CN109558701B - Medical CT image secret sharing method - Google Patents
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Abstract
The invention discloses a medical CT image secret sharing method which comprises an encryption stage and a decryption stage, wherein in the encryption stage, a CT image subgraph and a decimal matrix with the definition corresponding to the authority level of a receiver are obtained through sparse singular value decomposition, then a key of two-dimensional Logistic mapping is obtained through the decimal matrix, two chaotic sequences are generated through the mapping, the pixel position of the CT image subgraph is scrambled to obtain a snowflake graph, then the snowflake graph is divided into five function value matrixes through a polynomial, and finally elements in the function value matrixes are embedded into the lower two positions of a camouflage graph selected by a user to obtain five shadow graphs. By the scheme, the invention achieves the aim of completely recovering the secret CT image subgraph only by simultaneously participating in decryption by the receiver obtaining the five shadow images and the receiver storing the secret key, and has very high practical value and popularization value.
Description
Technical Field
The invention belongs to the field of medical information security, and particularly relates to a medical CT image secret sharing method.
Background
With the rapid development of telemedicine technology, more and more patients benefit from it. Telemedicine is an important component of telemedicine, and the widespread use of telemedicine is accompanied by the storage and transmission of large numbers of CT images over the internet. Due to the high acquisition cost and high scientific research value of the CT images, the CT images of some important figures with great influence in the fields of politics, military affairs and economy also have important confidentiality value. The theft and tampering of the CT image during transmission can cause huge losses. Therefore, the CT image is encrypted before being transmitted, so that the CT image has extremely high practical value. The current CT image encryption scheme cannot effectively protect CT images from being stolen and tampered in practical application due to the ubiquitous defect of weak ability to resist plaintext or selective plaintext attack. Meanwhile, the current CT image encryption scheme cannot transmit CT image subgraphs with different definitions according to the authority level of a receiver, and the transmitted encrypted image is often a snowflake image similar to image noise, so that the interest of a thief is easily aroused, and the practical value of the CT image encryption scheme is further reduced.
Disclosure of Invention
The invention aims to provide a medical CT image secret sharing method, which mainly solves the problem that in the prior art, a CT image encryption scheme cannot effectively protect CT images from being stolen and tampered in practical application due to the defect of poor plaintext or selective plaintext attack resistance generally existing in the prior art.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a secret sharing method for medical CT images comprises the following steps:
1) In the encryption stage, firstly, a CT image subgraph and a decimal matrix with the definition corresponding to the authority level of a receiver are obtained through sparse singular value decomposition, then a key of two-dimensional Logistic mapping is obtained through the decimal matrix, two chaotic sequences are generated through the mapping, scrambling operation is carried out on the pixel position of the CT image subgraph to obtain a snowflake graph, then the snowflake graph is divided into five function value matrixes through a polynomial, and finally elements in the five function value matrixes are embedded into the lower two bits of the five camouflage graphs selected by a user to obtain the corresponding five shadow graphs;
2) In the decryption stage, a user recombines five function value matrixes by collecting five different shadow maps and extracting the lower two bits of the shadow maps, then obtains the snowflake map by a table look-up method, finally obtains two chaotic sequences used for scrambling by a secret key, and restores the scrambled pixel positions in the snowflake map by the two chaotic sequences to obtain the secret CT subgraph.
Further, the sparse singular value decomposition in the step 1 obtains a CT image subgraph with the definition corresponding to the authority level of the receiver and a decimal matrix, and the acquisition of the CT subgraph with the definition matched with the authority level of the receiver is completed by rounding elements downwards.
Further, one decimal matrix in step 1 is a decimal matrix B with a size of M × N obtained by means of key acquisition of two-dimensional Logistic mapping k Dividing into four equal blocks to obtain four blocks with equal size
A small matrix of (a).
Further, the four small matrixes are respectively B 1,k 、B 2,k 、B 3,k 、B 4,k And respectively use mu 1 、μ 2 、γ 1 、γ 2 Represents the mean value thereof, wherein B k (1, 1) as x 0 ，B k (m, n) as y 0 。
Further, the polynomial in the step 1 is
Specifically, in step 1, the binary sequence of the pixel point at the position corresponding to the polynomial is recombined in the following specific manner: a is a 0 ＝s 8 s 7 、a 1 ＝s 6 s 5 、a 2 ＝s 4 s 3 、a 3 ＝s 2 s 1 。
Compared with the prior art, the invention has the following beneficial effects:
the invention can determine the definition grade of the CT image to be encrypted to be transmitted according to the authority grade of a receiver, meanwhile, the CT images with different definitions have different corresponding keys when being encrypted, the use of the keys is realized by one figure and one secret, the information of the secret image is divided by the polynomial of the invention, and the secret image can be completely restored only by making up five divided parts. Meanwhile, the shadow map is basically consistent with the original common camouflage map seen by naked eyes, and the suspicion that an eavesdropper suspects that the image contains the secret information can be reduced to the maximum extent even if the shadow map is stolen in the transmission process.
