CN112838922B - DICOM image asymmetric encryption method based on chaotic mapping and selective Signcryption - Google Patents
DICOM image asymmetric encryption method based on chaotic mapping and selective Signcryption Download PDFInfo
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- H04L63/0442—Network architectures or network communication protocols for network security for providing a confidential data exchange among entities communicating through data packet networks wherein the data content is protected, e.g. by encrypting or encapsulating the payload wherein the sending and receiving network entities apply asymmetric encryption, i.e. different keys for encryption and decryption
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- H04L63/0478—Network architectures or network communication protocols for network security for providing a confidential data exchange among entities communicating through data packet networks wherein the data content is protected, e.g. by encrypting or encapsulating the payload applying multiple layers of encryption, e.g. nested tunnels or encrypting the content with a first key and then with at least a second key
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- H04L9/06—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols the encryption apparatus using shift registers or memories for block-wise or stream coding, e.g. DES systems or RC4; Hash functions; Pseudorandom sequence generators
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- H04L9/3239—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials using cryptographic hash functions involving non-keyed hash functions, e.g. modification detection codes [MDCs], MD5, SHA or RIPEMD
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- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
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- H—ELECTRICITY
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- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
- H04L9/3247—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures
- H04L9/3252—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures using DSA or related signature schemes, e.g. elliptic based signatures, ElGamal or Schnorr schemes
Abstract
The invention provides a DICOM image asymmetric encryption method based on chaotic mapping and selective Signcryption, which comprises the following steps: inputting an image sequence and performing multi-level wavelet transformation processing to obtain a wavelet coefficient; the generalized two-peak chaotic system and the three-dimensional interweaving chaotic system generate an encryption sequence, a point selection sequence and a scrambling sequence; carrying out chaotic encryption on the wavelet coefficient according to the encryption sequence; selecting partial chaotically encrypted wavelet coefficients according to the point selection sequence for ECC encryption, simultaneously carrying out ECC signature on MD5hash of the original coefficient sequence, combining the two steps for Signcryption, and forming ECC signature; and carrying out bit level scrambling on the ECC signed image according to the scrambling sequence to generate an encrypted image. The DICOM image is subjected to chaos and ECC dual encryption processing, so that the security of image encryption is improved; meanwhile, the image is subjected to multi-level wavelet transformation to select a part of data to be subjected to asymmetric encryption, so that the encryption efficiency is effectively improved, and the influence of partial encryption is ensured to be expanded to the whole image through bit-level chaotic scrambling.
Description
Technical Field
The invention relates to the technical field of medical image encryption processing, in particular to a DICOM image asymmetric encryption method and system based on chaotic mapping and selective Signcryption.
Background
Medical imaging is a science that studies the interaction with human body by means of a certain medium (such as X-ray, electromagnetic field, ultrasonic wave, etc.), the internal tissue organ structure and density of human body are expressed in an image mode, and diagnosis doctors can judge according to the information provided by the image, so as to evaluate the health condition of human body, and the medical imaging system and the medical image processing are relatively independent study directions. Common formats for medical images are DICOM, mosaic, analysis, NIFTI, and so on.
The Kanso team proposed in 2015 that a comprehensive and specific chaos-based image encryption combination is suitable for medical image encryption applications. The proposed model consists of several steps, where one step consists of two stages, a shuffle stage, and a cover stage. The two phases are based on block and utilize chaotic cat mapping to rearrange and overlay the information image. The simulation result shows the superiority of the scheme, and the security of the scheme on the cryptoanalysis attack is proved, so that the rationality of the scheme for continuous secure image communication is confirmed.
MoreshMukhedkar et al, 2015, suggested that Blowfish algorithm be used to complete image encryption, and since the algorithm has the characteristics of high speed, strong execution force, high speed, basic, controllable bits, and the like, the algorithm is suitable for the Least Significant Bit (LSB) algorithm for image hiding. In order to improve the security, a hybrid method combining image encryption with image encryption and image hiding is proposed.
In protecting important data, the random number is a critical part of the quality of the cryptographic primitive, which is represented by the encryption key. The processing and transmission of digital medical images presents some security issues, and it is therefore important to maintain the integrity and confidentiality of the images. The verification of medical images is mainly intended to ensure the integrity and security of medical data stored in the information system.
The medical image is different from a common image, the pixel of the medical image is usually 12 bits and contains a negative value, most of the encryption of the current medical image is to scramble and replace the original medical image respectively to generate an encrypted image, or to encrypt the image once by using a double encryption method and then continue to perform signature encryption processing on subsequent images. However, the image encryption method has low encryption efficiency, and the security after encryption is not strong enough, so that the image encryption method is easy to crack.
The chinese patent publication No. CN104468489a discloses a file security mechanism of a cloud video platform in 2015, 3, 25, which effectively keeps the image file, greatly improves the security of the image file, prevents anyone except the user from obtaining the image file, and effectively prevents the image file from leaking out of the cloud video platform. However, this method is also not applicable to encryption of medical images.
Disclosure of Invention
The invention provides a DICOM image asymmetric encryption method and system based on chaotic mapping and selective Signcryption, aiming at overcoming the technical defects that the existing image encryption technology is low in encryption efficiency and safety and is not suitable for medical images.
In order to solve the technical problems, the technical scheme of the invention is as follows:
the DICOM image asymmetric encryption method based on chaotic mapping and selective Signcryption comprises the following steps:
s1: inputting a sequence of images and generating a key;
s2: performing multilevel wavelet transform processing on the image sequence, moving the coefficient sequence to a non-negative domain as a whole, and acquiring a non-negative wavelet coefficient;
s3: generating an initial value and intermittent parameters of the chaotic system by using a secret key, and constructing and initializing a generalized two-peak chaotic system and a three-dimensional interweaving chaotic system;
s4: generating an encryption sequence and a point selection sequence by utilizing a generalized two-peak chaotic system, and generating a scrambling sequence by utilizing a three-dimensional interweaving chaotic system;
s5: carrying out chaotic encryption on the wavelet coefficients according to the encryption sequence until image pixels are controlled to be 0-4095;
s6: determining ECC parameters, selecting partial chaotically encrypted wavelet coefficients according to the point selection sequence to perform ECC encryption, simultaneously performing ECC signature on MD5hash of the original coefficient sequence, and performing two-step combination to perform Signcryption to form an ECC signature;
s7: and carrying out bit-level scrambling on the ECC signed image according to the scrambling sequence to generate an encrypted image.
In the scheme, the security of image encryption is improved by performing chaos and ECC dual encryption processing on the DICOM image; the image is digitally signed by applying a Signcryption technology, so that the safety and the integrity of the encrypted image are ensured; meanwhile, the image is subjected to multi-level wavelet transformation to select a part of data to be subjected to asymmetric encryption, so that the encryption efficiency is effectively improved, and the influence of partial encryption is ensured to be expanded to the whole image through bit-level chaotic scrambling.
