CN103761702B - Image hiding and authentication method based on secret sharing - Google Patents

Abstract

The invention discloses an image hiding and authentication method based on secret sharing, and belongs to the technical field of secret image sharing. The image hiding and authentication method is characterized by comprising the steps that firstly, difference Huffman encoding is conducted on a secret image, every three generated bit sequences are set to be one group to be converted into decimal numbers which are used as coefficients of a sharing polynomial in the Shamir (k, n) threshold scheme, the k and the n are positive integers, the k is smaller than or equal to the n, and n shadow images are generated; secondly, n significant carrier images are selected, the generated shadow images are embedded into the carrier images in a matrix encoding mode, authentication bits generated by the hash function are also embedded into the carrier images, and n disguise images are formed and are in the charge of n different participants respectively. The disguise images generated through the image hiding and authentication method has higher visual quality, existence of secret information cannot be perceived by attackers easily, and the safety of the secret information is ensured. Meanwhile, before the secret information is recovered, the disguise images provided by each participant need to be authenticated, only the disguise images passing through authentication can participate in recovery of the secret information, and the safety of the secret information is further strengthened.

Description

A kind of image concealing based on privacy share and authentication method

Technical field

The invention belongs to Secret Image Sharing technical field, be specifically related to a kind of image concealing based on privacy share and recognize Card method.

Background technology

Information hiding, as an important technology of information security cybertimes, has become one of information security the most New study hotspot.Information Hiding Techniques is that by certain mode, a certain secret information is hidden in media information disclosed in another In, transmit secret information by the transmission of public information.The purpose of this technology is that the existence of hiding secret information, makes Obtain any third party in addition to communicating pair all without perceiving the existence of secret information, thus provide into one for Digital Media The protection of step.Additionally, the authenticity and integrity of digital picture also becomes the emphasis of multi-media information security, image authentication is just It it is the important technology differentiating and detecting image's authenticity and integrity.

But, a certain secret information is hidden in single open media information by traditional information concealing method, and by list Individual is managed, and once this manager either intentionally or unintentionally distorts or damage media information, and secret will be lost, to this, base Method of Steganography in privacy share can solve this problem well.This method by former Secret Image according to certain Computing splits into n shadow vector (non-correlation between each element in vector), and is hidden in by these shadow vectors and selects in advance In n the carrier image selected, form n camouflage test and be distributed to different participant's management, only collecting k therein (k≤n) individual or more camouflage test can recover the information of former Secret Image, and just cannot less than k camouflage test Recover any information of former Secret Image.Can either prevent right from excessively concentrating by this technology, Secret Image can be strengthened again Safety and integrity.Additionally, before reconstruct secret information, the verity of the camouflage test being provided participants is recognized Card is also very important, because can the verity of camouflage test directly decide secret information and be successfully recovered.

2004, Lin and Tsai proposed image concealing based on privacy share and certificate scheme first, and the program utilizes Shamir (Secret Image is divided into n shadow vector, and element value each in shadow vector is passed through LSB by k, n) threshold technique The mode that (Least Significant Bit) substitutes is hidden in carrier image, and the parity bits by 1 is real simultaneously The authentication capability of existing image.But the weakness of this scheme maximum is: the secret information of reconstruct can produce certain distortion.It After, Yang et al. is improved on the basis of this, overcomes the weakness of this scheme, and further increases recognizing of image Card ability.2008, Chang and Hsieh used Chinese remainder theorem to strengthen the authentication capability of image, the puppet simultaneously obtained Dress image is higher than the quality of the camouflage test in front scheme.But, though these schemes are in authentication capability and camouflage test matter Improve in amount, but they still exist two problems: in (1) shadow vector, each element is by the most hidden Ensconce in each carrier image block, when element number is less than the number of carrier image block in the shadow vector that need to embed, carry Body image portion piecemeal does not just have the embedding of secret information, therefore, embeds the part of secret information and do not embed in camouflage test The statistical property of the part of secret information has difference clearly, and this difference can cause the attention of assailant, thus reduces The safety of secret information.(2) scheme before all uses LSB substitution method to hide secret information, and this method is held very much Easily detected the existence of embedding information by steganalysis such as RS analysis etc., and the length of embedding information can be judged exactly, this Also certain potential safety hazard is brought to scheme.

