CN110086600A - A kind of image encryption method based on hyperchaotic system and variable step Joseph's problem - Google Patents
A kind of image encryption method based on hyperchaotic system and variable step Joseph's problem Download PDFInfo
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/001—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols using chaotic signals
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
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- H—ELECTRICITY
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- H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
- H04N1/00—Scanning, transmission or reproduction of documents or the like, e.g. facsimile transmission; Details thereof
- H04N1/32—Circuits or arrangements for control or supervision between transmitter and receiver or between image input and image output device, e.g. between a still-image camera and its memory or between a still-image camera and a printer device
- H04N1/32101—Display, printing, storage or transmission of additional information, e.g. ID code, date and time or title
- H04N1/32144—Display, printing, storage or transmission of additional information, e.g. ID code, date and time or title embedded in the image data, i.e. enclosed or integrated in the image, e.g. watermark, super-imposed logo or stamp
- H04N1/32149—Methods relating to embedding, encoding, decoding, detection or retrieval operations
- H04N1/32267—Methods relating to embedding, encoding, decoding, detection or retrieval operations combined with processing of the image
- H04N1/32272—Encryption or ciphering
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Abstract
The invention proposes a kind of image encryption method based on hyperchaotic system and variable step Joseph's problem, its step are as follows: original image being input in Key generation functions and generates binary sequence, calculates the initial value of hyperchaotic system；It is iterated using hyperchaotic system, generates four pseudorandom sequencesX、Y、Z、W；Utilize sequenceXThe every a line being input in variable step Joseph's function scramble original image as key obtains imageI 1；By sequenceYElement as key pair imageI 1It carries out the location of pixels based on reducing subspaces and disorderly obtains imageI 2；By sequenceZVariable step Joseph's function scramble image is input to as keyI 2Each column obtain imageI 3；By sequenceWElement to imageI 3It carries out two binary add/subtractions and obtains ciphertext image.The present invention will be connected with key in plain text, is had plaintext sensibility, can be resisted chosen -plain attact；With powerful key space and sharp key sensitivity.
Description
Technical field
The present invention relates to the technical fields of safety of image transmission, more particularly to one kind to be based on hyperchaotic system and variable step about
The image encryption method of plucked instrument husband's problem.
Background technique
In recent years, the SHA-1 cryptographic algorithm and MD5 cryptographic algorithm that were once commonly used successively are cracked.Once,
The safety of SHA-1 cryptographic algorithm and MD5 cryptographic algorithm is very high, even if carrying out cracking operation using state-of-the-art computer,
Need the time of intimate a century.But the proposition of mould differential bit analytic approach is improved and is cracked including SHA-1, MD5 cryptographic algorithm
The probability of the international hash function algorithm of 5 inside, enables these algorithms to be cracked in a short time.It is strong in face of hacker
It is strong to crack attack, it is traditional based on the cryptographic system of mathematical computations due to safety deficiency etc., cannot expire completely
The needs of sufficient information encryption.Since the demand to protection information security is huge, in recent years, numerous scientific research personnel propose very much
The safety of new Encryption Algorithm protection information.Wherein, image information due to data volume it is big, correlation is strong between data, encrypt difficulty
Huge, finding a kind of suitable image encryption method is always the target that numerous scientific research personnel pursue.
Chaos system is one kind of nonlinear dynamic system, has complicated pseudo-randomness, not only no periodic but also has not been restrained, and
And it is very sensitive to the initial value of system, the small variations of system initial value will affect the differentiation of whole system.Chaos system exists
Great application value in cryptography, because system initial value is sensitive, the strong feature of track ergodic is normally used as pseudorandom for it
Number generator uses.The Encryption Algorithm for having used chaos system has high safety, can make up conventional encryption algorithm with
Machine is insufficient and the weak disadvantage of plaintext relevance.1997, Fridrich J proposed a kind of encryption calculation based on chaotic maps
Chaos system is applied in image encryption by method for the first time.Then, much the resume image based on chaos system is mentioned successively
Out, chaos system is also gradually from Low-dimensional Chaotic Systems to hyperchaotic system, and Multistage Chaotic System, the directions such as hybrid chaotic system are sent out
Exhibition.These new chaos systems keep the intension of cryptography more abundant.
Summary of the invention
It is insufficient for existing encryption method safety, the technical issues of information encryption requirements cannot be fully met, this hair
It is bright to propose a kind of image encryption method based on hyperchaotic system and variable step Joseph's problem, there is great key space,
Good pseudo-randomness can resist various typical attacks to very sensitive in plain text, can be used in the field of image encryption
In.
