] Wherein, Z1[x,y] represents the pixel value of the xth row and yth column of the first noise image; Z2[x,y] represents the pixel value of the xth row and yth column of the second noise image;

[0056] In this example, the mapping function ρ is used to obtain three polynomials of the highest order 7 for the pixel values ​​of the red (r), green (g), and blue (b) channels of ρ1 and Z2, respectively. Then, the mapping function The high-level area polynomials s1(x) and s2(x) are obtained. The high-level area polynomials s1(x) and s2(x) are kept secret by the dealer.

[0057] (2.8) Dealer from polynomial ring Select α1(x), α2(x), and the selected polynomials must satisfy Condition, and then use α1(x), α2(x) and s1(x), s2(x) to generate two high-level secret polynomials f1(x), f2(x):

[0058] f1(x)=s1(x)+α1(x)·x 24

[0059] f2(x)=s2(x)+α2(x)·x 24

[0060] Where x represents the variable of the polynomial,

[0061] In this example, polynomials α1(x) and α2(x) are randomly selected polynomials, and high-level secret polynomials f1(x) and f2(x) are kept secret by the dealer;

[0062] (2.9) The dealer uses polynomials f1(x), f2(x), r1(x),…,r i (x),…,r n (x) Generates the advanced regional share polynomial m1(x),…,m i (x),…m n (x):

[0063]

[0064] Among them, mod represents the modular operation, r i (x) represents the i-th modular polynomial;

[0065] (2.10) Distributor's advanced regional share polynomial m i (x) Using the mapping function The inverse operation generates the pixel values ​​of the share image, where m i (x) is the i-th advanced regional share polynomial;

[0066] (2.11) The dealer repeats steps (2.7) to (2.10) for all pixel values ​​of the noise images Z1 and Z2, and obtains the shares A1,…,A of n high-level secret areas. i ,…,A n In this example, the share of the high-level secret area is A i The same size as the advanced secret area A, 1≤i≤n;

[0067] (2.12) The dealer removes the high-level secret area A from the secret image S to obtain the remaining image, and sets the remaining image to the common area R. Two mapping functions are used for the pixels in the common area R. Generate a general area polynomial s(x):

[0068]

[0069] Where R[x,y] represents the pixel value of the xth row and yth column of the common region R. In this example, the common region polynomial s(x) is kept secret by the dealer;

[0070] (2.13) The dealer is from the polynomial ring Select a polynomial α(x) from , and the selected polynomial must satisfy: Generate the common secret polynomial f(x) using the polynomials s(x) and α(x):

[0071] f(x)=s(x)+α(x)·x 24

[0072] In this example, the polynomial α(x) is a randomly selected polynomial, and the common secret polynomial f(x) is kept secret by the dealer;

[0073] (2.14) The dealer uses f(x), g(x), r1(x),…,r i (x),…,r n (x) Generates the common area share polynomial q1(x),…,q i (x),…q n (x):

[0074] q i (x) = f(x) mod (r i (x)·g(x)),1 <i≤n;

[0075] (2.15) Repeat steps (2.13) to (2.14) until each common area share polynomial q i (x) satisfies x 24 ,x 25 The coefficient of the polynomial q is 0. i (x) Using the mapping function The inverse operation of generates the pixel values ​​of the share image;

[0076] (2.16) Repeat steps (2.12) to (2.15) for all pixel values ​​in the common region R to obtain the shares R1,…,R of n common regions. i ,...,R n In this example, the share of the common area is R i The same size as the normal area R;

[0077] (2.17) The dealer combines A1,…,A i ,...,A n and R1,…,R i ,...,R n Get the shared image SHATE1,SHATE of the secret image i ,…,SHARE n , SHARE1,…,SHARE t Send them to the necessary share holders respectively, and SHARE t+1 ,…,SHARE i ,…,SHARE n Sent to non-essential share holders separately. In this example, SHARE i By A i and R iCombine and get the shared image SHARE i The size of the shared image is the same as that of the secret image S. No information about the secret image S can be obtained from the shared image alone.