Wherein, the step S1 specifically comprises: inputting an original plaintext image, performing an SHA256 hash function on the original image to generate 256-bit IKey, and simultaneously using an external 256-bit string as EKey; the key consists of 512 bits of IKey and EKey.
Wherein, the step S2 specifically comprises: and performing 3-layer wavelet transformation on the image sequence by adopting a lossless LeGall53 integer wavelet, moving the whole image sequence to a non-negative domain, and acquiring wavelet coefficients.
In step S3, the process of generating the initial value and the intermittent parameter of the chaotic system specifically includes:
s301: the EKey is partitioned into 8 groups of 32-bit blocks, namely:
EKey＝{Ek 0 ，Ek 1 ，…，Ek 7 }，Ek i ＝{Ek i，0 ，Ek i，1 ，…，Ek i，31 }
similarly, IKey is partitioned into 8 groups of 32-bit blocks, namely:
IKey＝{Ik 0 ，Ik 1 ，…，Ik 7 }，Ik i ＝{Ik i，0 ，Ik i，1 ，…，Ik i，31 }
s302: compute summation terms se and si:
wherein Ek i，j Represents the value of the j bit of the ith block in the EKey; ik i，j The same process is carried out;
s303: calculating initial values and intermittent parameters:
1) Initial value u of generalized two-peak chaotic system 0 ：
2) Initial value x of three-dimensional interweaving chaotic system 0 、y 0 、z 0 And parameters λ, k 1 、k 2 、k 3 ：
3) Chaotic encryption parameter α:
wherein, in the step S3, the generalized bimodal chaotic systemf GDH The specific expression of (u, r, c) is as follows:
u n+1 ＝r(u n -c) 2 (c 2 -(u n -c) 2 )＝f GDH (u，r，c)
determining generalized bimodal function parameters r, c and initial value u 0 (ii) a According to the property of the generalized bimodal function, when the generalized parameter c obtains different values, the value range of the parameter r which can make x chaotic is different; at the same time, the initial value u 0 Substituting the initial value into a generalized bimodal function for iteration, initializing the generalized bimodal chaotic system, eliminating the influence of the initial value, and recording the new initial value as u 0 (ii) a Will u 0 Substituting the parameters r and c into f GDH In (u, r, c), a chaotic sequence { u, is obtained n }；
The three-dimensional interweaving chaotic system has the specific expression as follows:
wherein, λ is more than 0 and less than 3.999, | k 1 |＞33.5，|k 2 |＞37.9，|k 3 L > 35.7; calculating the initial value x 0 、y 0 、z 0 Substituting into the three-dimensional interweaving chaotic system function group for iteration, initializing the three-dimensional interweaving chaotic system, and recording the new initial value as x 0 、y 0 、z 0 (ii) a Initial vector (x) 0 ，y 0 ，z 0 ) And a parameter vector (λ, k) 1 、k 2 、k 3 ) Substituting into the three-dimensional interweaving chaotic system function group to generate a chaotic sequence { x n }、 {y n }、{z n }。
In step S4, the process of generating the encrypted sequence k specifically includes: setting the input image specification size as M multiplied by N; setting an initial value of an encryption sequence according to the chaotic encryption parameter alpha as follows:
k[0]＝[f GDH (α，r，c)*10 14 ]mod 4096
let the initial value of the sequence n be the initial value u of the generalized two-peak chaotic system 0 After initializationThe values of (c) are expressed in particular as:
n[0]＝GDH_init(u 0 )
wherein, GDH _ init represents an initialized generalized two-peak chaotic system; and then, calculating, specifically:
for i＝1，2，...，size-1：
i.n[i]＝f GDH (n[i-1]，r，c)
k[i]＝[(k[i-1]+n[i]×10 10 mo d 4096)mo d 4096]
wherein, the obtained sequence k is an encryption sequence.
In step S4, the scrambling sequence generation process specifically includes:
obtaining dimension transformation size a multiplied by b multiplied by c';
after the three-dimensional interweaving chaotic system is initialized and iterated for t = max (a, b, c') times, a vector group V = { V } containing t three-dimensional random number vectors is obtained 0 ，V 1 ，ΛV t-1 }，V i ＝{V i，0 ，V i，1 ，V i，2 }；
Order:
L＝{V 0，0 ，V 1，0 ，…，V a-1，0 }
W＝{V 0，1 ，V 1，1 ，…，V b-1，1 }
H＝{V 0，2 ，V 1，2 ，…，V c′-1，2 }
respectively carrying out rapid sequencing on L, W, H to obtain L ', W ' and H '; obtaining three scrambling position one-dimensional vectors X, Y, Z according to the position changes of the elements L ', L, W ', W, H ' and H, specifically:
for i＝0，1，2，...，a-1：
X[i]＝get_p osition(L[i]，L′)
wherein get _ position (x, B) represents the position of element x in sequence B; obtaining Y [ j ] and Z [ k ] in the same way to obtain a one-dimensional vector X, Y, Z;
and finally, generating a three-dimensional scrambling sequence according to X, Y, Z, wherein a specific expression is as follows:
for i＝0，1，2，...，a-1：
for j＝0，1，2，...，b-1：
for k＝0，1，2，...，c′-1：
P[i][j][k]＝(X[i]，Y[j]，Z[k])
wherein P is a scrambling sequence.
In step S4, the dimension transformation size specifically includes:
acquiring the original dimension size as M multiplied by N multiplied by D, wherein M multiplied by N is the length and the width of an image respectively, and D is the number of image pixel bits; setting M to be more than or equal to N to be more than or equal to D;
scaling M × N such that M 'and N' are close to each other, specifically:
for i＝1，2，3...：
N′＝N×i
wherein M' is updated to be a pair
Getting the whole; calculating a parameter i ' to minimize | M ' -N ' |, and recording M ' and N ' at the moment;
then, scaling M 'XN' and D to make
And D is close to, specifically:
forj＝1，2，3...：
D′＝D×j 2
calculating a parameter j' such that
At a minimum, record M ", N", and D' at this time;
if the dimension is set to M "× N" × D ', s = M × N × D-M "× N" × D ' bits overflow, and the shortest side c = min (M ", N", D '), where a and b are the other two sides, c needs to be extended and the length needs to be extended in order to reduce the overflow as much as possible
Let c '= c + k, the dimension transform size is finally determined to be a × b × c'.