Summary of the invention

It is an object of the present invention to provide a kind of image concealing based on privacy share and authentication method, can be efficiently against existing The shortcoming that technology exists.

The present invention is achieved in that and it is characterized in that by privacy share and Information hiding and image authentication and secret letter Breath recovers two parts composition.

I. privacy share and Information hiding, comprise the following steps:

The first step, reads in Secret Image SE of a width h × g, and wherein, h represents the line number of Secret Image SE, and g represents secret The columns of image SE；

Second step, uses formula (1) that Secret Image SE is converted to difference image DIFF={diff_ij}；

${\mathrm{diff}}_{ij}=\left\{\begin{array}{cc}{\mathrm{se}}_{ij}& \begin{array}{cccc}if& i=0& and& j=0\end{array}\\ {\mathrm{se}}_{ij}-{\mathrm{se}}_{(i-1)j}& \begin{array}{cccc}if& i\≠0& and& j=0\end{array}\\ {\mathrm{se}}_{ij}-{\mathrm{se}}_{i(j-1)}& otherwise\end{array}\right.---\left(1\right)$

Wherein, i represents the i-th row, and j represents that jth arranges；

3rd step, does Huffman encoding to difference image DIFF, the bit sequence y after being encoded, and records coding code Table；

3 bits every in sequences y are divided into one group by the 4th step, and will often to organize bits switch be decimal number as sharing Coefficient, obtains coefficient vector d, and in note d, element number is M；

5th step, by privacy share multinomial, produces n shadow to be concealed vectorial:

(1). from vector d, order chooses k the element not having the to share shared coefficient as formula (2),

f_i(x)=(a₀+a₁x+a₂x²+…+a_k-₁x^k-1)mod2³, i=1,2 ..., l (2)

Wherein a₀,a₁,…,a_k-1Being k shared coefficient, l is the total number of element in each shadow vector, l=" M/k] (rounding up)；

(2). take x=1,2 ..., n, calculate f respectively_i(1),f_i(2),…,f_i(n), and it is respectively added to n in order Row vector S⁽¹⁾,S⁽²⁾,…,S⁽ⁿ⁾In (S⁽¹⁾,S⁽²⁾,…,S⁽ⁿ⁾Initial value is empty)；

S⁽¹⁾={ f_i(1)},S⁽²⁾={ f_i(2)},…,S⁽ⁿ⁾={ f_i(n) }, i=1,2 ..., l (3)

(3). repeat step (1)-(2), until all elements is processed complete in d, S⁽¹⁾,S⁽²⁾,…,S⁽ⁿ⁾Treat hidden for n The shadow vector hidden；

6th step, chooses n width landscape or character image as carrier image C^(j), j=1,2 ..., a n and key K；

7th step, uses formula (4) and (5) that key K is shared as n sub-key K₁,…,K_j,…,K_n:

Q (x)=K+a₁x+a₂x²+…+a_k-₁x^k-1 (4)

K₁=q (1), K₂=q (2) ..., K_n=q (n) (5)

Wherein a₁,…,a_k-1It is k-1 the integer randomly selected；

8th step, embeds carrier image according to matrix coder is theoretical by shadow vector to be concealed, and step is as follows:

(1). by carrier image C^(j)Be divided into non-overlapping copies 1 × 3 block of pixels, and each pixel value in block is used it 8bit binary representation, as shown in Figure 1；

(2). determine S by following steps^(j)In each element at carrier image C^(j)In be randomly-embedded position:

A) carrier image C is set^(j)In the sum of all pieces be L, then:

In t block of every continuous print, i.e. randomly choose a block as embedded block；

B) sub-key K is used_jProduce Random number sequence

C) formula (7) is utilized to determine S^(j)In i-th^(j)Individual element is at carrier image C^(j)In embedded location:

(3). by S^(j)In i-th^(j)Individual value is converted to binary bit sequence { s₁s₂s₃, then according to shown in Fig. 2, extract public affairs Hidden unit { the m of embedded location determined by formula (7)₁,m₂,m₃,m₄,m₅,m₆,m₇}；

(4). setBy the relation shown in table 1, can be by bit sequence by most amendment 1bit {s₁s₂s₃It is embedded into this hidden unit { m₁,m₂,m₃,m₄,m₅,m₆,m₇In }；

Table 1

(5). repeat step (2)-(4), until S^(j)In all elements be all hidden in carrier image block；

9th step, calculates the certification bit p of each piece in carrier image by formula (8)₁,p₂, and embed it in Fig. 2 In relevant position；

$p_1{p}_2=XOR<H_{K_j}\left({\mathrm{TH}}^{\left(j\right)}\right|\left|B_{ID}^{\left(j\right)}\right){>}_2---\left(8\right)$

In formula,It is with sub-key K_jHash function, TH^(j)Certification bit p is removed in each piece₁,p₂And it is hidden Hide unit { m₁,m₂,m₃,m₄,m₅,m₆,m₇Remaining 15bit sequence outside },Mark for block；

Tenth step, is converted to the binary representation (as shown in Figure 2) of each pixel in the carrier image after embedding information Decimal number, forms camouflage testAnd by n camouflage testAnd corresponding sub-key K_jMeet at n different participation Person's keeping；

II. image authentication and secret information recover, and at least k or k above participant are in the secret recovery process, Secret information just can be resumed.Comprise the following steps:

The first step, the camouflage test that the participants recovered that are in the secret provide them to be heldAnd it is sub accordingly Key K_j；

Second step, divides camouflage testFor the block of pixels of the 1 × 3 of non-overlapping copies, and each pixel value in block is used Its 8bit binary representation；

3rd step, it is achieved verification process:

(1). extract the certification bit p on corresponding certification position in camouflage test block₁,p₂；

(2). use formula (8) to calculate the certification bit of camouflage test blockAnd compare p₁WithAnd p₂WithWhether Equal, if equal, then camouflage test block is not tampered with, if unequal, then this camouflage test block is tampered, and camouflage test does not leads to Cross certification, it is impossible to for the recovery of secret information；

(3). repeat step (1) and (2) and all complete certification until in camouflage test all of piece；

4th step, the extraction (the step for of only could being participated in by the camouflage test of certification) of shadow vector:

(1). use sub-key K that participant provides_jProduce Random number sequence

(2). utilize formula (7) to determine in shadow vector i-th^(j)Individual element is at camouflage testIn embedded location, and carry Take the hidden unit { m ' of embedded block on this position₁,m′₂,m′₃,m′₄,m′₅,m′₆, m '₇}；

(3). use formula (9) to calculate the bit sequence { s of this element₁s₂s₃, and it is converted into decimal number, remember successively Record is at vectorIn；

$\left\{\begin{array}{c}{s}_1=m_1^{\&prime;}\&CirclePlus;m_3^{\&prime;}\&CirclePlus;m_5^{\&prime;}\&CirclePlus;m_7^{\&prime;}\\ s_2=m_2^{\&prime;}\&CirclePlus;m_3^{\&prime;}\&CirclePlus;m_6^{\&prime;}\&CirclePlus;m_7^{\&prime;}\\ s_3=m_4^{\&prime;}\&CirclePlus;m_5^{\&prime;}\&CirclePlus;m_6^{\&prime;}\&CirclePlus;m_7^{\&prime;}\end{array}\right.---\left(9\right)$

(4). repeat (2)-(3), until all of element is all extracted in shadow vector；

5th step, it is assumed that by the quantity of the camouflage test of certification more than or equal to k, respectively these camouflage test are entered The operation of above-mentioned 4th step of row, extracts the shadow vector embedded；

6th step, collects at least k shadow vector, by the shared coefficient of Lagrange interpolation polynomial recovery, and successively Being stored in vector d ', vector d ' have recorded the shared coefficient after recovery；

7th step, is converted to binary bit sequence by middle for vector d ' element, uses pre-recorded coding code table, completes Decoding sequence is also converted to matrix and represents by Hafman decoding, obtains difference image；

8th step, recovers former Secret Image by the inverse process of difference.