[0078] (2.18) The dealer uses the common secret polynomial f(x) and the verification polynomial g(x) to calculate the dealer's two verification coefficients a and b:

[0079] b=f(x)mod(x·g(x))

[0080] a=(f(x)modg(x)-b)modx

[0081] Where x represents the variable of the polynomial;

[0082] (2.19) Use a and b to calculate the dealer's verification message h, and publish the verification message h to the shareholders and the group members:

[0083]

[0084] Among them, H(a) represents the hash value of a, and H(b) represents the hash value of b. Represents the exclusive-or operation.

[0085] Step 3: The share holder verifies the share image.

[0086] (3.1) The share holder receives the share image SHARE′ i Extract the common region R′ i , for R′ i The pixels use the mapping function Generator polynomial q′ i (x):

[0087]

[0088] Among them, R′ i [x,y] represents the general area R′ i The pixel value of the xth row and yth column;

[0089] (3.2) Using the polynomial q′ i (x) and the verification polynomial g(x) to calculate the two verification coefficients a′, b′ of the shareholder:

[0090] b′=q′ i (x)mod(x·g(x))

[0091] a′=(q′ i (x)modg(x)-b′)modx

[0092] Where x represents the variable of the polynomial;

[0093] (3.3) Use a′, b′ to calculate the verification message h′ of the shareholder:

[0094]

[0095] Where H(a′) represents the hash value of a′, and H(b′) represents the hash value of b′. Represents XOR operation;

[0096] (3.4) Determine whether h′=h:

[0097] If true, the share holder accepts the share image and saves it;

[0098] Otherwise, the share holder rejects the share image and broadcasts it to the dealer and other share holders;

[0099] In this example, the share image received by the share holder may have been tampered with by the attacker during transmission, so it is necessary to first calculate the verification message h′ to verify the authenticity of the share image. If h′=h, it means that the share image has not been attacked or tampered with during transmission. The share holder accepts and saves the share image. When the secret image needs to be reconstructed, the share image is sent to the assembler. If h′=h is not true, it means that the share image has been attacked and tampered with during transmission. The share holder rejects the share image and broadcasts it to everyone. After receiving the notification, the dealer regenerates the share image and sends it to the share holder.

[0100] Step 4: The combiner verifies the share image and reconstructs the secret image S.

[0101] (4.1) The combiner collects the share images SHARE″1,…,SHARE″ t ,…,SHARE″ i ,…,SHARE″ k , where SHARE″ i Represents the share image obtained by the combiner from the i-th share holder, and extracts the common area R″ i , for R″ i The pixels use the mapping function The generating polynomial q″ i (x):

[0102]

[0103] Where R i [x,y] represents the general area R″ i The pixel value of the xth row and yth column;

[0104] (4.2) Using the polynomial q″ i (x) and the verification polynomial g(x), calculate the two verification coefficients a″ and b″ of the combiner:

[0105] b″=q″ i (x)mod(x·g(x))

[0106] a″=(q″ i (x)modg(x)-b″)modx

[0107] Where x represents the variable of the polynomial;

[0108] (4.3) Use a″, b″ to calculate the combiner’s verification message h″:

[0109]

[0110] Where H(a″) represents the hash value of a″, and H(b″) represents the hash value of b″. Represents the exclusive-or operation.

[0111] (4.4) Determine whether h″=h:

[0112] If it is satisfied, the combiner accepts this share image and reconstructs the secret image;

[0113] Otherwise, the Assembler rejects the share image and broadcasts a notification to the distributor and share holders.

[0114] In this example, the share image collected by the assembler from the share holder may be tampered with by the attacker during the transmission process, or the attacker may corrupt the share holder and thus tamper with the share image, so it is first necessary to calculate the verification message h″ to verify the authenticity of the share image. If h′=h, it means that the share image has not been attacked or tampered with during the transmission process, and the identity of the share holder is legal. The assembler accepts the share image and reconstructs the secret image. If h′=h does not hold, it means that the share image has been attacked and tampered with during the transmission process, and the share image is not authentic. The assembler rejects this share image and broadcasts it to everyone, thereby terminating the reconstruction process of the secret image S.

