CN111177746A - Efficient visual secret sharing method with core participants - Google Patents

Abstract

The invention belongs to the technical field of multimedia information security, and relates to an efficient visual secret sharing method with core participants. When the access structure of the (t, s, k, n) -VCS is decomposed into a plurality of optimal (k, k) -VCS access structures, the performance of the (t, s, k, n) -VCS is further improved, the size expansion of the shared part is reduced, and the visual quality of a reconstructed image is improved.

Description

Efficient visual secret sharing method with core participants

Technical Field

The invention belongs to the technical field of multimedia information security, and relates to an efficient visual secret sharing method with core participants.

Background

The visual secret sharing technology is that secret images are coded into a plurality of images called sharing shares according to pixel points, and black and white pixel points in the sharing shares are randomly distributed, so that no information related to the secret images can be obtained. The secret recovery algorithm is very simple, and people can directly recognize secret information through a visual system only by printing a certain number of shared shares on a transparent film and overlapping the shared shares. Due to the theoretical security of visual secret sharing and the simplicity of secret recovery, the application prospect is very wide. Size expansion and contrast are two main indexes for evaluating the visual secret sharing method, wherein size expansion refers to the size ratio of a reconstructed image to a secret image, and contrast refers to the visual quality of the reconstructed image relative to the secret image. Larger size expansion increases the storage and transmission burden of shares, and lower contrast affects the discrimination of reconstructed images by the human visual system.

With the development of the visual secret sharing technology, various visual secret sharing schemes have been proposed. In order to solve the problem of different importance of shares, visual secret sharing with core participants, abbreviated as (t, s, k, n) -VCS, has been proposed; (t, s, k, n) -VCS is a process for producing n shares of a secret image, wherein the first s shares are referred to as core shares and the remaining n-s shares are referred to as non-core shares. When we reconstruct the secret image, at least k shares need to be collected, including at least t core shares. Many scholars have intensively studied visual secret sharing techniques with core participants, and various construction methods have been proposed. But these methods have poor performance, i.e., large size expansion and small contrast. Therefore, it is of great interest to study and design an efficient visual secret sharing method with core participants.

The visual secret sharing is that image pixels are used as units to operate to obtain a plurality of shares, each share is disordered like random noise, and an attacker cannot directly solve secret information from a ciphertext. The following describes the visual secret sharing process, taking (k, n) -VCS as an example.

Visual secret sharing first constructs two n × M basis matrices M₀And M₁Wherein the matrix M₀Called white basis matrix (white basis matrix for short), matrix M₁Referred to as black matrix (black matrix for short). Then, the two basic matrixes are used for sharing the black-white (binary) secret image, and the method comprises the following specific steps:

inputting: secret image S and basis matrix M₀And M₁。

And (3) outputting: n shares S₁,S₁,…,S_n。

(1) Repeating steps 2-4 for each pixel s of the secret image;

(2) if the pixel s is a white pixel, the matrix M is selected₀As a shared matrix M; otherwise, the matrix M is selected₁As a shared matrix M;

(3) performing column permutation operation on the shared matrix M;

(4) assigning the ith row of the shared matrix M to the ith share S_iWherein i is 1,2, …, n;

(5) n shares S are obtained₁,S₁,…,S_n。

In the secret image recovery stage, the original secret image can be decrypted by only randomly selecting k shares from n shares, printing the k shares on a transparent film, and finally physically superposing the k shares. In the encryption and decryption stages of the image, information loss and size expansion exist, and the visual quality of the decrypted image is low. It is therefore desirable to devise a method to reduce the size expansion of shares and improve the visual quality of the decrypted image.

A method of constructing a (t, s, k, n) -VCS fundamental matrix (p.li and z.liu, "a novel cryptography scheme with a differential architecture of shadrows," international work on Digital watermark in springer,2017, pp.365-377.), which decomposes a (t, s, k, n) -VCS into a plurality of (t, k, n) -VCSs for processing by utilizing the decomposability of an access structure. First, the basic matrix of each (t, k, n) -VCS is constructed separately, and then these basic matrices are matrix-connected, and the obtained matrix is the basic matrix of the (t, s, k, n) -VCS. And finally sharing the secret image by using the constructed (t, s, k, n) -VCS basic matrix. The disadvantages are:

(1) it is difficult to determine whether the base matrix of (t, k, n) -VCS is optimal;

(2) since (t, k, n) -VCS is not the most basic access structure, the performance of (t, s, k, n) -VCS has room for improvement.

Disclosure of Invention

To solve the above problems in the background art, the present invention provides an efficient method for sharing visual secrets by a core participant, which can generate shares with a smaller size and improve the visual quality of reconstructed images.

The technical scheme for solving the problems is as follows: an efficient method of sharing visual secrets with a core participant, characterised by the steps of:

1) minimum grant set Γ for input (t, s, k, n) -VCS₀Dividing the access structure to obtain d sub-access structures

2) Using the definition of equivalent access structure to d sub-access structures

The equivalent access structures in (1) are merged to obtain g merged sub-access structures

Wherein g is less than or equal to d;

3) for each sub-access structure gamma_iBuilding a base matrix

And

wherein i is more than or equal to 1 and less than or equal to g;

4) for any participant j, if participant j is not included in the sub-access structure Γ_iIn, matrix

(or

) The number of jth row of (a) is all equal to 0; otherwise, the matrix

(or

) Is equal to the j-th row number of the matrix

(or

) The row of values corresponding to participant j, where 1. ltoreq. i.ltoreq.g, 1. ltoreq. j.ltoreq.n;

5) will matrix

Are connected in series to obtain a matrix S₀The matrix is formed by

Are connected in series to obtain a matrix S₁；

6) Will matrix S₀And S₁Deletion of the same column;

7) finally, obtaining a basic matrix S of (t, S, k, n) -VCS₀And S₁。

The invention has the advantages that:

1) when the access structure of the (t, s, k, n) -VCS is decomposed, the access structure is decomposed into a plurality of optimal (k, k) -VCS access structures, so that the performance of the (t, s, k, n) -VCS is further improved;

2) the invention reduces the size expansion of the share;

3) the invention improves the visual quality of the reconstructed image.

