AU2021104272A4 - An authenticable image sharing scheme based on QR code - Google Patents

Abstract

: In the field of secret image sharing, it is more and more common to use carrier image to transfer secret. In this study, an authenticable image sharing scheme based on the embedded small size shadow quick response (QR) code is proposed. In this scheme, a small shadow image is obtained by using the secret image sharing method based on Chinese remainder theorem, and the shadow image is embedded into the QR code with error correction. The proposed method not only ensures the security and integrity of the shadow image transmission in the public channel. Compared with the existing schemes, this scheme uses hash authentication flow to achieve the purpose of authentication. Experiments show that the recovered secret medical image is lossless, and cover QR code is more robust and secure, which is suitable for medical image content protection and security sharing. (a)Secret image (b)SCI (c)SC 2 (d)SC 3 (e)SC4 Figure 1. SC represents the pixel value of ith shadow image. (a)CoverQRcode (b)CoverQRcode2 (c)CoverQRcode3 (d)CoverQRcode4 (e)Stego-QRcodel (/)Stego-QRcode2 (g)Stego-QRcode3 (h)Stego-QRcode4 (i)Recovered image Figure 2. The experimental results from the certified shadow image extracted from stego QR code

Description

(a)Secret image

(b)SCI (c)SC 2 (d)SC 3 (e)SC4 Figure 1. SC represents the pixel value of ith shadow image.

(a)CoverQRcode (b)CoverQRcode2 (c)CoverQRcode3 (d)CoverQRcode4

(e)Stego-QRcodel (/)Stego-QRcode2 (g)Stego-QRcode3 (h)Stego-QRcode4

(i)Recovered image Figure 2. The experimental results from the certified shadow image extracted from stego QR code

1. Background and Purpose

Secret sharing technology is a good solution to the problem that a single secret carrier is easy to be destroyed and cannot be recovered. Since 1979, Shamir and Blakley have proposed the concept of secret sharing. Secret sharing technology is gradually developed, and its secret is also changed from text data to image data, which realizes the sharing of digital secret image. With the deepening of research, more and more scholars have proposed great secret image sharing scheme. For example, Yan et al. proposed an authenticated secret image sharing scheme suitable for both dealer participation and non-participation. By improving the secret image sharing algorithm based on polynomial, the secret image can be restored with higher quality. However, there is a defect in many schemes, that is, the shadow images generated by them are noise like. Because the shadow image is transmitted on the common channel, if it is a noise like image, it is easy to attract the attention of attackers. Once the shadow image is attacked, the original secret image cannot be completely recovered or even recovered. Moreover, this kind of noise like image is difficult to identify and manage for participants. Therefore, a meaningful secret image sharing scheme (MSISS), also called extended secret image sharing scheme, is proposed. Quick Response (QR) code is a two-dimensional, machine readable optical label composed of black and white modules. Because of its high capacity and fault tolerance, QR code is widely used in various fields, such as ID, food traceability, commodity management, advertising, mobile payment, etc. At the same time, QR code as a carrier can also be well applied in thefield of secret image sharing, and researchers from various universities have done relevant research in this field. Yan et al. proposed an extended secret image sharing method for lossless restoration based on Chinese Remainder Theorem and QR code. The secret image and several standard two-dimensional codes were used to generate the secret two-dimensional code, and the original secret image could be recovered losslessly after the secret two-dimensional code with specified threshold was collected. However, from the experimental results, the secret information of the code generated by this method may still be leaked. In the research of Huang et al., the secret two-dimensional code is divided and encoded into n carrier two-dimensional codes. The carrier two-dimensional code still carries the carrier information and is not easy to be suspected. Secret QR codes can be obtained by XOR operation of these marked cover QR codes. However, the threshold of the scheme is set to (n, n), that is to say, it is necessary to collect all the shares to recover the original secret image, and there is no authentication function. Based on the above analysis, in this study, we proposes an authenticated image sharing scheme based on QR code, which combines blockchain and secret sharing technology, and uses QR code as a meaningful carrier. Under the blockchain architecture, the proposed scheme can not only recover the secret image losslessly, but also get small shadow image, which improves the embedding capacity of QR code to a certain extent.