Drawings
FIG. 1 is a flow chart of an encryption scheme of the present invention.
FIG. 2 is a flowchart of the decryption structure according to the present invention.
FIG. 3 shows (a) the original CT image of the present invention, (b) the CT sub-image with k taken at 300 times, and (c) the snowflake image obtained by scrambling the CT sub-images.
Fig. 4 shows five different camouflage images a-e according to the invention.
Fig. 5 is five shadow images corresponding to fig. 4.
FIG. 6 is a CT sub-graph obtained by decryption according to the present invention.
Detailed Description
The present invention is further illustrated by the following figures and examples, which include, but are not limited to, the following examples.
Examples
As shown in fig. 1 to 6, a method for secret sharing of medical CT images includes the following steps:
in the encryption stage, a CT image subgraph and a decimal matrix with the definition corresponding to the authority level of a receiver are obtained through sparse singular value decomposition, then a key of two-dimensional Logistic mapping is obtained through the decimal matrix, two chaotic sequences are generated through the mapping, scrambling operation is carried out on the pixel position of the CT image subgraph to obtain a snowflake graph, then the snowflake graph is divided into five function value matrixes through a polynomial, and finally elements in the function value matrixes are embedded into the lower two bits of the camouflage graph selected by a user to obtain five shadow graphs; in a decryption stage, a user recombines five function value matrixes by collecting five different shadow maps and extracting low two bits of the shadow maps, then obtains a snowflake map by a table look-up method, finally obtains two chaotic sequences used for scrambling by a secret key, and restores the scrambled pixel positions in the snowflake map by the two chaotic sequences to obtain a secret CT sub-map.
(1) And (3) making CT sub-images with different definitions:
inputting the CT image (M multiplied by N) into an encryption module to carry out Sparse Single Value Decomposition (SSVD) to obtain an outer product expansion formula of a CT image matrix A
Front k sub-formula (k)<N) is formed
Will matrix A k Each element of the array is subjected to a down rounding operation to obtain a new integer matrix A' k And a decimal matrix B k ＝A k -A‘ k . The larger the value of k is, the closer the obtained image is to the original image, the original image is obtained when k = n, CT image subgraphs with different definitions can be obtained by the method, meanwhile, according to the authority level of the receiver, the sender can select the CT image subgraphs with different definitions to make a camouflage image and send the camouflage image to the receiver, for example, when n =300, the outer product expansion of the CT image matrix A is
Form by taking the first 300 pieces
Will matrix A 300 Performing a rounding down operation on each element to obtain a new integer matrix A' 300 And a decimal matrix B 300 ＝A 300 -A‘ 300 ；
(2) Scrambling of CT subgraphs:
a decimal matrix B with the size of 340 multiplied by 338 300 Divided into four equal-sized blocks to obtain four blocks with equal sizes
Respectively let it be B 1,300 、B 2,300 、B 3,300 、B 4,300 . Finding B 1,300 、B 2,300 、B 3,300 、B 4,300 And are respectively made equal to mu 1 、μ 2 、γ 1 、γ 2 . Get B at the same time 300 (1, 1) as x 0 Taking out B 300 (340, 338) as y 0 . At a setting of mu 1 、μ 2 、γ 1 、γ 2 、x 0 And y 0 After the six initial parameters, calling two-dimensional pairwise Logistic mapping shown in formula (1) to generate two chaotic sequences x m ∈{1,2,…,340}，m＝1,2,…,340,y n E {1,2, \ 8230;, 338}, n =1,2, \8230; 338, according to the formula (m, n) = A' 300 (x m ,y n ) (m =1,2, \ 8230;, 340,n =1,2, \ 8230;, 338) to accomplish the pair A' 300 Scrambling the pixel positions to obtain a snowflake image after scrambling;
(3) Cutting of snowflake pattern:
each pixel value of the snowflake map is converted into a binary sequence by decimal. For example, the pixel value of the mth row and nth column is (m, n) = s 8 s 7 s 6 s 5 s 4 s 3 s 2 s 1 Each pixel value corresponding to a polynomial
