CN109003218A - A method of construction thresholding visual cryptography matrix - Google Patents

Abstract

The present invention relates to a kind of methods for constructing thresholding visual cryptography matrix.The present invention enables R⁰And R¹For access structure (Γ '_Qual, Γ '_Forb) basic matrix, T⁰And T¹For access structure (Γ "_Qual, Γ "_Forb) basic matrix；Enable (Γ '_Qual, Γ '_Forb) and (Γ "_Qual, Γ "_Forb) it is two access structures for having n participant；Make general access structure (Γ_Qual, Γ_Forb) meet (Γ_Qual, Γ_Forb)=(Γ '_Qual∪Γ″_Qual, Γ '_Forb∩Γ″_Forb)；Known participant's set P, Minimal authorized subset Γ₀, set Γ '₀With Γ "₀And matrix R⁰、R¹、T⁰、T¹；Determine matrix R^0′Line number be participant's set P in element number；According to R⁰Structural matrix R^0′, set Γ '₀The numerical value of middle element is matrix R^0′The required row value filled in；And so on, matrix R^0′And T^0′According to Γ '₀Construction, matrix R^1′And T^1′According to Γ "₀Construction, obtains matrix R^0′、T^0′、R^1′、T^1′；Join-matrixBasic matrix S can be obtained⁰And S¹.The building of the basis matrix of arbitrary structures visual cryptography may be implemented in the present invention.

Description

A method of construction thresholding visual cryptography matrix

Technical field

The present invention relates to secret sharing and visual cryptography field, specifically a kind of construction thresholding visual cryptography The method of matrix.

Background technique

With the fast development of internet, digital picture is widely used, and the safety problem of image is increasingly worth closing Note.To protect image, the technologies such as image encryption, Information hiding and digital watermarking propose in succession, however when the decryption of these methods all It needs to calculate.

Visual cryptography (Visual Cryptograghy) is by Naor and Shamir in European cryptography annual meeting in 1994 It is proposed, it is combined privacy sharing and digital picture based on threshold secret sharing thought, form one it is new Research hotspot.The principle of visual cryptography is that original image resolves into the random visual cryptography subgraph of two width, from single view Feel that it is impossible for wanting to obtain original image information in password subgraph.It is former only when two width visual cryptography subgraphs are completely coincident Beginning image can be just 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 are shared, therefrom cannot get any about Secret Image Information.The algorithm of Restore Secret in visual cryptography is very simple, need to only print shared part of certain amount to transparent film And be overlapped, the vision system of people can directly recognize information.

It is that effect is generated and the comparison with ambient enviroment when the decryption principle of visual cryptography is eye-observation object Fruit, and the vision system of the mankind is there is no the color that method clearly identifies each pixel in image, out one can only be experienced The average effect that block region all pixels color shows.Therefore, when shared part is superimposed, as long as the gray scale difference of monochrome pixels Sufficiently large, human visual system can interpret Secret Image.

Briefly, (k, n) visual cryptography scheme that Naor and Shamir in 1994 is put forward for the first time, by Secret Image with Pixel is that unit is encrypted, and obtains n and shares part.Each sharing part is disorderly and unsystematic all as random noise, attacker Part directly can not be shared by individual and get secret information.It, can be by eye recognition when sharing part superposition when k or more than k Secret information out is not necessarily to any calculating；And when sharing part superposition less than k, then it is unable to Restore Secret information.

Summary of the invention

Aiming at the defects existing in the prior art, the technical problem to be solved in the present invention is to provide a kind of structures The method for making thresholding visual cryptography matrix proposes that is, premised on the general access structure of the Naor and Shamir model of extension Two kinds of technologies are configured to the visual cryptography scheme of general access structure.

Present invention technical solution used for the above purpose is: a kind of side constructing thresholding visual cryptography matrix Method, comprising the following steps:

Step 1: enabling R⁰And R¹For access structure (Γ '_Qual, Γ '_Forb) basic matrix, T⁰And T¹For access structure (Γ″_Oual, Γ "_Forb) basic matrix；Enable (Γ '_Oual, Γ '_Forb) and (Γ "_Oual, Γ "_Forb) it is to there are two of n participant to deposit Take structure；Make general access structure (Γ_Qual, Γ_Forb) meet (Γ_Qual, Γ_Forb)=(Γ '_Qual∪Γ″_Qual, Γ '_Forb∩ Γ″_Forb)；

Step 2: known participant's set P, Minimal authorized subset Γ₀And its subset Γ '₀With Γ "₀And access structure (Γ′_Qual, Γ '_Forb) basic matrix R⁰、R¹With access structure (Γ "_Qual, Γ "_Forb) basic matrix T⁰、T¹；

Step 3: determining matrix R^0′Line number be participant's set P in element number；

Step 4: according to R⁰Structural matrix R^0′, set Γ '₀The numerical value of middle element is matrix R^0′The required row filled in Value；

Step 5: and so on, matrix R^0′And R^1′According to Γ '₀Construction, matrix T^0′And T^1′According to Γ "₀Construction, obtains Matrix R^0′、T^0′、R^1′、T^1′；

Step 6: join-matrix S⁰=R^0′oT^0′, S¹=R^1′oT^1′, basic matrix S can be obtained⁰And S¹, o expression join-matrix.