In order to achieve the above object, the technical scheme of the present invention is realized as follows: a kind of be based on hyperchaotic system and change
The image encryption method of step-length Joseph's problem, its step are as follows:
Step 1: the original image that size is height*width is input to generation binary system sequence in Key generation functions
Column calculate the initial value of hyperchaotic system by binary sequence；
Step 2: it brings the initial value that step 1 calculates into hyperchaotic system and is iterated, generating four length is
(height*width) pseudorandom sequence X, sequence Y, sequence Z and sequence W；
Step 3: sequence X is converted to the matrix X of height*width1, utilize matrix X1In every a line sequence conduct
Key is input to variable step Joseph's function and obtains index sequence and utilize every a line in index sequence scramble original image, obtains
To encrypted image I1；
Step 4: sequence Y is converted to the matrix Y for the height*width that all elements are respectively positioned in section [1,30]1,
To image I1In each pixel use matrix Y1In element corresponding with its position carry out as key based on reducing subspaces
Location of pixels disorderly operates, and obtains encrypted image I2；
Step 5: sequence Z is converted to the matrix Z of height*width1, utilize matrix Z1In each column sequence conduct
Key is input to variable step Joseph's function and obtains index sequence using index sequence scramble image I2Each column, encrypted
Image I afterwards3；
Step 6: sequence W is converted to the matrix for the height*width that all elements are respectively positioned in section [0,255]
W1, use image I3In each pixel and matrix W1The element of corresponding position carries out two binary additions or subtraction pair
Pixel is replaced, and encrypted ciphertext image C is obtained.
The Key generation functions are SHA-256 functions, SHA-256 function by original image be converted into the two of 256 into
Hash sequence H processed.
The method of the initial value that hyperchaotic system is calculated by binary sequence are as follows: by 256 binary system Hash
Sequence H is divided into 8 binary sequence h of 32 parts of equal lengths1, h2, h3…h32, calculate the initial value x of hyperchaotic system1、
y1、z1And w1:
Wherein,For XOR operation, x '1、y′1、z′1With w '1Indicate given initial parameter value.
The hyperchaotic system are as follows:
Wherein,It is the inverse of state variable x, y, z, w respectively, a, b, c, d, e, f, g is hyperchaotic system
Parameter；Work as a=1.55, b=1.24, c=0.25, d=0.05, e=2.6, when f=0.21, g=0.48, the hyperchaos system
System is in hyperchaos state.
The pseudorandom sequence X, sequence Y, sequence Z and sequence W are hyperchaotic system respectively with initial value x1、y1、z1With
w1The iterative value of the state variable x, y, z and w chosen after being iterated 1000 times.
The matrix X that sequence X is converted to height*width1Method are as follows:
Sequence Y is converted to the matrix Y for the height*width that all elements are respectively positioned in section [1,30]1Method
Are as follows:
Sequence Z is converted to the matrix Z of height*width1Method are as follows:
Sequence W is converted to the matrix W for the height*width that all elements are respectively positioned in section [0,255]1Method
Are as follows:
Wherein,To be rounded symbol downwards, mod () is MOD function, recombination functions reshape (a1, b1, c1)
It indicates array a1 being rearranged into the array that size is b1 × c1 by preferential sequence is arranged.
Variable step Joseph function is f (M, N, D, L) in the step 3 and step 5, wherein parameter D is circulation side
To indicating right-hand circular as D=1, indicate left-hand circular as D=-1；Parameter L is circulation step-length；Parameter N be containing
The pseudo-random sequence N ' (N ' of M element1, N '2, N '3...N′M), i-th loop parameter N=N ' (i) when traversal, wherein M is
The element number of pseudo-random sequence N '.
It is the scramble of location of pixels using the method for index sequence scramble image in the step 3 and step 5, i.e., by square
Battle array X1In every a line sequence or matrix Z1In each column sequence as pseudo-random sequence N ' input variable step Joseph's function,
Index sequence s ' is obtained, by the row of original image or image I2Column composition pixel sequence s { 1,2,3,4...M } → s '
{s′1, s '2, s '3, s '4...s′MRegular scramble.
The method that location of pixels in the step 4 based on reducing subspaces disorderly operates are as follows: by matrix Y1Middle position be (h1,
G1 value) obtains index sequence s '=f (8, Y as key input Joseph's function1(h1, g1), L)；By image I1Middle position is
The pixel of (h1, g1) is converted to 8 bits；By the position of pixel s { 1,2,3,4...8 } → s ' { s '1, s '2, s '3, s
′4...s′8Regular scramble；Wherein, 1≤h1≤height, 1≤g1≤width, L are circulation step-length.