The coefficients of the polynomial are respectively a 0 ＝s 8 s 7 、a 1 ＝s 6 s 5 、a 2 ＝s 4 s 3 、a 3 ＝s 2 s 1 . All polynomials form a 340X 338 polynomial matrix, which is then respectively substituted into the set value x 1 ＝1、x 2 ＝2、x 3 ＝3、x 4 ＝4、x 5 =5 to the polynomial matrix, to obtain five function value matrices F, respectively i (i =1,2,3,4,5), f (x) is given by four coefficients, four of which take on values 1 )、f(x 2 )、f(x 3 )、f(x 4 )、f(x 5 ) There are 4^4=256 combinations. Since mod16 operation is performed, F 1 、F 2 、F 3 、F 4 、F 5 All elements of (2) have values of [0,15 ]]While due to F 1 The middle elements are each OR-ed by four two-bit binary numbers, thus F 1 The value range of the medium element is [0,3 ]]。
(4)F i (i =1,2,3,4,5) and the lower two-bit substitution of the camouflage pattern:
the next step is to randomly pick 5 worthless grayscale images C as shown in FIG. 4 (a-e) 1 、C 2 、C 3 、C 4 、C 5 As a dummy image, the 5 function value matrixes F i (i =1,2,3,4,5) the lowest 2 bits are replaced, and a shadow map S is generated respectively 1 、S 2 、S 3 、S 4 、S 5 . Due to F 2 、F 3 、F 4 、F 5 The value of the element(s) of (1) is converted from decimal to binary with a maximum of 4 bits, requiring two pixel points to accommodate, thus F 2 、F 3 、F 4 、F 5 Corresponding camouflage figure C 2 、C 3 、C 4 、C 5 It needs to be twice as large as the original CT image. If the size of the original CT image is 340 × 338, the camouflage image C 2 、C 3 、C 4 、C 5 It is required to be 340 × 676. And C 1 It is only necessary to maintain the same size as the original CT image.
To C 1 The specific flow of the lowest two-bit replacement is as follows:
inputting: camouflage figure C as shown in figure 4 1 Matrix of function values F 1 ；
And (3) outputting: shadow map S 1 。
Step 4, repeating the step 3 till C 1 All pixel values in the group are replaced.
Suppose i is equal to {2,3,4,5}, m is equal to {1,2, \8230, 340}, n is equal to {1,2, \8230, 388}, and for C i The specific flow of the lowest two-bit replacement is as follows:
inputting: camouflage C as shown in FIG. 4 i Matrix of function values F i ；
And (3) outputting: shadow map S i 。
Step 4, adding C i The lowest two bits of (m, 2 xn) are replaced by F i,2 The lowest two bits of (m, n) are obtained to obtain S i (m,2×n)＝c 8 c 7 c 6 c 5 c 4 c 3 f 2 f 1 ；
Step 5, repeating the step 3 and the step 4 until C i All the pixel values in (a) complete the replacement.
The five shadowgraphs obtained after completion are identical in appearance to the camouflage graph, which greatly reduces the likelihood of interest to the thief.
The detailed operation flow of the decryption module is as follows:
the recovery of the secret CT image subgraph requires the participation of a plurality of receivers with different authorities, and the decryption of the participation of the receivers with different authority levels and numbers can obtain different results, generally speaking, there are several situations as follows:
case 1: if only n (n < 5) receivers storing different shadow images participate in decryption, any information about the secret CT image subgraph cannot be obtained;
case 2: if 5 receivers storing different shadow maps participate in decryption, the snowflake map of the scrambled map can be recovered;
and 3, if 5 receivers storing different shadow maps and receivers storing the secret key participate in decryption at the same time, the secret CT image subgraph can be completely recovered.
Where the decryption steps in cases 1,2 are only part of the decryption step of case 3. The decryption step of case 3 is specifically set forth below.
Inputting: 5 different shadow maps, key mu 1 、μ 2 、γ 1 、γ 2 、x 0 And y 0 ；
And (3) outputting: and (5) CT image subgraph.
Step 1-confirmation S of the size of the image 1 And converting the elements therein into a binary sequence, e.g. the m-th row and n-th column having S elements 1 (m,n)＝s 8 s 7 s 6 s 5 s 4 s 3 s 2 s 1 Then extracting the lowest two bits of all elements to form a matrix F 1 Of corresponding positions, e.g. F 1 (m,n)＝000000s 2 s 1 ；
step 4, bringing the secret key into two-dimensional Logistic mapping to obtain a scrambled chaotic sequence x m ∈{1,2,…,340},m＝1,2,…,340,y n E {1,2, \8230;, 338}, n =1,2, … 338), the pixels in the snowflake map are transferred to the correct positions through the two chaotic sequences, resulting in the secret CT image subgraph shown in fig. 6.
The above-described embodiments are only preferred embodiments of the present invention, and are not intended to limit the scope of the present invention, but all changes that can be made by applying the principles of the present invention and performing non-inventive work on the basis of the principles shall fall within the scope of the present invention.