Advantages of the present invention and good effect thereof be:

(1) in shadow vector, each element is embedded in carrier image block by uniformly random, which ensure that carrier after embedding The statistical property of image does not have obvious difference, improves the safety of secret information；

(2) mode that present invention employs matrix coder embeds shadow vector in image block, overcomes in conventional scheme Employing LSB alternative method is prone to detected shortcoming, reduces the risk that the person of being hacked suspects.

(3) use matrix coder theoretical, hidden the quantity of information of 3 bits by the amendment amount of 1 bit, further increase The picture quality of camouflage test.

(4) present invention has a higher authentication capability, any all can not be passed through certification, more by the premeditated camouflage test distorted The recovery of the information that can not be in the secret, further ensures the safety of secret information.

Accompanying drawing explanation

The carrier image partitioned organization figure of Fig. 1 present invention, wherein X, V, W represent three pixels in block, { x respectively₁,x₂, x₃,x₄,x₅,x₆,x₇,x₈It is 8 binary representations of pixel X, { v₁,v₂,v₃,v₄,v₅,v₆,v₇,v₈It is that 8 two of pixel V enter Tabulation is shown, { w₁,w₂,w₃,w₄,w₅,w₆,w₇,w₈It is 8 binary representations of pixel W；

The hidden unit of Fig. 2 embedded block and the scattergram of certification bit, wherein,Represent in block the information that embeds respectively Three pixels, { m₁,m₂,m₃,m₄,m₅,m₆,m₇It is hidden unit, p₁,p₂For certification bit.

Detailed description of the invention

We select Matlab7.0 as software platform, the design of programming realization the present invention program.Implementation process is chosen The standard testing image " Jet " of 256 × 256 as Secret Image, the standard testing image " Lena " of 4 512 × 512, " Peppers ", " Baboon ", " Elaine " as carrier image, Selecting All Parameters k=3, n=4 in secret sharing.

It is a feature of the present invention that it is to be recovered two parts by privacy share and Information hiding with image authentication and secret information Composition.Concrete operation step is:

I. privacy share and Information hiding, comprise the following steps:

The first step, reads in the standard testing image " Jet " of 256 × 256 as Secret Image SE；

Second step, uses formula (1) that Secret Image SE is converted to difference image DIFF={diff_ij}；

${\mathrm{diff}}_{ij}=\left\{\begin{array}{cc}{\mathrm{se}}_{ij}& \begin{array}{cccc}if& i=0& and& j=0\end{array}\\ {\mathrm{se}}_{ij}-{\mathrm{se}}_{(i-1)j}& \begin{array}{cccc}if& i\&NotEqual;0& and& j=0\end{array}\\ {\mathrm{se}}_{ij}-{\mathrm{se}}_{i(j-1)}& otherwise\end{array}\right.---\left(1\right)$

3rd step, does Huffman encoding to difference image DIFF, the bit sequence y after being encoded, and records coding code Table；

3 bits every in sequences y are divided into one group by the 4th step, and will often to organize bits switch be decimal number as sharing Coefficient, obtains coefficient vector d, then draws element number M=116556 in d by experiment；

5th step, by privacy share multinomial, produces 4 shadows to be concealed vectorial:

(1). from vector d, order chooses 3 elements not having to share shared coefficient as formula (2),

f_i(x)=(a₀+a₁x+a₂x²)mod2³, i=1,2 ..., l (2)

Wherein a₀,a₁,a₂It is 3 shared coefficients, total number l=38852 of element in shadow vector；