[0115] (4.5) The combiner uses the shared image SHARE″ i Extract the high-level secret area A″1,…,A″ t ,A″ t+1 ,…,A″ i ...,A″ k , and for the i-th advanced secret area A″ i The pixels use two mapping functions Generator polynomial m″i (x), and then calculate and reconstruct the high-level secret polynomials f′1(x) and f′2(x):

[0116] f′1(x)=CRT(m″1(x),…,m″ t (x),r1(x),…,r t (x))

[0117] f′2(x)=CRT(m″ t+1 (x),…,m″ k (x),r t+1 (x),…,r k (x))

[0118] Where CRT represents the function used to solve the congruence equation system;

[0119] (4.6) Use the mapping function to reconstruct the high-level secret polynomials f′1(x) and f′2(x) The inverse operation of generates pixel values ​​of the first noise image A1 and the second noise image A2;

[0120] (4.7) For A″1,…,A″ t ,A″ t+1 ,…,A″ i ...,A″ k Repeat steps (4.5) to (4.6) for all pixel values ​​in the region to obtain a first noise image A1 and a second noise image A2, and perform an XOR operation on A1 and A2 to obtain a high-level secret region A;

[0121] (4.8) The assembler uses the shared image SHARE″ i Extract the common area R″1,…,R″ i ,...,R″ n , and for the i-th common region R″ i The pixels use two mapping functions Generator polynomial q″ i (x), calculate and reconstruct the ordinary secret polynomial f′(x):

[0122] f′(x)=CCRT(q″1(x),…,q″ k (x),r1(x),…,r k (x),g(x))

[0123] Where CCRT represents a function for solving a system of congruence equations with common polynomial factors;

[0124] (4.9) Use the mapping function to reconstruct the general secret polynomial f′(x) The inverse operation generates the pixel value of the common area R;

[0125] (4.10) for R″1,…,R″ i ,...,R″ n Repeat steps (4.8) to (4.9) for all pixel values ​​in the region to obtain a normal region R;

[0126] (4.11) The high-level secret area A and the ordinary area R are combined to obtain the restored secret image S.

[0127] The above description is only a specific example of the present invention and does not constitute any limitation to the present invention. It is obvious that for professionals in this field, after understanding the content and principles of the present invention, it is possible to make various modifications and changes in form and details without departing from the principles and structures of the present invention. However, these modifications and changes based on the ideas of the present invention are still within the scope of protection of the claims of the present invention.