2. Framework of proposed authenticable image sharing scheme

The proposed scheme can be divided into three phases: Secret Sharing phase, secret embedding phase and authentication recovery phase. In the sharing stage, firstly, the secret medical image is used to obtain n small shadow images by CRT-SSIS. In the embedding stage, the shadow image and the corresponding participant ID are used to generate the authentication bit stream by the hash function, and the shadow image and the authentication bit stream are embedded into the cover QR code to obtain the stego-QR code. In the authentication and recovery stage, the shadow image and the authentication bit stream are extracted from the stego-QR code, and then a new authentication bit stream is generated from the shadow image, By comparing two authentication streams, authentication can be realized. When no less than k stego-QR codes are authenticated, the shadow image is used to recover the secret image. 2.1 Sharing Phase In this scheme, an improved small-size secret image sharing method based on Chinese remainder theorem(CRT-SSIS) is adopted, and a little improvement is made on the basis of the traditional secret image sharing method based on Chinese remainder theorem, so that the shadow image generated is 1/[k- (1+t)/8] of the original secret image. Suppose a secret image is SI and its size is WxH. The specific process is as follows: Step 1: Set the initial parameter (k, n) threshold, prime set {p,m,m2, ... -,m}. p is set to 128 or 131, and prime set satisfies the following conditions: J 128 p<m,<m 2 .-. <M,256.

gcd(m,mi)=1,iwj. gcd(m,p)= 1fori=1,2,--,n. M > pN. Step 2: Calculate M, N and T according to the equations (1)- (3). M= mi (1) N= klmni+ (2) T =[(LM / p-1 - FN/ p)/2+FN/ p]| (3) Here, p, N and T are open to all participants. mI,m2 ,...,m, are private to SCI, SC2,...,SC of each shadow image. Only the participants who own a shadow image know the corresponding prime value. Step 3: Binarize the secret image s to get a data stream B, and divide B into 8k-1-t blocks, where t e [1,7]. Step 4: For each block, the first 8 bits are converted to a decimal number x, and the remaining 8(k-1)-1-t bits are randomly added with t bits and then converted to a decimal number A*. For further calculation, if 0 <x<p,A=A*+(T+1),y= x+Ap , otherwise, A=A*+|Np, y=x-p+Ap. Step 5: For each block, calculate a = y(mod mi), let SC, = a1(i = 1,2,-,k) . For the same block, SCj represents the pixel value of ith shadow image. Through above steps 1-5, the secret image SI will generate n shadow images, of which any k can be reconstructed losslessly. 2.2 Embedding Phase In order to prevent the attacker from using the false shadow image to cheat the secret image, this scheme uses the hash function to generate the authentication bits, and in order to prevent the attacker from using the shadow image of other participants to cheat the verification process, this scheme takes the ID of each participant and its shadow image together as the input of the hash function. Let the authentication bitstream be Auj, and the expression is shown in the equation (4). Au,=Hk(SC,|1) (4) A QR code is divided into two regions, data area and error correction area. Authentication bitstream is embedded in QR code data filling area, that is, data area except public information part in data area. The shadow image is embedded in the error correction area of QR code. In fact, there are several RS blocks in a QR code, and the embedded data information is in each RS block. Suppose that there are a total of R codewords in each RS block, and the data area has D codewords. In the process of embedding shadow image and authentication bit stream into cover QR code, the embedding of authentication bitstream is accomplished by using it to do different or operation with the original data area of cover QR code. However, shadow image is different. It needs to find the embedding position first. Suppose that there are le code words in error correction area in an RS block, le is calculated by the equation (5). The index of QR code embedded in shadow image is I, and the index Iis 1 to le. ,=R - D (5) i shadow r (6) Assuming that the QR code used has r RS blocks, the shadow image is divided into r RS blocks, Ir is the number of pixels containing shadow images in each block, Ir is shown in the equation (6), where shadow is the number of pixels in the shadow. This scheme is to generate index I by using a random number Ra, where Ra, = {aj | 1 <a.<1li = 1,2,..., }(1 jn) , Raj is distributed to each of the participating agencies.