(2). take x=1,2,3,4, calculate f respectively_i(1),f_i(2),f_i(3),f_i(4) 4, and in order it are respectively added to Individual row vector S⁽¹⁾,S⁽²⁾,S⁽³⁾,S⁽⁴⁾In (S⁽¹⁾,S⁽²⁾,S⁽³⁾,S⁽⁴⁾Initial value is empty)；

S⁽¹⁾={ f_i(1)},S⁽²⁾={ f_i(2)},S⁽³⁾={ f_i(3)},S⁽⁴⁾={ f_i(4) }, i=1,2 ..., l (3)

(3). repeat step (1)-(2), until all elements is processed complete in d, S⁽¹⁾,S⁽²⁾,S⁽³⁾,S⁽⁴⁾It is 4 and treats hidden The shadow vector hidden；

6th step, chooses 4 width carrier images " Lena ", " Peppers ", " Baboon ", " Elaine ", and a key K =214 (value of K can randomly select)；

7th step, uses formula (4) and (5) that key K is shared as 4 sub-key K₁,K₂,K₃,K₄:

Q (x)=214+7625x+5435x² (4)

K₁=q (1)=13274, K₂=q (2)=37204, K₃=q (3)=72004, K₄=q (4)=117674 (5)

Wherein, in formula (4), coefficient 7625 and 5435 is the integer randomly selected；

8th step, embeds carrier image by shadow vector to be concealed, with shadow vector S according to matrix coder is theoretical⁽¹⁾Embedding As a example by entering carrier image " Lena ", step is as follows:

. carrier image " Lena " is divided into non-overlapping copies 1 × 3 block of pixels, and by each pixel value in block With its 8bit binary representation, as shown in Figure 1；

(2). determine S by following steps⁽¹⁾In each element in carrier image " Lena ", be randomly-embedded position:

A) calculating the sum of all pieces in carrier image " Lena " is L=87040, then:

I.e. in 2 blocks of every continuous print, randomly choose a block as embedded block；

B) sub-key K is used₁=13274 generation Random number sequences 10790,13885,24583 ... }；

C) formula (7) is utilized to determine S⁽¹⁾In the 1st value (i.e. i⁽¹⁾=1) embedded location in carrier image " Lena " is Loc (1)=2, both second block was chosen as embedded block:

$\left\{\begin{array}{cc}Loc\left(i^{\left(j\right)}\right)-i^{\left(j\right)}\&times;t+r_i\mathrm{mod}t,& r_i\mathrm{mod}t=0\\ Loc\left(i^{\left(j\right)}\right)-(i^{\left(j\right)}-1)\&times;t+r_i\mathrm{mod}t,& r_i\mathrm{mod}t\&NotEqual;0\end{array}\right.---\left(7\right)$

(3). by S⁽¹⁾In the 1st value 2 be converted to binary bit sequence { s₁s₂s₃}={ 010}, and according to shown in Fig. 2, carry Take the hidden unit { m on second block of carrier image₁,m₂,m₃,m₄,m₅,m₆,m₇}={ 0001101}；

(4). calculateBy the relation shown in table 1, by the m in amendment hidden unit₄Will { 010} is embedded into hidden unit { m to bit sequence₁,m₂,m₃,m₄,m₅,m₆,m₇In }, after embedding, hidden unit is revised as { m '₁, m′₂,m′₃,m′₄,m′₅, m '₆,m′₇}={ 0000101}；

Table 1

(5). repeat step (2)-(4), until S⁽¹⁾In all elements be all hidden in carrier image " Lena "；

9th step, calculates the certification bit p of each piece in carrier image by formula (8)₁,p₂, and embed it in Fig. 2 In relevant position:

$p_1,p_2=XOR<H_{K_1}\left({\mathrm{TH}}^{\left(1\right)}\right|\left|B_{ID}^{\left(1\right)}\right){>}_2---\left(8\right)$

In formula,It is with sub-key K₁Hash function, TH⁽¹⁾Certification bit p is removed in each piece₁,p₂And it is hidden Hide unit { m₁,m₂,m₃,m₄,m₅,m₆,m₇Remaining 15bit sequence outside },Mark for block；

Tenth step, is converted to the binary representation (as shown in Figure 2) of each pixel in the carrier image after embedding information Decimal number, forms camouflage testAccording to same method by S⁽²⁾,S⁽³⁾,S⁽⁴⁾It is respectively embedded in carrier image In " Peppers ", " Baboon ", " Elaine ", and formed 4 camouflage test and corresponding sub-key are met at 4 Different participant's keepings.