Claims

1. A regional secret image sharing method based on public polynomial factors, characterized in that: The steps include: (1) Initialize the system including the dealer, the share holder, and the combiner, and determine their common parameters as (t, k, n), n ≥ k ≥ t, where n is the number of share holders, k is the minimum number of share images required to reconstruct the image, and the n share holders are divided into t necessary share holders and nt non-essential share holders according to their rights; (2) The dealer generates a share image and publishes a verification message h: (2a) The dealer selects a color image of size M×N as the secret image S, where M is the image height and N is the image width; (2b) The dealer selects n mutually prime modular polynomials r1(x),…,r t (x),r t+1 (x),…,r i (x),…,r n (x), r1(x),…,r t (x) is sent to t necessary share holders respectively, r t+1 (x),…,r i (x),…,r n (x) is sent to nt non-essential share holders respectively, and a verification polynomial g(x) is selected and made public, where r i (x) is the i-th modular polynomial; (2c) The dealer determines the high-level secret area A of the secret image S, uses A to generate two noise images Z1 and Z2 of the same size, and applies two mapping functions to the pixels of Z1 and Z2 respectively. Generate advanced regional polynomials s1(x), s2(x); (2d) The dealer generates random polynomials α1(x), α2(x), and uses ɑ1(x), ɑ2(x) and s1(x), s2(x) to generate two high-level secret polynomials f1(x), f2(x); (2e) The dealer uses polynomials f1(x), f2(x), r1(x),…,r i (x),…,r n (x) Generates the advanced regional share polynomial m1(x),…,m i (x),…m n (x), and then for the advanced regional share polynomial m i (x) Using the mapping function The inverse operation generates the pixel values ​​of the share image, where m i (x) is the i-th advanced regional share polynomial; (2f) Repeat steps (2d) to (2e) for all pixel values ​​of the noise images Z1 and Z2 to obtain the shares A1, ..., A of n high-level secret areas. i ,...,A n ; (2g) The dealer determines the common region R of the secret image S using two mapping functions Generate a common local polynomial s(x), and then use s(x) and a random polynomial α(x) to generate a common secret polynomial f(x); (2h) Using f(x), g(x), r1(x),…,r i (x),…,r n (x) Generates the common area share polynomial q1(x),…,q i (x),…q n (x), where: q i (x) = f(x) mod (r i (x)·g(x)) is the i-th common area share polynomial, 1≤i≤n; (2i) Repeat steps (2g) to (2h) until each common area share polynomial q i (x) satisfies x 24 ,x 25 The coefficient of the polynomial q is 0. i (x) Using the mapping function The inverse operation of generates the pixel values ​​of the share image; (2j) Repeat steps (2g) to (2i) for all pixel values ​​in the common region R to obtain the shares R1,…,R i ,...,R n ; (2k) Dealer combines A1,…,A i ,...,A n and R1,…,R i ,...,R n The shared images of the secret image will be obtained as SHARE1,…,SHARE t Send them to the necessary share holders respectively, and SHARE t+1 ,…,SHARE i ,…,SHARE n Send them to non-essential share holders respectively, and use the common secret polynomial f(x) and the verification polynomial g(x) to calculate the dealer's two verification coefficients a and b, and then use a and b to calculate the dealer's verification message h, and publish h among the share holders and combiners; (3) Shareholders receive the share image SHARE′ i Extract the common region R′ i , for R′ i The pixels use the mapping function Generator polynomial q′ i (x), using the polynomial q′ i (x) and the verification polynomial g(x) calculate the two verification coefficients a′, b′ of the shareholder, and then use a′, b′ to calculate the verification message h′ of the shareholder, and determine whether h′=h holds: If so, the share holder accepts the share image and executes step (4); Otherwise, the share holder rejects the share image and broadcasts it to the dealer and other share holders; (4) The combiner collects the shared images SHARE″1,…,SHARE″ t ,…,SHARE″ i ,…,SHARE″ k , where SHARE″ i Represents the share image obtained by the combiner from the i-th share holder, and extracts the common area R″ i , for R″ i The pixels use the mapping function The generating polynomial q″ i (x), using the polynomial q″ i (x) and the verification polynomial g(x), calculate the combiner's two verification coefficients a″ and b″, then use a″, b″ to calculate the combiner's verification message h″, and determine whether h″=h: If it is satisfied, the combiner accepts this share image and reconstructs the secret image; Otherwise, the Assembler rejects the share image and broadcasts a notification to the distributor and share holders.

2. The method according to claim 1, characterized in that In step (2b), the dealer selects n mutually prime modular polynomials r1(x),…,r i (x),…,r n (x) and verification polynomial g(x), implemented as follows: (2b1) Dealer selection finite field GF(2), polynomial ring and the function deg(·), where: The finite field GF(2) represents a finite field with only two elements, 0 and 1. represents the polynomial ring consisting of polynomials whose coefficients are in the finite field GF(2), x represents the variable in the polynomial, and deg(·) represents the function of finding the highest degree of the polynomial; (2b2) ​​From the polynomial ring Select r1(x),…,r t (x),r t+1 (x),…,r i (x),…,r n (x) and g(x), and the selected polynomial must satisfy deg(r i (x))=24, deg(g(x))=2, g(x) and r i (x) are mutually prime.