Wherein, in step S4, if the encryption sequence generated according to the size M × N of the input image is k, then step S5 specifically includes:
s51: converting the image sequence after wavelet transform into a pixel stream L of (M multiplied by N, 1), namely, primarily encrypting the wavelet coefficients by using an encryption sequence k, wherein the encryption formula is as follows:
s52: checking the value range of the image pixel, if the pixel value is larger than 12 bits, recording the position of the pixel for the points larger than 12 bits and generating a new encryption sequence according to the number of abnormal points, wherein each value of the new encryption sequence has the same bit number as the corresponding abnormal point and the highest bit is 1; the encryption processing of step S51 is carried out on the abnormal points and the new encryption sequence, the step is circulated until all the points are between 0 and 4095, and a pixel stream L' is output;
s53: and carrying out second encryption on the pixel stream L', wherein the encryption formula is as follows:
wherein, when i =0,
s is any of 0 to 4095A random number; finally, obtaining a sequence C;
s54: and converting the sequence C obtained in the step S53 into (M multiplied by N) to complete the chaotic encryption process.
In step S7, 12 bits of the sequence after ECC signcryption are performed, each element in the sequence is bit-converted to form a bitstream L, and the length and width of the image are M and N, so that the length of the bitstream is mxnx12;
truncating the bitstream L according to the dimension transformation size a × b × c', which is specifically represented as:
L 1 ＝[L 0 ，L 1 ，…，L a×b×c′-1 ]；
L 2 ＝[L a×b×c′ ，L a×b×c′+1 ，…，L M×N×12 ]；
and will L 1 Converting into three-dimensional matrix Cube of (a × b × c'), and calculating bit stream L 2 Length R = M × N × 12-a × b × c';
the Cube is specifically represented according to the scrambling sequence P and the scrambling sequence as follows:
for i＝0，1，2，...，a-1：
for j＝0，1，2，...，b-1：
for k＝0，1，2，...，c′-1：
s＝P[i][j][k]
Cube′[i][j][k]＝Cube(s[0]，s[1]，s[2])
restoring the scrambling result Cube' to the bitstream L 1 ', calculating
Mixing L with 2 Element (ii) and L 1 Replacing one random element in every h elements to obtain a bit stream L 2 '; after completion, L is obtained 1 ′、L 2 ' splicing the two to form a final bit stream, converting the bit stream back to (M × N, 12), recovering the elements of the bit stream to 12-bit pixels, forming a pixel stream, and then converting the pixel stream back to (M × N) size, so that the bit level scrambling is completed, and an encrypted image is generated.
Compared with the prior art, the technical scheme of the invention has the beneficial effects that:
the invention provides a DICOM image asymmetric encryption method based on chaotic mapping and selective Signcryption, which improves the security of image encryption by performing chaotic and ECC dual encryption processing on a DICOM image; the image is digitally signed by applying a Signcryption technology, so that the safety and the integrity of the encrypted image are ensured; meanwhile, the image is subjected to multi-level wavelet transformation to select a part of data to be subjected to asymmetric encryption, so that the encryption efficiency is effectively improved, and the influence of partial encryption is ensured to be expanded to the whole image through bit-level chaotic scrambling.
Drawings
FIG. 1 is a schematic flow diagram of the process of the present invention;
FIG. 2 is a diagram illustrating an embodiment of generating a point selection sequence;
FIG. 3 is a flow diagram of decryption in one embodiment;
FIG. 4 is a diagram illustrating an exemplary process of elliptic curve encryption and decryption;
FIG. 5 is a diagram illustrating an implementation of an elliptic curve signcryption process in an embodiment.
Detailed Description
The drawings are for illustrative purposes only and are not to be construed as limiting the patent;
for the purpose of better illustrating the present embodiments, certain elements of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product;
it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
The technical solution of the present invention is further described below with reference to the accompanying drawings and examples.
Example 1
As shown in fig. 1, the DICOM image asymmetric encryption method based on chaotic mapping and selective Signcryption includes the following steps:
s1: inputting a sequence of images and generating a key;
s2: performing multilevel wavelet transform processing on the image sequence, moving the coefficient sequence to a non-negative domain as a whole, and acquiring a non-negative wavelet coefficient;
s3: generating an initial value and intermittent parameters of the chaotic system by using a secret key, and constructing and initializing a generalized bimodal chaotic system and a three-dimensional interweaving chaotic system;
s4: an encryption sequence and a point selection sequence are generated by utilizing a generalized two-peak chaotic system, a scrambling sequence is generated by utilizing a three-dimensional interweaving chaotic system, and the two chaotic systems are mixed to improve the encryption safety;
s5: carrying out chaotic encryption on wavelet coefficients according to an encryption sequence, and adopting independent record processing on high bits exceeding 12 bits of an abnormal point due to the fact that the wavelet transform and the integral moving possibly cause the situation that the pixel value exceeds 12 bits, generating a strategy that a new encryption sequence has the same number of bits as the abnormal point, the highest bit is 1, and then carrying out encryption, and circulating the inspection step until the pixel range is controlled to be 0-4095;
s6: determining ECC parameters, selecting partial chaotically encrypted wavelet coefficients according to the point selection sequence to perform ECC encryption, simultaneously performing ECC signature on MD5hash of the original coefficient sequence, and combining the two steps to perform Signcryption to form an ECC signature;
s7: and carrying out bit level scrambling on the ECC signed image according to the scrambling sequence, scrambling the encryption result, further improving the security, and finally generating the encrypted image.
In the specific implementation process, the DICOM image is subjected to chaos and ECC dual encryption processing, so that the security of image encryption is improved; the image is digitally signed by applying a Signcryption technology, so that the safety and the integrity of the encrypted image are ensured; meanwhile, the image is subjected to multi-level wavelet transform, partial data is selected to be subjected to asymmetric encryption, the encryption efficiency is effectively improved, and the influence of partial encryption is guaranteed to be expanded to the whole image through bit-level chaotic scrambling.
More specifically, the step S1 specifically includes: inputting an original plaintext image, performing an SHA256 hash function on the original image to generate 256-bit IKey, and simultaneously using an external 256-bit string as EKey; the key consists of 512 bits of IKey and EKey.
In the specific implementation process, the method finally executes Signcryption on the IKey and the EKey in the specific implementation process, and comprehensively encrypts the images to form an integral Signcryption scheme.
More specifically, the step S2 specifically includes: and performing 3-layer wavelet transformation on the image sequence by adopting a lossless LeGall53 integer wavelet, moving the whole image sequence to a non-negative domain, and acquiring wavelet coefficients.
In the specific implementation process, the lossless LeGall53 integer wavelet is adopted to process the image sequence, so that the accuracy of the image can be ensured. Since the wavelet transform produces negative values, adding the absolute value of the minimum of all points to all points moves the sequence as a whole to the non-negative domain.