II. image authentication and secret information recover, and at least the participant of 3 or more than 3 is in the secret recovery process, Secret information just can be resumed.Comprise the following steps:

The first step, the camouflage test that the participants recovered that are in the secret provide them to be heldAnd it is sub accordingly Key K_j；

Second step, divides camouflage testFor the block of pixels of the 1 × 3 of non-overlapping copies, and each pixel value in block is used Its 8bit binary representation；

3rd step, it is achieved verification process (as a example by the first width camouflage test " Lena "):

(1). extract the certification bit p on corresponding certification position in first block of pixels₁=1, p₂=1；

(2). use formula (8) to calculate the certification bit of this blockAndThis camouflage test block By certification；

(3). repeat step (1) and (2) until in camouflage test all of piece all by certification, then camouflage test is not usurped Change, otherwise camouflage test authentification failure, it is impossible to be in the secret Information recovering.

4th step, the extraction (the step for of only could being participated in by the camouflage test of certification) of shadow vector:

(1). use sub-key K that participant provides₁=13274 generation Random number sequences 10790,13885, 24583,…}；

(2). utilize formula (7) to determine shadow vector S⁽¹⁾In first element embedding position in camouflage test " Lena " Put, and extract embedded block on this position hidden unit { m '₁,m′₂,m′₃,m′₄,m′₅,m′₆,m′₇}={ 0000101}；

(3). use formula (9) to calculate the bit sequence s of this element₁=0, s₂=1, s₃=0, and it is converted into decimal scale Several 2, it is sequentially recorded in vectorIn:

$\left\{\begin{array}{c}{s}_1=0\&CirclePlus;0\&CirclePlus;1\&CirclePlus;1=0\\ s_2=0\&CirclePlus;0\&CirclePlus;0\&CirclePlus;1=1\\ s_3=0\&CirclePlus;1\&CirclePlus;0\&CirclePlus;1=0\end{array}\right.---\left(9\right)$

(4). repeat (2)-(3), until all of element is all extracted in shadow vector；

5th step, it is assumed that by the quantity of the camouflage test of certification more than or equal to 3, respectively these camouflage test are entered The above-mentioned FOUR EASY STEPS of row, extracts the shadow vector embedded；

6th step, collects at least 3 shadow vectors, by the shared coefficient of Lagrange interpolation polynomial recovery, and successively It is stored in vector d '；

7th step, is converted to binary bit sequence by middle for vector d ' element, uses pre-recorded coding code table, completes Decoding sequence is also converted to matrix and represents by Hafman decoding, obtains difference image；

8th step, recovers former Secret Image by the inverse process of difference；

In order to the present invention superiority compared with other schemes is described, we arrange lower to this at identical experiment condition and parameter Scheme of the invention and other schemes have done emulation experiment.Experimental result is as shown in table 2.

Table 2

Other the scheme from table 2 it can be seen that compare, our scheme is in hiding secret information and the mistake of certification bit Cheng Zhong, the average amendment amount to pixel each in carrier image is minimum, and this also implies that the solution of the present invention is in camouflage Image can obtain better image quality.Meanwhile, the PSNR value of the 4 width camouflage test be given in table 2 also demonstrates this point. In terms of authentication capability, the scheme of the scheme of Lin and Tsai and Yang et al. is more weak, and the scheme of Chang and Hsieh is relatively The authentication capability of the present invention program is slightly higher, but their scheme have employed the certification position of 4bit, reduces to a certain extent The visual quality of camouflage test, and the solution of the present invention is only with the certification position of 2bit, it is also possible to obtain well certification energy Power, makes again the visual quality of camouflage test be substantially improved simultaneously.