3. The method according to claim 1, characterized in that In step (2c), the dealer determines the high-level secret area A of the secret image S, and uses A to generate two noise images A1 and A2 of the same size. The implementation steps include the following: (2c1) The dealer determines the size of the advanced secret area A to be m×n, and uses [x, y] to represent the position coordinates of the pixel, where m is the height of the advanced secret area, n is the width of the advanced secret area, 1≤m≤M, 1≤n≤N; (2c2) Select a noise image of the same size as the high-level secret area A as the first noise image Z1, and use A and Z1 to generate the second noise image Z2, which is expressed as follows: Where Z2[x,y] represents the pixel value of the xth row and yth column of the second noise image, [x,y] represents the pixel value of the xth row and yth column of the high-level secret area, and Z1[x,y] represents the pixel value of the xth row and yth column of the first noise image. Represents the exclusive-or operation.

4. The method according to claim 1, characterized in that: In step (2c), the dealer applies two mapping functions to the pixels of Z1 and Z2 respectively. Generate high-level regional polynomials s1(x), s2(x). The implementation steps include the following: (2c3) The dealer chooses two polynomial rings in: (7) represents the polynomial ring consisting of polynomials of degree 8 or higher whose coefficients are in the finite field GF(2), (23) represents the polynomial ring consisting of polynomials of degree 23 or higher whose coefficients are in the finite field GF(2); (2c4) In the two selected polynomial rings Generate mapping function Where [0,255] represents the range of pixel values, a i Indicates the i-th bit of the pixel value, b i Indicates the i-th bit of the red channel of the pixel value, c i Indicates the i-th bit of the green channel of the pixel value, d i Indicates the i-th bit of the blue channel of the pixel value, x i represents the i-th term of the polynomial expansion; (2c5) Using the mapping function Generate two advanced area polynomials s1(x), s2(x) for the pixels of Z1 and Z2: Wherein, Z1[x,y] represents the pixel value of the xth row and yth column of the first noise image; Z2[x,y] represents the pixel value of the xth row and yth column of the second noise image.

5. The method according to claim 1, characterized in that In step (2d), the dealer generates random polynomials α1(x), α2(x), and uses α1(x), α2(x) and s1(x), s2(x) to generate two high-level secret polynomials f1(x), f2(x). The implementation steps include the following: (2d1) From the polynomial ring Select α1(x), α2(x), and the selected polynomials must satisfy where deg(·) represents the function of finding the highest degree of a polynomial; (2d2) The two high-level secret polynomials f1(x) and f2(x) generated by α1(x), α2(x) and s1(x), s2(x) are expressed as follows: f1(x)=s1(x)+α1(x)·x 24 f2(x)=s2(x)+α2(x)·x 24 Here, x represents the variable of the polynomial.

6. The method according to claim 1, characterized in that In step (2e), the dealer uses polynomials f1(x), f2(x), r1(x),…,r i (x),…,r n (x) Generates the advanced regional share polynomial m1(x),…,m i (x),…m n (x), which is represented as follows: Among them, mod represents the modular operation, r i (x) represents the i-th modular polynomial.

7. The method according to claim 1, characterized in that In step (2g), the dealer determines the common region R of the secret image S using two mapping functions Generate a common local polynomial s(x), and then use s(x) and a random polynomial α(x) to generate a common secret polynomial f(x), as follows: (2g1) The dealer removes the advanced secret area A from the secret image S and sets the remaining part as the common area R; (2g2) Two mapping functions are used for pixels in the common area R Generate a general area polynomial s(x): Where R[x,y] represents the pixel value of the xth row and yth column of the normal area R; (2g3) From the polynomial ring Select a polynomial α(x) that satisfies: where deg(·) represents the function of finding the highest degree of a polynomial; (2g4) Generate the common secret polynomial f(x) using the polynomials s(x) and α(x): f(x)=s(x)+α(x)·x 24 。 8. The method according to claim 1, characterized in that Step (2k) The dealer uses the common secret polynomial f(x) and the verification polynomial g(x) to calculate the dealer's two verification coefficients a and b, and then uses a and b to calculate the dealer's verification message h, which are expressed as follows: b=f(x)mod(x·g(x)) a=(f(x)mod g(x)-b)mod x Among them, H(a) represents the hash value of a, and H(b) represents the hash value of b. Represents the exclusive-or operation.