More specifically, in the step S3, the process of generating the initial value and the intermittent parameter of the chaotic system specifically includes:
s301: the EKey is partitioned into 8 groups of 32-bit blocks, namely:
EKey＝{Ek 0 ，Ek 1 ，…，Ek 7 }，Ek i ＝{Ek i，0 ，Ek i，1 ，…，Ek i，31 }
similarly, IKey is partitioned into 8 groups of 32-bit blocks, namely:
IKey＝{Ik 0 ，Ik 1 ，…，Ik 7 }，Ik i ＝{Ik i，0 ，Ik i，1 ，…，Ik i，31 }
s302: compute summation terms se and si:
wherein Ek i，j Represents the value of the j bit of the ith block in the EKey; ik i，j The same process is carried out;
s303: calculating initial values and intermittent parameters:
1) Initial value u of generalized two-peak chaotic system (GDH map) 0 ：
2) Initial value x of three-dimensional interweaving chaotic system 0 、y 0 、z 0 And parameters λ, k 1 、k 2 、k 3 ：
3) Chaotic encryption parameter α:
4) ECC encryption parameter a, initial random number seed:
more specifically, in the step S3, the generalized two-peak chaotic system f GDH The specific expression of (u, r, c) is as follows:
u n+1 ＝r(u n -c) 2 (c 2 -(u n -c) 2 )＝f GDH (u，r，c)
determining generalized bimodal function parameters r, c and initial value u 0 (ii) a According to the property of the generalized bimodal function, when the generalization parameter c has different values, different value ranges of the parameter r capable of making x chaotic exist, and during testing, c =1 and r =8 are adopted. U is calculated according to the secret key 0 (ii) a At the same time, the initial value u 0 Substituting the generalized dual-peak function for iteration for 100 times, initializing the generalized dual-peak chaotic system, eliminating the influence of the initial value, and recording the new initial value as u 0 (ii) a Will u 0 Substituting parameters r and c into f GDH (u, r, c) to obtain a chaotic sequence { u n }；
The specific expression of the three-dimensional interweaving chaotic system (3D map) is as follows:
wherein, 0<λ<3.999，|k 1 |>33.5，|k 2 |>37.9，|k 3 |>35.7; calculating the initial value x 0 、y 0 、z 0 The three-dimensional interweaving chaotic system is substituted into the three-dimensional interweaving chaotic system function group for iteration for 100 times, the three-dimensional interweaving chaotic system is initialized, and a new initial value is still recorded as x 0 、y 0 、z 0 (ii) a Initial vector (x) 0 ，y 0 ，z 0 ) And a parameter vector (λ, k) 1 、k 2 、k 3 ) Substituting into the three-dimensional interweaving chaotic system function group to generate a chaotic sequence { x n }、{y n }、{z n }。
More specifically, in step S4, the process of generating the encryption sequence k specifically includes: setting the input image specification size as M multiplied by N; setting an initial value of an encryption sequence according to the chaotic encryption parameter alpha as follows:
k[0]＝[f GDH (α，r，c)*10 14 ]mod4096
let the initial value of the sequence n be the initial value u of the generalized two-peak chaotic system 0 The initialized value is specifically expressed as:
n[0]＝GDH_init(u 0 )
wherein, GDH _ init represents an initialized generalized two-peak chaotic system; and then, calculating, specifically:
for i＝1，2，...，size-1：
i.n[i]＝f GDH (n[i-1]，r，c)
k[i]＝[(k[i-1]+n[i]×i0 10 mod4096)mod4096]
wherein, the obtained sequence k is an encryption sequence.
More specifically, in step S4, the scrambling sequence generation process specifically includes:
obtaining dimension transformation size a multiplied by b multiplied by c';
after the three-dimensional interweaving chaotic system is initialized and iterated for t = max (a, b, c') times, a vector group V = { V } containing t three-dimensional random number vectors is obtained 0 ，V 1 ，ΛV t-1 }，V i ＝{V i，0 ，V i，1 ，V i，2 }；
Order:
L＝{V 0，0 ，V 1，0 ，…，V a-1，0 }
W＝{V 0，1 ，V 1，1 ，…，V b-1，1 }
H＝{V 0，2 ，V 1，2 ，…，V c′-1，2 }
respectively carrying out rapid sequencing on L, W, H to obtain L ', W ' and H '; obtaining three scrambling position one-dimensional vectors X, Y, Z according to the position changes of the elements L ', L, W ', W, H ' and H, specifically:
for i＝0，1，2，...，a-1：
X[i]＝get_position(L[i]，L′)
wherein get _ position (x, B) represents the position of element x in sequence B; obtaining Y [ j ] and Z [ k ] in the same way to obtain a one-dimensional vector X, Y, Z;
and finally, generating a three-dimensional scrambling sequence according to X, Y, Z, wherein the specific expression is as follows:
for i＝0，1，2，...，a-1：
for j＝0，1，2，...，b-1：
for k＝0，1，2，...，c′-1：
P[i][j][k]＝(X[i]，Y[j]，Z[k])
wherein, P is a scrambling sequence.
More specifically, in step S4, since bit-level scrambling is three-dimensional scrambling, in order to efficiently obtain a set of non-repetitive scrambling positions, we adopt fast sorting to obtain the scrambling positions, and since the average time complexity of fast sorting is O (nlogn), in order to ensure efficiency, it is necessary to change the dimensions so that the dimensions are as close as possible. The dimension transformation size specifically comprises:
acquiring the original dimension size as M multiplied by N multiplied by D, wherein M multiplied by N is the length and the width of the image respectively, and D is the pixel digit of the image; setting M to be more than or equal to N to be more than or equal to D;
scaling M × N such that M 'and N' are close to each other, specifically:
for i＝1，2，3...：
N′＝N×i
wherein M' is updated to be a pair
Getting the whole; calculating a parameter i ', minimizing | M ' -N ' |, and recording M ' and N ' at the moment;
then, scaling M 'x N' and D to make
And D is close to, specifically:
for j＝1，2，3...：
D′＝D×j 2
calculating a parameter j' such that
At a minimum, record M ", N", and D' at this time;
if the dimension is set to M "× N" × D ', bits of s = M × N × D-M "× N" × D ' overflow, the shortest side c = min (M ", N", D ') is set, and a and b are the other two sides
Let c '= c + k, the dimension transform size is finally determined to be a × b × c'.