The n participant indicates the number for being divided into Secret Image.

The present invention has the following advantages and beneficial effects:

1, the building of the basis matrix of arbitrary structures visual cryptography may be implemented in the present invention.

2, the columns for the basic matrix that the present invention obtains is less, this can largely guarantee the quality of image.

3, building method proposed by the invention, can also be with even if the people for not grasping visual cryptography and related mathematical knowledge Thresholding visual cryptography scheme is constructed by simple algebraic expression evaluation, construction process is simple and efficient.

Specific embodiment

The present invention will be further described in detail below with reference to the embodiments.

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, application prospect is boundless.But in practical applications, 2 basic matrix S are often used⁰With S¹Share scheme, i.e. set of matrices C to construct (k, n) visual secret⁰And C¹It is to S respectively⁰And S¹All column all over taking various rows What column were constituted.

Basic conception

General access structure is that P={ 1 ..., n } is enabled to indicate that participant gathers, 2^pIndicate the power set of set P, then generally 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:

(1)

(2)Γ_Qual∩Γ_Forb=φ, if this access structure is healthy and strong structure, Γ_Qual∪Γ_Forb=2^p.It enables Γ₀=A | A ∈ Γ_Qual, it is not presentSo that A ' ∈ Γ_Qual, then 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_Oual, 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, K, i_p}∈Γ_QualBy being superimposed their transparent adhesive tape Piece can restore the picture shared.It is, to arbitrary M ∈ C₀, the i-th of M₁, i₂, K, i_pWhat row vector or operation obtained Vector V meets w (V)≤t_X- α (m) m, and for arbitrary M ∈ C₁, the i-th of M₁, i₂, K, i_pRow vector or operation obtain to Amount V meets w (V) >=t_X。

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

Enable (Γ '_Oual, Γ '_Forb) and (Γ "_Qual, Γ "_Forb) it is to have two access structures of n participant (in matrix structure During making, what n referred to is exactly the line number of matrix；During sharing Secret Image, what n referred to is exactly by Secret Image point At number), it is assumed that (Γ '_Qual, Γ '_Forb) and (Γ "_Oual, Γ "_Forb) basic matrix be respectively R⁰, R¹And T⁰, T¹, then just (Γ can be constructed_Oual, Γ_Forb) access structure, wherein (Γ_Qual, Γ_Forb)=(Γ '_Qual∪Γ″_Qual, Γ '_Forb ∩Γ″_Forb).From R⁰, R¹And T⁰, T¹In can obtain two couples of matrix (R^0′, R^1′) and (T^0′, T^1′), S at this time⁰=R^0′oT^0′, S¹ =R^1′oT^1′, wherein o indicates series connection.

Step 1: enabling R⁰And R¹For access structure (Γ '_Qual, Γ '_Forb) basic matrix, T⁰And T¹For access structure (Γ″_Oual, Γ "_Forb) basic matrix；

Step 2: (Γ_Qual, Γ_Forb) meet (Γ_Qual, Γ_Forb)=(Γ '_Qual∪Γ″_Qual, Γ '_Forb∩Γ″_Forb)；

Step 3: known participant's set P, Minimal authorized subset Γ₀And its subset Γ '₀With Γ "₀And matrix R⁰、 R¹、T⁰、T¹；Minimal authorized subset Γ₀It is arbitrarily designated, set Γ '₀With Γ "₀It is Γ₀Subset, i.e. Γ₀By Γ '₀Γ″₀Group At.

Step 4: determining matrix R^0′Line number be participant's set P in element number；

Step 5: according to R⁰Structural matrix R^0′, set Γ '₀The numerical value of middle element is structural matrix R^0′It is required to fill in Row value, such as matrix R⁰Three behaviors 101010, Γ '₀={ { 1,2 }, { 1,5 } }, then R^0′The 1st, 2 rows and the 1st, 5 rows be respectively 101010,0 filling of remaining the 3rd, 4 row；

Step 6: and so on, matrix R^0′And R^1′According to Γ '₀Construction, matrix T^0′And T^1′According to Γ "₀Construction, obtains Matrix R^0′、T^0′、R^1′、T^1′；

Step 7: join-matrix S⁰=R^0′oT^0′, S¹=R^1′oT^1′, basic matrix finally can be obtained.