Claims (1)

1. an image concealing based on privacy share and authentication method, it is characterised in that be by privacy share and Information hiding with Image authentication and secret information recover two parts composition, and concrete operation step is as follows:

I. privacy share and Information hiding, comprise the following steps:

The first step, reads in Secret Image SE of a width h × g, and wherein, h represents the line number of Secret Image SE, and g represents Secret Image The columns of SE；

Second step, uses formula (1) that Secret Image SE is converted to difference image DIFF={diff_ij}；

${\mathrm{diff}}_{ij}=\left\{\begin{array}{cc}{\mathrm{se}}_{ij}& \begin{array}{cccc}if& i=0& and& j=0\end{array}\\ {\mathrm{se}}_{ij}-{\mathrm{se}}_{(i-1)j}& \begin{array}{cccc}if& i\&NotEqual;0& and& j=0\end{array}\\ {\mathrm{se}}_{ij}-{\mathrm{se}}_{i(j-1)}& otherwise\end{array}\right.---\left(1\right)$

Wherein, i represents the i-th row, and j represents that jth arranges；

3rd step, does Huffman encoding to difference image DIFF, the bit sequence y after being encoded, and records coding code table；

3 bits every in sequences y are divided into one group by the 4th step, and will often organize bits switch be decimal number as shared coefficient, Obtaining coefficient vector d, in note d, element number is M；

5th step, by privacy share multinomial, produces n shadow to be concealed vectorial:

(1). from vector d, order chooses k the element not having the to share shared coefficient as formula (2),

f_i(x)=(a₀+a₁x+a₂x²+…+a_k-1x^k-1)mod2³, i=1,2 ..., l (2)

Wherein a₀,a₁,…,a_k-1Being k shared coefficient, l is the total number of element in each shadow vector,

(2). take x=1,2 ..., n, calculate f respectively_i(1),f_i(2),…,f_i(n), and be respectively added in order n row to Amount S⁽¹⁾,S⁽²⁾,…,S⁽ⁿ⁾In, wherein S⁽¹⁾,S⁽²⁾,…,S⁽ⁿ⁾Initial value is empty；

S⁽¹⁾={ f_i(1)},S⁽²⁾={ f_i(2)},…,S⁽ⁿ⁾={ f_i(n) }, i=1,2 ..., l (3)

(3). repeat step (1)-(2), until all elements is processed complete in d, S⁽¹⁾,S⁽²⁾,…,S⁽ⁿ⁾To be concealed for n Shadow vector；

6th step, chooses n width landscape or character image as carrier image C^(j), j=1,2 ..., a n and key K；

7th step, uses formula (4) and (5) that key K is shared as n sub-key K₁,…,K_j,…,K_n:

Q (x)=K+a₁x+a₂x²+…+a_k-1x^k-1 (4)

K₁=q (1), K₂=q (2) ..., K_n=q (n) (5)

Wherein a₁,…,a_k-1It is k-1 the integer randomly selected；

8th step, embeds carrier image according to matrix coder is theoretical by shadow vector to be concealed, and step is as follows:

(1). by carrier image C^(j)Be divided into non-overlapping copies 1 × 3 block of pixels, and by its 8bit of each pixel value in block Binary representation；

(2). determine S by following steps^(j)In each element at carrier image C^(j)In be randomly-embedded position:

A) carrier image C is set^(j)In the sum of all pieces be L, then:

In t block of every continuous print, i.e. randomly choose a block as embedded block；

B) sub-key K is used_jProduce Random number sequence

C) formula (7) is utilized to determine S^(j)In i-th^(j)Individual element is at carrier image C^(j)In embedded location:

(3). by S^(j)In i-th^(j)Individual value is converted to binary bit sequence { s₁s₂s₃, and extract embedding determined by formula (7) Hidden unit { the m of position₁,m₂,m₃,m₄,m₅,m₆,m₇}；