More specifically, if the encryption sequence generated according to the input image size M × N in step S4 is k, then step S5 specifically includes:
s51: the wavelet-transformed image sequence reshape is a pixel stream L of (M × N, 1), that is, the wavelet coefficients are primarily encrypted by using an encryption sequence k, where the encryption formula is:
s52: checking the value range of the image pixel, if the pixel value is larger than 12 bits, recording the position of the pixel for the points larger than 12 bits and generating a new encryption sequence according to the number of the abnormal points, wherein each value of the new encryption sequence has the same number of bits as the corresponding abnormal point and the highest bit is 1; if the pixel value is found to be larger than 12 bits, recording the position of the pixel again and generating a new encryption sequence, wherein each value of the new encryption sequence has the same bit number as the corresponding abnormal point and the highest bit is 1, encrypting the points and the new encryption sequence, checking the value range of the points, and circulating the steps until all the points are between 0 and 4095, and outputting a pixel stream L';
s53: and carrying out second encryption on the pixel stream L', wherein the encryption formula is as follows:
wherein, when i =0, the control unit controls the control unit,
s is any random number between 0 and 4095, and s = [ (alpha x 0.43+ 3.57) × x is adopted during test 0 ×(1-x 0 )×10 14 ]mod4096, finally obtaining a sequence C;
s54: and converting the sequence C obtained in the step S53 into (M multiplied by N) to complete the chaotic encryption process.
More specifically, in step S7, 12 bits of the sequence after ECC signcryption are performed, for example, if a certain pixel of the original sequence is 4095, the 12 bits of the result is [1,1,1,1,1,1,1,1,1,1,1, 1]. Each element in the sequence is bit-converted to form a bit stream L, and the length of the bit stream is M multiplied by N multiplied by 12 if the length and the width of an image are M and N;
truncating the bitstream L according to the dimension transformation size a × b × c', which is specifically represented as:
L 1 ＝[L 0 ，L 1 ，…，L a×b×c′-1 ]；
L 2 ＝[L a×b×c′ ，L a×b×c′+1 ，…，L M×N×12 ]；
and mixing L 1 Converting into three-dimensional matrix Cube of (a × b × c'), and calculating bit stream L 2 Length R = M × N × 12-a × b × c';
the Cube is specifically represented according to the scrambling sequence P and the scrambling sequence as follows:
for i＝0，1，2，...，a-1：
for j＝0，1，2，...，b-1：
for k＝0，1，2，...，c′-1：
s＝P[i][j][k]
Cube′[i][j][k]＝Cube(s[0]，s[1]，s[2])
restoring the scrambling result Cube' to the bitstream L 1 ', calculating
Will L 2 Of (5) with L 1 Replacing one random element in every h elements (random position is generated by generalized double-peak chaotic system) to obtain bit stream L 2 ', to achieve the effect of disturbing the scrambling result, further improving the security. After completion, L is obtained 1 '、 L 2 ' the two are spliced together to form a final bit stream, the bit stream reshape is returned to (M × N, 12), the elements thereof are restored to 12-bit pixels, the pixel stream is formed, and then the reshape is returned to (M × N) size, so that the bit level scrambling is completed, and the encrypted image is generated.
In the specific implementation process, the invention improves the security of image encryption by performing chaos and ECC dual encryption processing on the DICOM image; the image is digitally signed by applying a Signcryption technology, so that the safety and the integrity of the encrypted image are ensured; meanwhile, the image is subjected to multi-level wavelet transform, partial data is selected to be subjected to asymmetric encryption, the encryption efficiency is effectively improved, and the influence of partial encryption is guaranteed to be expanded to the whole image through bit-level chaotic scrambling.
Example 2
Further, in order to meet the use requirement of the current medicine, the invention further provides a DICOM image asymmetric encryption system based on chaotic mapping and selective Signcryption on the basis of embodiment 1. The data encryption is carried out for multiple times aiming at the special medical image type, the safety and the integrity of the encrypted image are improved, meanwhile, the optimization processing is carried out on the aspect of time efficiency, the time cost is reduced, and the powerful application is provided for the follow-up patients/doctors to use the encrypted or decrypted medical image. The system can use the DICOM image asymmetric encryption method based on chaotic mapping and selective Signcryption, which specifically comprises the following steps:
1. input of original image and generation of key: initially a sequence of images is input. Meanwhile, SHA256 Hash is performed by using the original image sequence to generate 256-bit IKey, and an external 256-bit string is used as EKey. The master key consists of IKey and EKey, and is used to generate initial values and intermittent parameters for use in subsequent processes.
2. Multilevel wavelet transform processing: since the accuracy of medical images is required to avoid data loss, the conventional floating point wavelet cannot be used, and therefore, the image is subjected to 3-layer wavelet transform by using the lossless LeGall53 integer wavelet. Since the wavelet transform produces negative values, adding the absolute value of the minimum of all points to all points moves the sequence as a whole into the non-negative domain.
3. Generating an initial value and a control parameter of the chaotic system: two chaotic systems are mixed to encrypt images. Firstly, a key is used for generating an initial value and intermittent parameters of the chaotic system, then the generalized two-peak chaotic system is used for generating an encryption sequence and a point selection sequence, and then the three-dimensional interweaving chaotic system is used for generating a scrambling sequence. The multiple chaotic systems are used for generating different sequences, so that the safety of the whole encryption process is greatly improved, and brute force can be effectively prevented from being cracked.
4. Chaotic encryption processing: and (3) performing chaotic encryption by using the chaotic sequence and the wavelet coefficient after the step (2), wherein the situation that a very small number of pixel values exceed 12 bits can be caused after wavelet transformation and integral moving, so that a strategy that a new encryption sequence has the same number of bits as the abnormal point and the highest bit is 1 and then encryption is performed is generated by independently recording and processing the high bits of the abnormal point exceeding 12 bits, and the detection step is circulated until the pixel range is controlled to be 0-4095.
And 5, ECC signcryption processing: and (3) selecting partial wavelet coefficients by using the point selection sequence generated in the step (3) to carry out ECC encryption, simultaneously carrying out ECC signature on MD5Hash of the coefficient sequence, and simultaneously carrying out two steps to finish the ECC encryption step. The reason why ECC is chosen here for asymmetric encryption is: (1) the ECC encryption algorithm has better security and can better prevent cracking compared with other current asymmetric encryption algorithms. (2) ECC encryption algorithms can use shorter keys to provide better security than other asymmetric encryption methods.
6. Bit-level scrambling: finally, the sequence after the signcryption processing in the step 5 is according to the step 3;
7. and finally, the sequence after the signcryption processing in the step 5 is according to the step 3.
In the specific implementation process, 12-bit DICOM medical images are taken as research objects, the requirements of the medical images on safety, integrity and privacy during transmission are met, the composite chaotic mapping and ECC-based Signcryption-based multiple medical image encryption algorithm is improved in encryption effect and cracking difficulty compared with the existing common symmetric encryption, compared with the existing mainstream asymmetric encryption, the encryption algorithm is broken through in the aspects of encryption speed and algorithm efficiency, and meanwhile, the integrity of medical image information is guaranteed by carrying out digital signature on the images.