Example: participant's set P={ 1,2,3,4,5 }, Γ are enabled₀={ 1,2 }, { 2,3 }, { 3,4 }, { 4,5 }, { 1,5 }, 2, 5 } }, Γ '₀={ { 1,2 }, { 1,5 } }, Γ "₀={ { 2,3 }, { 3,4 }, { 4,5 }, { 2,5 } }, in which:

Then (R is constructed^0′, R^1′) and (T^0′, T^1′), if i is not (Γ '_Qual, Γ '_Forb) indispensable element, then R^0′In The full zero row of i behavior.

(1) according to R⁰Structural matrix R^0′, set Γ '₀The numerical value of middle element is structural matrix R^0′The required row filled in Value, in this way, Γ '₀={ { 1,2 }, { 1,5 } }, so 3,4 be not basic indispensable element, so R^0′In 3,4 behavior full 0 rows, such as Under:

(2) according to R¹Structural matrix R^1′, set Γ '₀The numerical value of middle element is structural matrix R^0′The required row filled in Value, in this way, Γ '₀={ { 1,2 }, { 1,5 } }, so 3 and 4 be not basic indispensable element, so R^0′In the 3rd, 4 behavior full 0s Row, as follows:

(3) according to T⁰Structural matrix T^0′, set Γ₀The numerical value of middle element is structural matrix T^0′The required row value filled in, In this way, Γ "₀={ { 2,3 }, { 3,4 }, { 4,5 }, { 2,5 } }, so 1 is not basic indispensable element, so R^0′In the 1st behavior Full 0 row, as follows:

(4) according to T¹Structural matrix T^1′, set Γ "₀The numerical value of middle element is structural matrix T^1′The required row filled in Value, in this way, Γ "₀={ { 2,3 }, { 3,4 }, { 4,5 }, { 2,5 } }, so 1 is not basic indispensable element, so R^0′In 1 behavior Full 0 row, as follows:

Last join-matrix S⁰=R^0′oT^0′, S¹=R^1′oT^1′, basic matrix finally can be obtained:

As one have hide with for the visual cryptography for sharing stealth technology, the judge mark of scheme quality itself Extremely important one in standard, as whether the pixel expansion of the program is sufficiently small and whether relative mistake is sufficiently large.Pixel expands The latitude of emulsion and the relationship of relative mistake are inversely proportional, and pixel expansion is smaller, and relative mistake is bigger, the effect that the program is implemented Better.Pixel expansion most intuitively shows, and the columns of the basic matrix exactly constituted is less as far as possible, otherwise extensive Image excessively stretches when multiple secret, will affect decryption effect.This advantage embodies in the present invention, as the columns of basic matrix Less, this can largely guarantee the quality of image.

Visual cryptography has the outstanding advantages of simplicity, is almost not required to the application of the visual cryptography scheme constructed Password is wanted to gain knowledge, but constructing visual cryptography scheme using the typical construction methods of existing document is not a simple mistake Journey.The building method that this patent is proposed, can also be by simple even if the people for not grasping visual cryptography and related mathematical knowledge Algebraic expression evaluation construct thresholding visual cryptography scheme, construction process is simple and efficiently.

Claims (2)

1. a kind of method for constructing thresholding visual cryptography matrix, which comprises the following steps:

Step 1: enabling R⁰And R¹For access structure (Γ '_Qual, Γ '_Forb) basic matrix, T⁰And T¹For access structure (Γ "_Qual, Γ″_Forb) basic matrix；Enable (Γ '_Qual, Γ '_Forb) and (Γ "_Qual, Γ "_Forb) it is two access structures for having n participant； Make general access structure (Γ_Qual, Γ_Forb) meet (Γ_Qual, Γ_Forb)=(Γ '_Qual∪Γ″_Qual, Γ '_Forb∩Γ″_Forb)；

Step 2: known participant's set P, Minimal authorized subset Γ₀And its subset Γ '₀With Γ "₀And access structure (Γ′_Qual, Γ '_Forb) basic matrix R⁰、R¹With access structure (Γ "_Qual, Γ "_Forb) basic matrix T⁰、T¹；

Step 3: determining matrix R^0′Line number be participant's set P in element number；

Step 4: according to R⁰Structural matrix R^0′, set Γ '₀The numerical value of middle element is matrix R^0′The required row value filled in；

Step 5: and so on, matrix R^0′And R^1′According to Γ '₀Construction, matrix T^0′And T^1′According to Γ "₀Construction, obtains matrix R^0′、T^0′、R^1′、T^1′；

Step 6: join-matrixBasic matrix S can be obtained⁰And S¹,Indicate join-matrix.

2. a kind of method for constructing thresholding visual cryptography matrix according to claim 1, which is characterized in that the n ginseng The number for being divided into Secret Image is indicated with person.