CN109727294A - A kind of thresholding visual cryptography Matrix Construction Method - Google Patents

Abstract

The present invention provides a kind of thresholding visual cryptography Matrix Construction Method, this method comprises: construct accumulative array, accumulative array is by | P | × | T | Matrix C A constitute；After determining array P, authorized subset and forbidding subset, it may be determined that F, F Γ_∞In set；Determine set Γ_∞, Γ_∞The number of middle set is equal to Γ_∞Number；Structural matrix CA；The basic matrix S of accumulative array is constructed according to (n, n) threshold schemes⁰' and S¹'；The distribution situation for the position that every row Hamming weight is 1 in observation matrix CA, the row sequence where the position that Hamming weight is 1 in Matrix C A, as basic matrix S⁰And S¹Row sequence；And so on, obtain final basic matrix S⁰And S¹.Since the columns of the basic matrix constituted is relatively fewer, and the more few then pixel expansion of columns is smaller, so that image will not be stretched excessively and influence to decrypt effect when Restore Secret, to largely ensure that the quality of decrypted image.

Description

A kind of thresholding visual cryptography Matrix Construction Method

Technical field

The invention belongs to secret sharing and visual cryptography fields, more particularly to a kind of novel thresholding visual cryptography square Battle array building method.

Background technique

By Naor and Shamir, in 1994, European cryptography annual meeting above mentioned visual cryptography (Visual Cryptograghy) Out, it is combined privacy sharing and digital picture based on threshold secret sharing thought, forms a new research Hot spot.The principle of visual cryptography is that original image resolves into the random visual cryptography subgraph of two width, close from single vision Want that it is impossible for obtaining original image information in numeral figure.Only when two width visual cryptography subgraphs are completely coincident, original graph As can just be reproduced.

Secret-sharing algorithm in visual cryptography is that Secret Image is encoded to several by pixel to be known as shared part (Shares) in image, black, the white pixel point random distribution in part is shared, therefrom cannot get any letter about Secret Image Breath.The algorithm of Restore Secret in visual cryptography is very simple, need to only print shared part of certain amount to transparent film simultaneously It is overlapped, the vision system of people can directly recognize information.

It when the decryption principle of visual cryptography is eye-observation object, is told on and the comparison with ambient enviroment , and the vision system of the mankind can only experience one piece out there is no the color that method clearly identifies each pixel in image The average effect that region all pixels color shows.Therefore, when shared part is superimposed, as long as the gray scale difference of monochrome pixels is enough Greatly, human visual system can interpret Secret Image.Due to visual cryptography theory α coefficient and Restore Secret it is simple Property, application prospect is boundless.

With the fast development of internet, digital picture is widely used, and the safety problem of image increasingly merits attention. To protect image, the technologies such as image encryption, Information hiding and digital watermarking propose in succession, however require when the decryption of these methods It calculates.Naor and Shamir is put forward for the first time (k, n) visual cryptography scheme within 1994, and the program is by Secret Image as unit of pixel It is encrypted, obtains n and share part.Each sharing part is disorderly and unsystematic all as random noise, attacker can not directly by Individual is shared part and gets secret information.When sharing part superposition when k or more than k, secret information can be gone out by eye recognition, Without any calculating；And when sharing part superposition less than k, then it is unable to Restore Secret information.

Summary of the invention

It is an object of the invention to propose one premised on the general access structure of the Naor and Shamir model of extension Kind is used for the visual cryptography Matrix Construction Method of general access structure.