Example 3
More specifically, on the basis of embodiment 1, in step S4, the process of generating the setpoint sequence specifically includes:
after three-layer wavelet transform, the coefficients form a tree structure as shown in fig. 2.
1. As shown in fig. 2, a layer 3 wavelet LL 3 All selecting partial pixel points;
2. layer 3 wavelet HL 3 、LH 3 、HH 3 In part according to layer 3 wavelet LL 3 Partial coordinate selection, as can be seen from FIG. 2, a layer 3 LL 3 Coefficient corresponding to layer 3 HL 3 、LH 3 、HH 3 The coefficients are each 1; 1. the 2 two-step result is a layer 2 wavelet LL 2 The coefficients are all selected;
3. for layer 3 wavelet HL 3 、LH 3 、HH 3 Each coefficient in a subband corresponds to the secondRandomly selecting one of 4 child coefficients in the wavelet sub-bands of the 2 layers, wherein the random position is generated by a generalized double-peak chaotic system;
4. for layer 3 wavelet HL 3 、LH 3 、HH 3 Each coefficient in the sub-band corresponds to 16 child coefficients in the wavelet sub-band of the layer 1, one of the 16 coefficients is randomly selected, and random numbers are generated by a generalized double-peak chaotic system, so that a point selection sequence is generated.
Example 4
More specifically, the present invention further provides a decryption method for the encryption method of the present invention, as shown in fig. 3. The decryption process is the inverse of the encryption process. Firstly, acquiring an encrypted image and a secret key, generating intermittent parameters and initial values required by decryption through the secret key, then generating an inverse scrambling sequence, a point selection sequence and a chaotic decryption sequence through a pseudo-random number generator, further performing inverse bit level scrambling, ECC decryption and chaotic decryption on the encrypted image, performing wavelet inverse transformation to reconstruct the image, finally performing image post-processing to change a zero-set negative value during preprocessing, then performing MD5Hash signature verification on the image, outputting the decrypted image if the verification is passed, and outputting the verification if the verification is not passed.
Example 5
More specifically, in step S6 of the present invention, the ECC encryption, that is, elliptic curve encryption, has the following mathematical principles and flow:
1. principle of mathematics
1. Discretizing an elliptic curve
The elliptic curve is defined in a real number domain and is a continuous function, so that the elliptic curve needs to be defined in a finite domain to be encrypted on a computer.
Finite field F p In p elements, finite field F p The operations in (1) include addition, multiplication, division and inversion. When there is a finite field F p Since any element has an inverse when the number p of the medium elements is a prime number, it is necessary to make p a prime number when discretizing the curve. Meanwhile, in the byte code of the bottom layer, in order to make the byte code use as much as possible, a large amount of waste is not generated, and a finite field F p Should be the Messen prime number, i.e. let p =2 n -1, wherein n is an integer.
Also, not all elliptic curves are suitable for encryption, y 2 ＝x 3 + ax + b is a type of curve that can be used for encryption, and is also the simplest type.
2. Addition of elliptic curves in prime field
(1) The infinity point is a zero element:
O∞+O∞＝O∞
O∞+P＝P
(2) The negative element of P (x, y) is-P (x, -y), having
P+(-P)＝O∞
(3) Let P (x) 1 ,y 1 )+Q(x 2 ,y 2 )＝R(x 3 ,y 3 ) Then there is
x 3 ≡(k 2 -x 1 -x 2 )mod p
y 3 ≡[k(x 1 -x 3 )-y 1 ]mod p
If a point P on the elliptic curve has the smallest positive integer n such that nP = O ∞, then n is said to be the order of P.
2. Elliptic curve encryption and decryption
1. Communication process
(1) The receiver A selects a certain elliptic curve E p (a, b) selecting a certain point as a base point base (x) 0 ,y 0 )。
(2) The receiving party A is set as u from the chaotic sequence of the generalized bimodal chaotic system m ) In which certain numbers are selected to generate the private key
Wherein n is the order of the base point, and a public key pubKey (x, y) = privey base (x) 0 ,y 0 )。
(3) Receiver a discloses a selected elliptic curve E p (a, b), base point base (x) 0 ,y 0 ) And the public key pubKey (x, y).
(4) Sender B encodes plaintext data into E p Selecting a random number r (r) at a point M (a, b) (the specific coding mode is determined according to the actual situation)<n)。
(5) Sender B calculates C 1 ＝M+r·pubKey(x,y)，C 2 ＝r·base(x 0 ,y 0 )。
(6) Sender B sends C 1 ,C 2 And sending the data to a receiver A.
(7) After receiving the data, the receiving party A calculates M = C 1 -priKey·C 2 And decoding the M to obtain plaintext data.
If information is leaked in the communication process, the thief can only see the information disclosed by the receiver A and the information C 1 ,C 2 Obtaining the private key by the public key, or else 1 ,C 2 It is relatively difficult to obtain r and to decipher the plaintext.
2. Elliptic curve encryption and decryption certification
C 1 -priKey·C 2
＝(M+r·pubKey)-priKey·(r·base)
＝M+r·(priKey·base)-priKey·(r·base)
＝M
3. Program implementation
The program implementation is as shown in fig. 4, (1) the receiver B initializes the selected elliptic curve, the base point, the private key, the computed public key, the public elliptic curve, the base point and the public key. All operations such as addition, subtraction, multiplication, inversion and the like of the midpoint of the elliptic curve only need the coefficient a of a primary term in the elliptic curve equation, and the constant b can be ignored when the elliptic curve is determined. The constant b may be determined by the coefficient a and the chosen base point. To ensure the security of the encryption, a finite field F p Is set to p =2 127 -1. When selecting base points, it can be seen that each base point corresponds to a different elliptic curve. The order of the base point is not necessarily the same, and the order of the base point determines the private key space, so the selection of the base point needs to calculate the order of the base point first (Schoof algorithm)) And screening out the base points meeting the requirements. Because the public key is calculated through the private key and the base point, when the public key and the base point are used for deducing the private key, the whole private key space needs to be traversed from 1, the cracking difficulty is high, and a thief is prevented from successfully cracking with less calculation amount.
(2) Sender a encodes the plaintext data to a certain point. Because the medical image is encrypted, the data volume is huge, the encoding of plaintext data to one point is not preferable, a single random value r is easy to leak, and the data is difficult to realize by reversely decoding from one point, a large number of data packets are encoded to some points by a sender, a plurality of random values are calculated during the encryption, and the encryption of the plurality of random values can be regarded as the combination encryption of a plurality of sub-keys, which means that each random value does not need to take too large value, and only the number of data packets is large enough. Because medical images generally take 12bit gray values and have a finite field F p Middle p =2 127 1, so that the 127 12-bit pixels are converted into 12 127-bit values as a packet, taking part in encryption, using as much bytecode space as possible.