9. The method according to claim 1, characterized in that: In step (3), the share holders have i The pixels use the mapping function The generating polynomial q′ i (x), using the polynomial q′ i (x) and the verification polynomial g(x) are used to calculate the two verification coefficients a′, b′ of the share holder, and then a′, b′ are used to calculate the verification message h′ of the share holder, which are expressed as follows: b′=q′ i (x)mod(x·g(x)) a′=(q′ i (x)modg(x)-b′)mod x Among them, R′ i [x,y] represents the general area R′ i The pixel value of the x-th row and y-th column of , H(a′) represents the hash value of a′, H(b′) represents the hash value of b′, x represents the variable of the polynomial, Represents the exclusive-or operation.

10. The method according to claim 1, characterized in that In step (4), the combiner is R″ i The pixels use the mapping function The generating polynomial q″ i (x), using the polynomial q″ i (x) and the verification polynomial g(x), calculate the two verification coefficients a″ and b″ of the combiner, and then use a″, b″ to calculate the verification message h″ of the combiner, which are expressed as follows: b″=q″ i (x)mod(x·g(x)) a″=(q″ i (x)modg(x)-b″)mod x Where R i [x,y] represents the general area R″ i The pixel value of the x-th row and y-th column of , H(a″) represents the hash value of a″, H(b″) represents the hash value of b″, x represents the variable of the polynomial, Represents the exclusive-or operation.

11. The method according to claim 1, characterized in that: In step (4), the combiner reconstructs the secret image, and the implementation steps include the following: (4.1) The assembler uses the shared image SHARE″ i Extract the high-level secret area A″1,…,A″ t ,A″ t+1 ,…,A″ i ...,A″ k , and for the i-th advanced secret area A″ i The pixels use two mapping functions Generator polynomial m″ i (x), and then calculate and reconstruct the high-level secret polynomials f′1(x) and f′2(x), the formula is as follows: f′1(x)=CRT(m″1(x),…,m″ t (x),r1(x),…,r t (x)) f′2(x)=CRT(m″ t+1 (x),…,m″ k (x),r t+1 (x),…,r k (x)) Where CRT represents the function used to solve the congruence equation system; (4.2) Use the mapping function to reconstruct the high-level secret polynomials f′1(x) and f′2(x) The inverse operation of generates pixel values ​​of the first noise image A1 and the second noise image A2; (4.3) For A″1,…,A″ t ,A″ t+1 ,…,A″ i ...,A″ k Repeat steps (4.1) to (4.2) for all pixel values ​​in the region to obtain a first noise image A1 and a second noise image A2, and perform an XOR operation on A1 and A2 to obtain a high-level secret region A; (4.4) The assembler uses the shared image SHARE″ i Extract the common area R″1,…,R″ i ,...,R″ n , and for the i-th common region R″ i The pixels use two mapping functions Generator polynomial q″ i (x), calculate and reconstruct the ordinary secret polynomial f′(x): f′(x)=CCRT(q″1(x),…,q″ k (x),r1(x),…,r k (x),g(x)) Where CCRT represents a function for solving a system of congruence equations with common polynomial factors; (4.5) Use the mapping function to reconstruct the general secret polynomial f′(x) The inverse operation generates the pixel value of the common area R; (4.6) for R″1,…,R″ i ,...,R″ n Repeat steps (4.4) to (4.5) for all pixel values ​​in the region to obtain a normal region R; (4.7) The high-level secret area A and the ordinary area R are combined to obtain the restored secret image S.

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