A kind of novel thresholding visual cryptography matrix construction scheme, comprising the following steps:

Step 1: construct accumulative array, accumulative array is by | P | × | T | Matrix C A constitutes, wherein array P is it is known that authorize Subset isForbidding subset is Γ_∞=B | B ∈ Γ_Forb,B∪ {i}∈Γ_QualTo all i ∈ P B；

Step 2: after determining array P, authorized subset and forbidding subset, it may be determined that F, F are set Γ_∞In subclass；

Step 3: determining set Γ_∞, Γ_∞The number of middle set is equal to Γ_∞Number；

Step 4: structural matrix CA；

Step 5: constructing the basic matrix S of accumulative array according to (n, n) threshold schemes⁰' and S¹'；

Step 6: the distribution situation for the position that every row Hamming weight is 1 in observation matrix CA, the Hamming weight in Matrix C A For the row sequence where 1 position, as basic matrix S⁰And S¹Row sequence；

Step 7: and so on, obtain final basic matrix S⁰And S¹；

Wherein, (Γ_Qual,Γ_Forb) indicate general access structure, general access structure be enable P={ 1 ..., n } be participate in Person's set, 2^pIndicate the power set of set P, Γ_QualAnd Γ_ForbIt is known respectively as authorized subset and forbids subset；They meet following Condition:

(2)Γ_Qual∩Γ_Forb=φ, if this access structure is healthy and strong structure, Γ_Qual∪Γ_Forb=2^p；

It enablesThen Γ₀Referred to as Minimal authorized subset；Enable Γ_∞ =B | B ∈ Γ_Forb,B∪{i}∈Γ_QualTo all i ∈ P B, then Γ_∞Referred to as maximum forbids subset.

Further, method as described above, in step 5, the building method of (n, the n) threshold schemes are as follows:

Step 1: determining the n value of threshold schemes, which is the line number of formation base matrix；

Step 2: basic matrix S⁰It is the column by being constituted from 0 to 0/1 value that Hamming weight n is even number；

Step 3: basic matrix S¹It is the column by being constituted from 0 to 0/1 value that Hamming weight n is even number；

Step 4: finally obtaining basic matrix S after Total enumeration⁰And S¹。

The utility model has the advantages that

The matrix of building method construction through the invention, since the columns of the basic matrix constituted is relatively fewer, and arranges The more few then pixel expansion of number is smaller, so that image will not be stretched excessively and influence to decrypt effect when Restore Secret, thus It largely ensure that the quality of decrypted image.In addition, building method proposed by the invention, even if it is close not grasp vision The people of code and related mathematical knowledge can also construct thresholding visual cryptography scheme, construction process by simple algebraic expression evaluation It is simple and efficient.

Specific embodiment

To make the object, technical solutions and advantages of the present invention clearer, the technical solution below in the present invention carries out clear Chu is fully described by, it is clear that described embodiments are some of the embodiments of the present invention, instead of all the embodiments.It is based on Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts every other Embodiment shall fall within the protection scope of the present invention.

It is proposed that basic matrix is the core of most of scheme so far from visual cryptography.Current major part visual cryptography scheme Definition is based on (k, n) thresholding.Classical thresholding visual cryptography scheme (k, n)-VCS is using n × m Boolean matrix as element Set C₀And C₁Composition.When sharing white (black) pixel, at random from C₀(C₁) one matrix of middle selection, determine n shared parts The color of middle m sub-pixel.C₀And C₁Meet following two condition:

(1) as k≤P≤n,B₀The obtained vector V of any P row inclusive-OR operation₀Meet W (V₀)≤t-α m；B₁The obtained vector V of any P row inclusive-OR operation₁Meet W (V₁) >=t. wherein W (V) indicate V Hamming weight Amount；

(2) as 0 < p < k, if D₀(D₁) it is C₀(C₁) in all matrix i₁,i₂,...,i_pThe matrix stack that row is constituted It closes, then D₀=D₁.

In above-mentioned definition, C₀And C₁It is basic matrix group, m is pixel expansion, and α is relative mistake.

When whether measure the building method of a certain basic matrix has universality, the aspect being considered as has two: first is that constructing Basis matrix pixel expansion it is whether sufficiently small, the sufficiently small number for meaning that original pixels and being extended to sub-pixel of m, i.e., The area of the distortion of image；Second is that whether the relative mistake as corresponding to the basic matrix constructed is sufficiently large, what α embodied is secret figure The recovery effects of picture, it is sufficiently large to mean that the image effect after restoring is more preferable.