Claims (1)
1. A secret sharing method for medical CT images is characterized by comprising the following steps:
1) In the encryption stage, a CT image subgraph and a decimal matrix, the definition of which corresponds to the authority level of a receiving party, are obtained through sparse singular value decomposition; then, a key of two-dimensional Logistic mapping is obtained through the decimal matrix, two chaotic sequences are generated by using the mapping, scrambling operation is carried out on the pixel position of the CT image sub-image to obtain a snowflake pattern, then the snowflake pattern is divided into five function value matrixes through a polynomial, and finally elements in the five function value matrixes are embedded into the lower two bits of the five camouflage patterns selected by a user to obtain the corresponding five shadow patterns;
2) In a decryption stage, a user recombines five function value matrixes by collecting five different shadow maps and extracting the lower two bits of the shadow maps, then obtains a snowflake map by a table look-up method, finally obtains two chaotic sequences used for scrambling by a secret key, and restores the scrambled pixel positions in the snowflake map by the two chaotic sequences to obtain a secret CT sub-map;
the method for acquiring the CT image subgraph comprises the following steps:
s11, inputting the CT image into an encryption module for sparse singular value decomposition to obtain an outer product expansion of a CT image matrix A;
s12, forming a matrix A by the first k sub-expressions of the outer product expansion k The value of k is determined according to the authority level of the receiver;
s13, combining the matrix A k Performing down-rounding operation on each element to obtain a CT image subgraph A' k ；
The formula for calculating the decimal matrix is:
B k ＝A k -A‘ k ；
the method for acquiring the two chaotic sequences comprises the following steps:
s21, forming a decimal matrix B k Divided into four equal-sized blocks, respectively denoted as B 1k 、B 2k 、B 3k 、B 4k ；
S22, respectively obtaining B 1k 、B 2k 、B 3k 、B 4k Respectively, are recorded as μ 1 、μ 2 、γ 1 、γ 2 ；
S23, recording decimal momentArray B k Is p × q, B is taken k (1, 1) is denoted by x 0 Taking out B k (p, q) is denoted by y 0 ；
S24, according to the secret key mu 1 、μ 2 、γ 1 、γ 2 、x 0 、y 0 Using two-dimensional pairwise Logistic mapping formula
Two chaotic sequences are generated and are respectively marked as x m And y n ；
The snowflake pattern acquisition method comprises the following steps:
according to the formula
(m,n)＝A‘ 300 (x m ,y n )，(m＝1,2,…,340,n＝1,2,…,338)
Finish sub-image A 'of CT image' k Scrambling the pixel positions to obtain a snowflake image after scrambling;
the method for acquiring the five shadow maps comprises the following steps:
converting each pixel value of the snowflake into a binary sequence from a decimal system, wherein each pixel value corresponds to a polynomial
The coefficients of the polynomial are respectively a 0 ＝s 8 s 7 、a 1 ＝s 6 s 5 、a 2 ＝s 4 s 3 、a 3 ＝s 2 s 1 The pixel values of a decimal representation are split into binary representations s i ,1≤i≤8，s i An ith bit, representing the low to high binary pixel value, having a value of 0 or 1,
all polynomials form a polynomial matrix of p × q, which is then respectively substituted into the set value x 1 ＝1、x 2 ＝2、x 3 ＝3、x 4 ＝4、x 5 =5 toThe polynomial matrix obtains five function value matrixes F i (i＝1,2,3,4,5)，
Randomly selecting 5 worthless gray level images C 1 、C 2 、C 3 、C 4 、C 5 As a dummy image, with a matrix of five function values F i (i =1,2,3,4,5) to carry out replacement of the lowest 2 bits, and obtain corresponding five shadow maps S 1 、S 2 、S 3 、S 4 And S 5 ；
The decryption stage specifically comprises the following steps:
s31, confirming a shadow map S according to the size of the image 1 Converting the elements into binary sequences, and extracting the lowest two bits of all the elements to form a matrix F 1 The element of the corresponding position of (a);
s32, respectively naming the remaining four shadow images as S a 、S b 、S c 、S d A, b, c, d ∈ {2,3,4,5}, and all elements of the four shadow images are converted into a binary sequence, and then according to a formula
Generation of F a 、F b 、F c 、F d ，a,b,c,d∈{2,3,4,5}；
S33, from F 1 (1,1)、F i (1, 1), i = a, b, c, d starts, to F 1 (p,q)、F i (p, q), i = a, b, c, d, sequentially finding the values of the four coefficients corresponding to the F (m, n) through a table look-up method, recombining the values into pixels at corresponding positions in the scrambled snowflake image, and finally obtaining the scrambled snowflake image;
s34, the key mu is processed 1 、μ 2 、γ 1 、γ 2 、x 0 、y 0 Substituting two-dimensional pairwise Logistic mapping formula
And obtaining two scrambled chaotic sequences, and transferring the pixels in the snowflake graph obtained in the step S33 to correct positions through the two chaotic sequences to obtain the secret CT subgraph.
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