(4). setBy the relation shown in table 1, can be by bit sequence by most amendment 1bit {s₁s₂s₃It is embedded into this hidden unit { m₁,m₂,m₃,m₄,m₅,m₆,m₇In }；

Table 1

(5). repeat step (2)-(4), until S^(j)In all elements be all hidden in carrier image block；

9th step, calculates the certification bit p of each piece in carrier image by formula (8)₁,p₂, and embed it in corresponding positions Put；

$p_1{p}_2=XOR<H_{K_j}\left({\mathrm{TH}}^{\left(j\right)}\left|\right|B_{ID}^{\left(j\right)}\right){>}_2---\left(8\right)$

In formula,It is with sub-key K_jHash function, TH^(j)Certification bit p is removed in each piece₁,p₂And hide single Unit { m₁,m₂,m₃,m₄,m₅,m₆,m₇Remaining 15bit sequence outside },Mark for block；

Tenth step, is converted to decimal number by the binary representation of each pixel in the carrier image after embedding information, forms puppet Dress imageAnd by n camouflage testAnd corresponding sub-key K_jMeet at n different participants keeping；

II. image authentication and secret information recover, and at least k or k above participant are in the secret recovery process, secret Information just can be resumed, and comprises the following steps:

The first step, the camouflage test that the participants recovered that are in the secret provide them to be heldAnd corresponding sub-key K_j；

Second step, divides camouflage testFor the block of pixels of the 1 × 3 of non-overlapping copies, and each pixel value in block is used it 8bit binary representation；

3rd step, it is achieved verification process:

(1). extract the certification bit p on corresponding certification position in camouflage test block₁,p₂；

(2). use formula (8) to calculate the certification bit of camouflage test blockAnd compare p₁WithAnd p₂WithIt is the most equal, If equal, then camouflage test block is not tampered with, if unequal, then this camouflage test block is tampered, and camouflage test is not by recognizing Card, it is impossible to for the recovery of secret information；

(3). repeat step (1) and (2) and all complete certification until in camouflage test all of piece；

4th step, the extraction of shadow vector, the step for of only could being participated in by the camouflage test of certification:

(1). use sub-key K that participant provides_jProduce Random number sequence

(2). utilize formula (7) to determine in shadow vector i-th^(j)Individual element is at camouflage testIn embedded location, and extract should Hidden unit { the m ' of embedded block on position₁,m′₂,m′₃,m′₄,m′₅,m′₆,m′₇}；

(3). use formula (9) to calculate the bit sequence { s of this element₁s₂s₃, and it is converted into decimal number, it is sequentially recorded in VectorIn；

$\left\{\begin{array}{c}{s}_1=m_1^{\&prime;}\&CirclePlus;m_3^{\&prime;}\&CirclePlus;m_5^{\&prime;}\&CirclePlus;m_7^{\&prime;}\\ s_2=m_2^{\&prime;}\&CirclePlus;m_3^{\&prime;}\&CirclePlus;m_6^{\&prime;}\&CirclePlus;m_7^{\&prime;}\\ s_3=m_4^{\&prime;}\&CirclePlus;m_5^{\&prime;}\&CirclePlus;m_6^{\&prime;}\&CirclePlus;m_7^{\&prime;}\end{array}\right.---\left(9\right)$

(4). repeat (2)-(3), until all of element is all extracted in shadow vector；

5th step, it is assumed that by the quantity of the camouflage test of certification more than or equal to k, respectively these camouflage test are carried out on State the operation of the 4th step, extract the shadow vector embedded；

6th step, collects at least k shadow vector, recovers to share coefficient by Lagrange interpolation polynomial, and be sequentially stored into In vector d ', vector d ' have recorded the shared coefficient after recovery；

7th step, is converted to binary bit sequence by middle for vector d ' element, uses pre-recorded coding code table, completes Hough Decoding sequence is also converted to matrix and represents by graceful decoding, obtains difference image；

8th step, recovers former Secret Image by the inverse process of difference.