The characteristics of visual cryptography is a kind of application of the Secret sharing techniques in digital image arts, inherits privacy sharing, There is recovery simplicity simultaneously.And in practical applications, often use 2 basis matrix S⁰And S¹To construct (k, n) visual secret Sharing scheme, i.e. set of matrices C⁰And C¹It is to S respectively⁰And S¹All column all over taking various be arranged to make up.

Basic conception

General access structure be enable P={ 1 ..., n } be participant set, 2^pIndicate the power set of set P, then general access Structure can use (Γ_Qual,Γ_Forb) indicate, Γ_QualAnd Γ_ForbIt is known respectively as authorized subset and forbids subset.They meet The following conditions:

(2)Γ_Qual∩Γ_Forb=φ, if this access structure is healthy and strong structure, Γ_Qual∪Γ_Forb=2^p。

It enablesThen Γ₀Referred to as Minimal authorized subset.Enable Γ_∞ =B | B ∈ Γ_Forb,B∪{i}∈Γ_QualTo all i ∈ P B, then Γ_∞Referred to as maximum forbids subset.

General access structure model is instruction (Γ_Qual,Γ_Forb) it is an access structure, then the Boolean matrix of two n × m C₀And C₁, define a general access structure visual cryptography (Γ_Qual,Γ_Forb, m)-VCS, and if only if existence value α (m) and SetMeet the following conditions:

(1) (comparative condition) any authorized subset X={ i₁,i₂,...,i_p}∈Γ_QualBy being superimposed their transparent Film can restore the picture shared.It is, to arbitrary M ∈ C₀, the i-th of M₁,i₂,...,i_pRow vector or operation obtain To vector V meet w (V)≤t_X- α (m) m, and for arbitrary M ∈ C₁, the i-th of M₁,i₂,...,i_pRow vector or operation obtain To vector V meet w (V) >=t_X。

(2) (safety conditions) arbitrarily forbid subset X={ i₁,i₂,...,i_p}∈Γ_ForbIt is unable to obtain about machine Close image file, it is, taking C₀In each matrix i-th₁,i₂,...,i_pRow constitutes new p × m matrix, by these matrixes Constitute p × m set of matrices D₀, take C₁In each matrix i-th₁,i₂,...,i_pRow constitutes new p × m matrix, by these matrixes Constitute p × m set of matrices D₁, D₀And D₁It include identical matrix (D with identical probability₀And D₁It is undistinguishable).

(n, n) threshold schemes are illustrated first below:

The constructing plan of (n, n) thresholding is equivalent to basic matrix S⁰And S¹Building, the method is as follows: matrix S⁰In 1 number that each column vector is included is even number, matrix S¹Each of column vector 1 number that is included all be Odd number.

Step 1: determining the n value of threshold schemes, which is the line number of formation base matrix；

Step 2: basic matrix S⁰It is such as n=3 by from 0 to the column that constitute of 0/1 value that Hamming weight n is even number, then S⁰It is the column that the Total enumeration for the various situations of 0/1 value for being 0 and 2 by Hamming weight is constituted；

Step 3: basic matrix S¹It is such as n=3 by from 0 to the column that constitute of 0/1 value that Hamming weight n is even number, then S¹It is the column that the Total enumeration for the various situations of 0/1 value for being 1 and 3 by Hamming weight is constituted；

Step 4: finally obtaining basic matrix S after Total enumeration⁰And S¹。

Embodiment 1:

Below according to specific embodiment that (n, the n) threshold schemes are illustrated:

If n=4, the line number of basis matrix is 4, and the construction of column is i.e. according to S⁰Only comprising Hamming weight be even number 0,2, 4, S¹It is only carried out comprising 1,3 method that Hamming weight is odd number, two basic matrixs are as follows:

Embodiment 2:

N=2 is enabled, then the line number of basis matrix is 2, and the construction of column is i.e. according to S⁰It is only 0, the 2 of even number comprising Hamming weight, S¹It is only carried out comprising 1 method that Hamming weight is odd number, two basic matrixs are as follows:

It is that the present invention is to provide the visual cryptography matrix construction sides of the integrating method realization arbitrary structures from array below Method.