(3) The sender A generates 2 times of data before encryption by a series of encryptions on the converted data, namely C 1 Group C and 2 and (4) grouping. In the encryption process, the number of elements of the finite field is 2 127 1, so a value of 127 bits is selected for encryption. However, there is a modular operation in the encryption process, and when the number of elements in the finite field is p, the range of the number which can participate in the encryption is [0,p-1 ]]. So when the encrypted number equals 2 127 1, it needs special treatment. Where C is arranged 3 Set for recording all values as 2 127 -1 and is represented by [0,2 ] 127 -2]Any number in place of the number participates in the cryptographic calculation. The public key disclosed by the receiver B and the base point are used for encryption, the obtained data is 127bit, the data is converted into 12bit data, and finally C is output 1 Group C 2 Group C 3 Group, this time encryption is complete.
(4) Sender A will process processed C 1 Group C 2 Group C 3 The group is sent to receiver B, which decrypts with the private key. Need to decryptFirstly, C is required to be 1 Group C 2 The data in the group is converted into a 127bit value and then participates in decryption. Decrypted and passed through C 3 The sequence of individual positions in the group recovers the replaced value (2) 127 -1), according to the coding mode of the sender A, converting the 127-bit data packet into 12-bit data, and after verification, completing decryption.
3. Elliptic curve signcryption verification
1. The signcryption verification process is illustrated in fig. 5.
And (3) signature process:
(1) Selecting a certain elliptic curve E p (a, b) and base point base (x) 0 ,y 0 ) Selecting a certain private key (the private key is larger than zero and smaller than the base point order n), and calculating a public key pubKey (x, y) = private key base (x) 0 ,y 0 )。
(2) Selecting a random number r (r)<n), calculating R (x) r ,y r )＝r·base(x 0 ,y 0 )。
(3) And calculating a hash value H of the signed content, and calculating S ≡ r-H & priKey (mod n).
(4) Publishing an elliptic curve E p (a, b), base point base (x) 0 ,y 0 ) Public key pubKey (x, y), value S, point R (x) r ,y r ) As a signature of the signcrypted content, the verification process is as follows:
calculating R' ≡ S.base (x) 0 ,y 0 )+H·pubKey(mod p)
If R' = R, then the verification is successful.
2. Verifying the proof of a signature
If received S and R are correct:
R'≡S·base(x 0 ,y 0 )+H·pubKey
≡(r-H·priKey)·base(x 0 ,y 0 )+H·priKey·base(x 0 ,y 0 )
≡r·base(x 0 ,y 0 )≡R
it should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.
Claims (10)
1. The DICOM image asymmetric encryption method based on chaotic mapping and selective Signcryption is characterized by comprising the following steps of:
s1: inputting a sequence of images and generating a key;
s2: performing multilevel wavelet transform processing on the image sequence, moving the coefficient sequence to a non-negative domain as a whole, and acquiring a non-negative wavelet coefficient;
s3: generating an initial value and intermittent parameters of the chaotic system by using a secret key, and constructing and initializing a generalized two-peak chaotic system and a three-dimensional interweaving chaotic system;
s4: generating an encryption sequence and a point selection sequence by utilizing a generalized two-peak chaotic system, and generating a scrambling sequence by utilizing a three-dimensional interweaving chaotic system;
s5: carrying out chaotic encryption on the wavelet coefficients according to the encryption sequence until image pixels are controlled to be 0-4095;
s6: determining ECC parameters, selecting partial chaotically encrypted wavelet coefficients according to the point selection sequence to perform ECC encryption, simultaneously performing ECC signature on MD5hash of the original coefficient sequence, and performing two-step combination to perform Signcryption to form an ECC signature;
s7: and carrying out bit level scrambling on the ECC signed image according to the scrambling sequence to generate an encrypted image.
2. The DICOM image asymmetric encryption method based on chaotic mapping and selective signing according to claim 1, wherein the step S1 specifically comprises: inputting an original plaintext image, performing an SHA256 hash function on the original image to generate 256-bit IKey, and simultaneously using an external 256-bit string as EKey; the key consists of 512 bits of IKey and EKey.
3. The DICOM image asymmetric encryption method based on chaotic mapping and selective Signcryption according to claim 1, wherein the step S2 specifically comprises: and performing 3-layer wavelet transformation on the image sequence by adopting a lossless LeGall53 integer wavelet, moving the whole image sequence to a non-negative domain, and acquiring wavelet coefficients.
4. The DICOM image asymmetric encryption method based on chaotic mapping and selective Signcryption according to claim 2, wherein in the step S3, the process of generating the initial values and intermittent parameters of the chaotic system specifically comprises:
s301: the EKey is partitioned into 8 groups of 32-bit blocks, namely:
EKey＝{Ek 0 ，Ek 1 ，…，Ek 7 }，Ek i ＝{Ek i，0 ，Ek i，1 ，…，Ek i，31 }
similarly, IKey is partitioned into 8 groups of 32-bit blocks, namely:
IKey＝{Ik 0 ，Ik 1 ，…；Ik 7 }，Ik i ＝{Ik i，0 ，Ik i，1 ，…，Ik i，31 }
s302: compute summation terms se and si:
wherein Ek i，j The value of j bit of ith block in EKey; ik i，j The same process is carried out;
s303: calculating initial values and intermittent parameters:
1) Initial value u of generalized two-peak chaotic system 0 ：
2) Initial value x of three-dimensional interweaving chaotic system 0 、y 0 、z 0 And parameters λ, k 1 、k 2 、k 3 ：
3) Chaotic encryption parameter α:
5. the DICOM image asymmetric encryption method based on chaotic mapping and selective Signcryption as claimed in claim 4, wherein in the step S3, the generalized bimodal chaotic system f GDH The specific expression of (u, r, c) is as follows:
u n+1 ＝r(u n -c) 2 (c 2 -(u n -c) 2 )＝f GDH (u，r，c)
determining generalized bimodal function parameters r, c and initial value u 0 (ii) a According to the property of the generalized bimodal function, when the generalized parameter c obtains different values, the value range of the parameter r which can make x chaotic exists; at the same time, the initial value u 0 Substituting the initial value into a generalized bimodal function for iteration, initializing the generalized bimodal chaotic system, eliminating the influence of the initial value, and recording the new initial value as u 0 (ii) a Will u 0 Substituting the parameters r and c into f GDH (u, r, c) to obtain a chaotic sequence { u n }；
The three-dimensional interweaving chaotic system has the specific expression as follows:
wherein, λ is more than 0 and less than 3.999, | k 1 |＞33.5，|k 2 |＞37.9，|k 3 L > 35.7; calculating the initial value x 0 、y 0 、z 0 Substituting into the three-dimensional interweaving chaotic system function group for iteration, initializing the three-dimensional interweaving chaotic system, and recording the new initial value as x 0 、y 0 、z 0 (ii) a Initial vector (x) 0 ，y 0 ，z 0 ) And a parameter vector (λ, k) 1 、k 2 、k 3 ) Substituting into the three-dimensional interweaving chaotic system function group to generate a chaotic sequence { x n }、{y n }、{z n }。
6. The DICOM image asymmetric encryption method based on chaotic mapping and selective signing according to claim 5, wherein in the step S4, the generation process of the encryption sequence k specifically comprises: setting the input image specification size as M multiplied by N; setting an initial value of an encryption sequence according to the chaotic encryption parameter alpha as follows:
k[0]＝[f GDH (α，r，c)*10 14 ]mod 4096
let the initial value of the sequence n be the initial value u of the generalized two-peak chaotic system 0 The initialized value is specifically expressed as:
n[0]＝GDH_init(u 0 )
wherein, GDH _ init represents an initialized generalized two-peak chaotic system; and then, calculating, specifically:
for i＝1，2，...，size-1：
i.n[i]＝f GDH (n[i-1]，r，c)
k[i]＝[(k[i-1]+n[i]×10 10 mod 4096)mod 4096]
wherein, the obtained sequence k is an encryption sequence.