Drawings

FIG. 1 illustrates a flow diagram of an efficient method of visual secret sharing with core participants;

FIG. 2 shows the experimental results of (2,3,3,5) -VCS;

wherein: (a) secret images, (b) - (f) share images, (g) reconstructed images of shares 1,2, 3, (h) reconstructed images of shares 1,2, 4, (i) reconstructed images of shares 1,2, 3, 4, (j) reconstructed images of all shares, (k) reconstructed images of shares 1,2, and (l) reconstructed images of shares 1, 4, 5;

FIG. 3 shows the experimental results of (2,4,3,6) -VCS;

wherein: (a) the secret image, (b) - (g) are shares, (h) are reconstructed images of shares 1,2, 3, (i) are reconstructed images of shares 1,2, 3, 4, (j) are reconstructed images of all shares, (k) are reconstructed images of shares 1,2, and (l) are reconstructed images of shares 1, 5, 6.

Detailed Description

In order to make the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings of the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention. Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention.

The present invention contemplates a method of visual secret sharing with core participants. The basic principle is as follows: an algorithm is designed for decomposing the (t, s, k, n) -VCS access structure into a plurality of optimal (k, k) -VCS access structures. The algorithm reduces the size expansion of shares and improves the contrast of the reconstructed image.

The following describes specific steps, and a flow chart of an efficient method for sharing visual secrets with a core participant is shown in fig. 1.

1) Minimum grant set Γ for input (t, s, k, n) -VCS₀Dividing the access structure to obtain d sub-access structures

2) Using the definition of equivalent access structure to d sub-access structures

The equivalent access structures in (1) are merged to obtain g merged sub-access structures

Wherein g is less than or equal to d.

3) For each sub-access structure gamma_iBuilding a base matrix

And

wherein i is more than or equal to 1 and less than or equal to g.

4) For any participant j, if participant j is not included in the sub-access structure Γ_iIn, matrix

(or

) The number of jth row of (a) is all equal to 0; otherwise, the matrix

(or

) Is equal to the j-th row number of the matrix

(or

) The row of values corresponding to participant j, where 1. ltoreq. i.ltoreq.g, 1. ltoreq. j.ltoreq.n.

5) Will matrix

Are connected in series to obtain a matrix S₀The matrix is formed by

Are connected in series to obtain a matrix S₁。

6) Will matrix S₀And S₁The same column in (c) is deleted.

7) Finally, obtaining a basic matrix S of (t, S, k, n) -VCS₀And S₁。

The present invention uses the image containing the letter "CAS" as the subject of (2,3,3,5) -VCS, and the image containing the letter "SIAT" as the subject of (2,4,3,6) -VCS, and the experimental results are shown in fig. 2 and 3, respectively. The results of the comparison of the present invention with the prior art are shown in table 1.

Table 1 comparison of the present invention with the prior art

[1]G.Ateniese,C.Blundo,A.De Santis,and D.R.Stinson,“Visualcryptography for general access structures,”Information and Computation,vol.129,no.2,pp.86–106,1996.

[2]P.Li and Z.Liu,“A novel visual cryptography scheme withdifferentimportance of shadows,”in International Workshop on DigitalWatermarking.Springer,2017,pp.365–377.

Discussion of the results: from the experimental simulation results of fig. 1 and 2, it is understood that the present invention is feasible, and from table 1, it is understood that the present invention is effective in that the size expansion is reduced and the contrast is increased.

The above description is only an embodiment of the present invention, and not intended to limit the scope of the present invention, and all equivalent structures or equivalent flow transformations made by using the contents of the specification and the drawings, or applied directly or indirectly to other related systems, are included in the scope of the present invention.

Claims (1)

1. An efficient method of sharing visual secrets with a core participant comprising the steps of:

1) minimum grant set Γ for input (t, s, k, n) -VCS₀Dividing the access structure to obtain d sub-access structures gamma₀ ¹,Γ₀ ²,…,Γ₀ ^d；

2) Using the definition of equivalent access structure to d sub-access structure gamma₀ ¹,Γ₀ ²,…,Γ₀ ^dThe equivalent access structures in (1) are merged to obtain g merged sub-access structures gamma₁,Γ₂,…,Γ_gWherein g is less than or equal to d;

3) for each sub-access structure gamma_iBuilding a base matrix

And

wherein i is more than or equal to 1 and less than or equal to g;

4) for any participant j, if participant j is not included in the sub-access structure Γ_iIn, matrix

(or

) The number of jth row of (a) is all equal to 0; otherwise, the matrix

(or

) Is equal to the j-th row number of the matrix

(or

) The row of values corresponding to participant j, where 1. ltoreq. i.ltoreq.g, 1. ltoreq. j.ltoreq.n;

5)will matrix

Are connected in series to obtain a matrix S₀The matrix is formed by

Are connected in series to obtain a matrix S₁；

6) Will matrix S₀And S₁Deletion of the same column;

7) finally, obtaining a basic matrix S of (t, S, k, n) -VCS₀And S₁。

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