2.3 Authentication and Reconstruction Phase After secret image sharing and embedding, the QR code with shadow image and authentication bit stream is obtained. For each stego-QR code, the shadow image and authentication bit stream are extracted respectively, and then another authentication bit stream Au' is generated by using the shadow image and the ID of the corresponding participant according to the equation (7). SC is the extracted shadow from stego-QR code. The authentication process is to compare Au and Au, if the match is successful, the authentication is passed; Otherwise, authentication is failed. Au'= HK (7) When there are no less than k shadow images that pass the authentication, the secret image can be recovered. The recovery process of secret image is as follows. Step 1: Collected k shadows SC', SC',...,SC' with size of Fx G , corresponding prime number mi, m2,..., iand the common parameters p, t, N, t.

Step 2: For a pixel (f, g)E {(f,g)|1!f F,1 g G} , let a, = SC,(f, g) for j= 1,2,...,k . Because y is unique, the original secret image can be obtained by solving the linear congruence equation system by the equation (8). y a1 (mod m,) (j=1,2,...,k) (8) Repeat step 2 until all the pixels of the shadows are solved. Step3:Calculate T*=Ly/pj.If T*>T ,then x =y(modp),A*=(y-x)/p-(T+1). Otherwise, x=y(modp)+p , A*=(y-x)/p-FN/p] . Then, binarize x and A, and connect 8 bits ofx and 8 (k-1)-1-tbits of a in order to form abit stream B' (B' isempty initially). Step4:Convert B' into a string of decimal numbers every 8 bits, construct and output the recovered secret image SI'. After the above secret image restoration process, the shadow image with successful authentication can get the lossless secret medical image.

1. Framework of proposed authenticable image sharing scheme

The proposed scheme can be divided into three phases: Secret Sharing phase, secret embedding phase and authentication recovery phase. In the sharing stage, firstly, the secret medical image is used to obtain n small shadow images by CRT-SSIS. In the embedding stage, the shadow image and the corresponding participant ID are used to generate the authentication bit stream by the hash function, and the shadow image and the authentication bit stream are embedded into the cover QR code to obtain the stego-QR code. In the authentication and recovery stage, the shadow image and the authentication bit stream are extracted from the stego-QR code, and then a new authentication bit stream is generated from the shadow image, By comparing two authentication streams, authentication can be realized. When no less than k stego-QR codes are authenticated, the shadow image is used to recover the secret image. 1.1 Sharing Phase In this scheme, an improved small-size secret image sharing method based on Chinese remainder theorem(CRT-SSIS) is adopted, and a little improvement is made on the basis of the traditional secret image sharing method based on Chinese remainder theorem, so that the shadow image generated is 1/[k- (1+t)/8] of the original secret image. Suppose a secret image is SI and its size is WxH. The specific process is as follows: Step 1: Set the initial parameter (k, n) threshold, prime set {p,m,m2 ... ,m,}. p is set to 128 or 131, and prime set satisfies the following conditions: J 128 p<m,<m 2 .-. <M,256. 2 gcd(mj,mi)=1,iwj. gcd(m,,p)=1fori=1,2,--,n. M > pN. Step 2: Calculate M, N and T according to the equations (1)- (3). M= mi (1) N= mk_1 (2) T=[(LM/p-1]-FN/p)/2+FN/p] (3) Here, p, N and T are open to all participants. mI,m2 ,...,m are private to SCI, SC 2,...,SC, of each shadow image. Only the participants who own a shadow image know the corresponding prime value.