7. The DICOM image asymmetric encryption method based on chaotic mapping and selective Signcryption according to claim 6, wherein in the step S4, the scrambling sequence generation process specifically comprises:
obtaining dimension transformation size a multiplied by b multiplied by c';
after the three-dimensional interweaving chaotic system is initialized and iterated for t = max (a, b, c') times, a vector group V = { V } containing t three-dimensional random number vectors is obtained 0 ，V 1 ，ΛV t-1 }，V i ＝{V i，0 ，V i，1 ，V i，2 }；
Order:
L＝{V 0，0 ，V 1，0 ，···，V a-1，0 }
W＝{V 0，1 ，V 1，1 ，···，V b-1，1 }
H＝{V 0，2 ，V 1，2 ，···，V c′-1，2 }
respectively carrying out rapid sequencing on L, W, H to obtain L ', W ' and H '; obtaining three scrambling position one-dimensional vectors X, Y, Z according to the position changes of the elements L ', L, W ', W, H ' and H, specifically:
for i＝0，1，2，…，a-1
X[i]＝get_position(L[i]，L′)
wherein get _ position (x, B) represents the position of element x in sequence B; obtaining Y [ j ] and Z [ k ] in the same way to obtain a one-dimensional vector X, Y, Z;
and finally, generating a three-dimensional scrambling sequence according to X, Y, Z, wherein the specific expression is as follows:
for i＝0，1，2，...，a-1：
for j＝0，1，2，...，b-1：
for k＝0，1，2，...，c′-1：
P[i][j][k]＝(X[i]，Y[j]，Z[k])
wherein, P is a scrambling sequence.
8. The DICOM image asymmetric encryption method based on chaotic mapping and selective signing according to claim 7, wherein in the step S4, the dimension transformation size is specifically:
acquiring the original dimension size as M multiplied by N multiplied by D, wherein M multiplied by N is the length and the width of an image respectively, and D is the number of image pixel bits; setting M to be more than or equal to N to be more than or equal to D;
scaling M × N such that M 'and N' are close to each other, specifically:
for i＝1，2，3...：
N′＝N×i
wherein M' is updated to be a pair
Getting the whole; calculating a parameter i ', minimizing | M ' -N ' |, and recording M ' and N ' at the moment;
then, scaling M 'XN' and D to make
And D is close to, specifically:
for j＝1，2，3...：
D′＝D×j 2
calculating a parameter j' such that
At a minimum, record M ", N", and D' at this time;
if the dimension is set to M "× N" × D ', the bits s = M × N × D-M "× N" × D' overflow, and the shortest side c = min (M ", N ', D'), where a and b are the other two sides, c needs to be extended and the length needs to be extended in order to reduce the overflow as much as possible
Let c '= c + k, the dimension transform size is finally determined to be a × b × c'.
9. The DICOM image asymmetric encryption method based on chaotic mapping and selective Signcryption according to claim 6, wherein in step S4, if the encryption sequence generated according to the size mxn of the input image is k, then step S5 specifically is:
s51: converting the image sequence after wavelet transform into a pixel stream L of (M multiplied by N, 1), namely, primarily encrypting the wavelet coefficients by using an encryption sequence k, wherein the encryption formula is as follows:
s52: checking the value range of the image pixel, if the pixel value is larger than 12 bits, recording the position of the pixel for the points larger than 12 bits and generating a new encryption sequence according to the number of abnormal points, wherein each value of the new encryption sequence has the same bit number as the corresponding abnormal point and the highest bit is 1; the encryption processing of step S51 is carried out on the abnormal points and the new encryption sequence, the step is circulated until all the points are between 0 and 4095, and a pixel stream L' is output;
s53: and carrying out second encryption on the pixel stream L', wherein the encryption formula is as follows:
wherein, when i =0,
s is any random number between 0 and 4095; finally, obtaining a sequence C;
s54: and converting the sequence C obtained in the step S53 into (M multiplied by N) to complete the chaotic encryption process.
10. The DICOM image asymmetric encryption method based on chaotic mapping and selective Signcryption according to claim 8, wherein in the step S7, the sequence after ECC Signcryption is subjected to 12-bit conversion, each element in the sequence is subjected to bit conversion to form a bit stream L, and the bit stream length is mxnx12 assuming that the image length and width are M and N;
truncating the bitstream L according to the dimension transformation size a × b × c', which is specifically represented as:
L 1 ＝[L 0 ，L 1 ，…，L a×b×c′-1 ]；
L 2 ＝[L a×b×c′ ，L a×b×c′+1 ，…，L M×N×12 ]；
and will L 1 Converting into three-dimensional matrix Cube of (a × b × c'), and calculating bit stream L 2 Length R = M × N × 12-a × b × c';
the Cube is specifically represented according to the scrambling sequence P and the scrambling sequence as follows:
for i＝0，1，2，...，a-1：
for j＝0，1，2，...，b-1：
for k＝0，1，2，...，c′-1：
s＝P[i][j][k]
Cube′[i][j][k]＝Cube(s[0]，s[1]，s[2])
restoring the scrambling result Cube' to the bitstream L 1 ', calculating
Mixing L with 2 Of (5) with L 1 Replacing one random element in every h elements to obtain a bit stream L 2 '; after completion, L is obtained 1 ′、L 2 ' splicing the two to form a final bit stream, converting the bit stream back to (M × N, 12), recovering the elements of the bit stream to 12-bit pixels, forming a pixel stream, and then converting the pixel stream back to (M × N) size, so that the bit level scrambling is completed, and an encrypted image is generated.
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