It add up to be constructed on the basis of above-mentioned (n, n) threshold schemes from array.An accumulative total is constructed first Group, add up array construction method: construction one | P | × | T | Matrix C A, wherein | T |=| Γ_∞|, and if only if When, CA (i, j)=1, F is set Γ_∞Middle subclass.

P is that the participant of visual cryptography scheme gathers, it is believed that array P is known.And T refer to forbidding subset and Gather included in authorized subset；The number for being intended to refer to element in set of set plus two vertical lines, constitutes accumulative total The line number and columns of group are the number of the number of element and element in set T in set P.Specifically, first in array P in example 3 Plain number is 4, and authorization that array T is included, to forbid the subclass number in set be 3, therefore accumulative array is 4 rows 3 column composition 's.

Assuming that S^0'、S^1'Be (| Γ_∞|, | Γ_∞|) basic matrix of scheme, S⁰And S¹It is the basic matrix of general access structure.If The row number that element is 1 in the i-th row in accumulative array CA is j_i,1,...,j_i,g, then by S^0'Jth_i,1,...,j_i,gCapable or conduct S⁰The i-th row, so can be obtained by the basic matrix S of general access structure⁰And S¹。

Due to being needed before constructing last basic matrix by means of first constructing accumulative array, and the basic matrix of accumulative array is just It is to be constructed according to (n, n) threshold schemes, basic matrix is S^0'And S^1', prime is intended merely to and " accumulating from array " side The basic matrix S finally constructed in method⁰And S¹It distinguishes.

Step 1: construct accumulative array, accumulative array is by | P | × | T | Matrix C A constitutes, wherein array P is it is known that authorize Subset isForbidding subset is Γ_∞=B | B ∈ Γ_Forb,B∪ {i}∈Γ_QualTo all i ∈ P B；

Step 2: after determining array P, authorized subset and forbidding subset, it may be determined that F, F Γ_∞In set；Step 3: Determine set Γ_∞, Γ_∞The number of middle set is equal to Γ_∞Number；

Step 4: structural matrix CA；

Step 5: constructing the basic matrix S of accumulative array according to (n, n) threshold schemes^0'And S^1'；

Step 6: the distribution situation for the position that every row Hamming weight is 1 in observation matrix CA, the Hamming weight in Matrix C A For the row sequence where 1 position, as basic matrix S⁰And S¹Row sequence；

Step 7: and so on, obtain final basic matrix S⁰And S¹。

Embodiment 3:

Matrix Construction Method of the present invention is illustrated below by way of the present embodiment:

Enable n=4, P={ 1,2,3,4 }, Γ₀={ { 1,2 }, { 2,3 }, { 3,4 } }, Γ_∞={ { 1,4 }, { 1,3 }, { 2,4 } } It can thus be concluded that F₁={ Isosorbide-5-Nitrae }, F₂={ 1,3 }, F₃={ 2,4 }, then | T |=| Γ_∞|=3, accumulative array is constructed first, can be obtained It arrives:

Then the basic matrix of (3,3) thresholding is constructed:

The available col1=of CA { 3 } are observed at this time, col2={ 1,2 }, col3={ 1,3 }, col4={ 2 } thus may be used It is as follows to calculate basic matrix, col1=3, therefore by S^0'And S^1'The 3rd row as S⁰And S¹The first row；Col2={ 1,2 }, By S^0'And S^1'1,2 rows do or operation after as S⁰And S¹The second row, therefore analogize, it is as follows that basic matrix can be obtained:

The building of the basis matrix of arbitrary structures visual cryptography may be implemented by the method for the invention.And have as one Hide with for the visual cryptography for sharing stealth technology, extremely important one in the judgment criteria of scheme quality itself, i.e., Whether the pixel expansion for the program is sufficiently small and whether relative mistake is sufficiently large.The relationship of pixel expansion and relative mistake is into Inverse ratio, pixel expansion is smaller, and relative mistake is bigger, and the effect that the program is implemented is also better.Pixel expansion is most intuitive Performance, the columns of the basic matrix exactly constituted is less as far as possible, and otherwise image excessively stretches and then can when Restore Secret Influence decryption effect.This advantage embodies in the present invention, and the columns of as basic matrix is less, this can largely be protected Demonstrate,prove the quality of image.

Visual cryptography has the outstanding advantages of simplicity, hardly needs to the application of the visual cryptography scheme constructed Password is gained knowledge, but constructing visual cryptography scheme using the typical construction methods of existing document is not a simple process. Building method proposed by the invention, can also be by simple generation even if the people for not grasping visual cryptography and related mathematical knowledge Numerical expression evaluation constructs thresholding visual cryptography scheme, and construction process is simple and efficient.Finally, it should be noted that above embodiments are only To illustrate technical solution of the present invention, rather than its limitations；Although having been carried out with reference to the foregoing embodiments to the present invention detailed Illustrate, those skilled in the art should understand that: its still can to technical solution documented by foregoing embodiments into Row modification or equivalent replacement of some of the technical features；And these are modified or replaceed, and do not make relevant art side The essence of case departs from the spirit and scope of the technical scheme of various embodiments of the present invention.

Claims (2)

1. a kind of novel thresholding visual cryptography matrix construction scheme, which comprises the following steps:

Step 1: construct accumulative array, accumulative array is by | P | × | T | Matrix C A constitute, wherein array P is it is known that authorized subset ForForbidding subset is Γ_∞=B | B ∈ Γ_Forb,B∪{i}∈ Γ_QualTo all i ∈ P B；

Step 2: after determining array P, authorized subset and forbidding subset, it may be determined that F, F are set Γ_∞In subclass；

Step 3: determining set Γ_∞, Γ_∞The number of middle set is equal to Γ_∞Number；

Step 4: structural matrix CA；

Step 5: constructing the basic matrix S of accumulative array according to (n, n) threshold schemes^0'And S^1'；

Step 6: the distribution situation for the position that every row Hamming weight is 1 in observation matrix CA, Hamming weight is 1 in Matrix C A Position where row sequence, as basic matrix S⁰And S¹Row sequence；

Step 7: and so on, obtain final basic matrix S⁰And S¹；

Wherein, (Γ_Qual,Γ_Forb) indicate general access structure, general access structure be enable P={ 1 ..., n } be participant collection It closes, 2^pIndicate the power set of set P, Γ_QualAnd Γ_ForbIt is known respectively as authorized subset and forbids subset；They meet following item Part:

(1)

(2)Γ_Qual∩Γ_Forb=φ, if this access structure is healthy and strong structure, Γ_Qual∪Γ_Forb=2^p；

It enablesThen Γ₀Referred to as Minimal authorized subset；Enable Γ_∞=B | B∈Γ_Forb,B∪{i}∈Γ_QualTo all i ∈ P B, then Γ_∞Referred to as maximum forbids subset.

2. the method according to claim 1, wherein in step 5, the building method of (n, the n) threshold schemes Are as follows:

Step 1: determining the n value of threshold schemes, which is the line number of formation base matrix；

Step 2: basic matrix S⁰It is the column by being constituted from 0 to 0/1 value that Hamming weight n is even number；

Step 3: basic matrix S¹It is the column by being constituted from 0 to 0/1 value that Hamming weight n is even number；

Step 4: finally obtaining basic matrix S after Total enumeration⁰And S¹。