Step 3: Binarize the secret image s to get a data stream B, and divide B into 8k-1-t blocks, where t e [1,7]. Step 4: For each block, the first 8 bits are converted to a decimal number x, and the remaining 8(k-1)-1-t bits are randomly added with t bits and then converted to a decimal number A*. For further calculation, if 0 <x<p,A=A*+(T+1),y= x+Ap , otherwise, A=A*+|Np, y=x-p+Ap. Step 5: For each block, calculate a = y(mod mi), let SC, = a1 (i = 1,2,-,k) . For the same block, SCj represents the pixel value of ith shadow image. Through above steps 1-5, the secret image SI will generate n shadow images, of which any k can be reconstructed losslessly. 1.2 Embedding Phase In order to prevent the attacker from using the false shadow image to cheat the secret image, this scheme uses the hash function to generate the authentication bits, and in order to prevent the attacker from using the shadow image of other participants to cheat the verification process, this scheme takes the ID of each participant and its shadow image together as the input of the hash function. Let the authentication bitstream be Auj, and the expression is shown in the equation (4). Au,=Hk(SC,|| ) (4) A QR code is divided into two regions, data area and error correction area. Authentication bitstream is embedded in QR code data filling area, that is, data area except public information part in data area. The shadow image is embedded in the error correction area of QR code. In fact, there are several RS blocks in a QR code, and the embedded data information is in each RS block. Suppose that there are a total of R codewords in each RS block, and the data area has D codewords. In the process of embedding shadow image and authentication bit stream into cover QR code, the embedding of authentication bitstream is accomplished by using it to do different or operation with the original data area of cover QR code. However, shadow image is different. It needs to find the embedding position first. Suppose that there are le code words in error correction area in an RS block, le is calculated by the equation (5). The index of QR code embedded in shadow image is I, and the index Iis 1 to le. l, = R - D (5)

S=shadow / r (6) Assuming that the QR code used has r RS blocks, the shadow image is divided into r RS blocks, Ir is the number of pixels containing shadow images in each block, Ir is shown in the equation (6), where shadow is the number of pixels in the shadow. This scheme is to generate index I by using a random number Ra, where Ra, = {aj | 1 <a<1li = 1,2,..., l,(1 jn) , Raj is distributed to each of the participating agencies.

1.3 Authentication and Reconstruction Phase After secret image sharing and embedding, the QR code with shadow image and authentication bit stream is obtained. For each stego-QR code, the shadow image and authentication bit stream are extracted respectively, and then another authentication bit stream Au' is generated by using the shadow image and the ID of the corresponding participant according to the equation (7). SC' is the extracted shadow from stego-QR code. The authentication process is to compare Au and Au, if the match is successful, the authentication is passed; Otherwise, authentication is failed. Au'= HK (7) When there are no less than k shadow images that pass the authentication, the secret image can be recovered. The recovery process of secret image is as follows. Step 1: Collected k shadows SCI, SC',...,SC' with size of Fx G , corresponding prime number mi, m2,..., iand the common parameters p, t, N, t. Step 2: For a pixel (f, g)E {(f,g)|1!f F,1 g G} , let a, = SC,(f, g) for j= 1,2,...,k . Because y is unique, the original secret image can be obtained by solving the linear congruence equation system by the equation (8). y = a' .(mod m,) (j= 1,2,..., k) (8) Repeat step 2 until all the pixels of the shadows are solved. Step3:Calculate T*=Ly/p.If T*>T ,then x =y(modp),A*=(y-x)/p-(T+1). Otherwise, x=y(modp)+p , A*=(y-x)/p-FN/p] . Then, binarize x and A, and connect 8 bits ofx and 8 (k-1)-1-tbits of a in order to form abit stream B' (B' isempty initially). Step4:Convert B' into a string of decimal numbers every 8 bits, construct and output the recovered secret image SI'.

After the above secret image restoration process, the shadow image with successful authentication can get the lossless secret medical image.

(a)Secret image 2021104272

(b)SC1 (c)SC2 (d)SC3 (e)SC4 Figure 1. SCi represents the pixel value of ith shadow image.

(a)CoverQRcode (b)CoverQRcode2 (c)CoverQRcode3 (d)CoverQRcode4

(e)Stego-QRcode1 (f)Stego-QRcode2 (g)Stego-QRcode3 (h)Stego-QRcode4

(i)Recovered image Figure 2. The experimental results from the certified shadow image extracted from stego QR code