The method for carrying out pixel replacement using two binary additions or subtraction in the step 6 are as follows: by image I3
The pixel of middle position (h1, g1) is converted to 8 bit binary numbers, this 8 bit binary number is then split into 4 two two
Binary digits, then 4 two bit binary numbers and matrix W1The value of position (h1, g1) be equally split into 4 two two into
The key of system number carries out two binary additions or subtraction, wherein 1≤h1≤height, 1≤g1≤width；It is described
The case where two binary additions or subtraction do not consider carry during addition or subtraction and borrow, only retains fortune
Last two bit binary number in result is calculated, 32 kinds of situations are shared are as follows:
| + | 00 | 01 | 10 | 11 | - | 00 | 01 | 10 | 11 |
| 00 | 00 | 01 | 10 | 11 | 00 | 00 | 11 | 10 | 01 |
| 01 | 01 | 10 | 11 | 00 | 01 | 01 | 00 | 11 | 10 |
| 10 | 10 | 11 | 00 | 01 | 10 | 10 | 01 | 00 | 11 |
| 11 | 11 | 00 | 01 | 10 | 11 | 11 | 10 | 01 | 00 |
。
Beneficial effects of the present invention: by being improved to classical Joseph's problem in-depth analysis to Joseph's problem,
Propose the solution by the pseudo-random sequence that hyperchaotic system generates and variable step Joseph's problem that Joseph's problem combines
Certainly method, and applied during image encryption, the pseudorandom chaos sequence that hyperchaotic system generates is asked with Joseph
Topic combines, and increases the rule of traversal reducing subspaces, while the method for increasing location of pixels scramble.The present invention will be in plain text and close
Key connects, and has plaintext sensibility, can resist chosen -plain attact；Meanwhile there is powerful key space and acumen
Key sensitivity.When carrying out classical attack test, present invention shows good security performances, while can also resist
The various classical attacks such as statistical attack, differential attack, shearing attack, therefore, the present invention can be effectively protected safety of image, can
It is widely used in the encryption and transmission of image information.
Detailed description of the invention
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below
There is attached drawing needed in technical description to be briefly described, it should be apparent that, the accompanying drawings in the following description is only this
Some embodiments of invention for those of ordinary skill in the art without creative efforts, can be with
It obtains other drawings based on these drawings.
Fig. 1 is the structural diagram of the present invention.
Fig. 2 is the phase rail figure of hyperchaotic system of the present invention.
Fig. 3 is the flow chart of the pixel permutation method based on pseudo-random sequence.
Fig. 4 is original image of the invention and ciphertext image, wherein (a) is the Camera original image of 128*128, (b)
For the Camera original image of 256*256, (c) the Brain original image for being 256*256, (d) original for the White of 256*256
Image is (e) the ciphertext image of (a), (f) is the ciphertext image of (b), (g) is the ciphertext image of (c), (h) is the ciphertext of (d)
Image.
Fig. 5 is the histogram of original image and ciphertext image, wherein (a) is Cameraman original image, (b) is
Cameraman ciphertext image (c) is Brain original image, (d) is Brain ciphertext image.
Fig. 6 is cropped ciphertext image and decrypted image, wherein (a) is the 1/64 ciphertext image cut, (b) is 1/
The 16 ciphertext images cut, (c) the ciphertext image cut for 1/4 are (d) decrypted image of (a), (e) are the decryption figure of (b)
Picture is (f) decrypted image of (c).
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, those of ordinary skill in the art are obtained every other under that premise of not paying creative labor
Embodiment shall fall within the protection scope of the present invention.
As shown in Figure 1, a kind of image encryption method based on hyperchaotic system and variable step Joseph's problem, step is such as
Under:
Step 1: the original image that size is height*width is input to generation binary system sequence in Key generation functions
Column calculate the initial value of hyperchaotic system by binary sequence.
The Key generation functions are SHA-256 functions, SHA-256 function by original image be converted into the two of 256 into
Hash sequence H processed.
The method of the initial value that hyperchaotic system is calculated by binary sequence are as follows: by 256 binary system Hash
Sequence H is divided into 8 binary sequence h of 32 parts of equal lengths1, h2, h3…h32, calculate the initial value x of hyperchaotic system1、
y1、z1And w1:
Wherein,For XOR operation, i.e. corresponding position carries out XOR operation in two 8 binary sequences.x′1、y′1、
z′1With w '1Indicate given initial parameter value.
Step 2: it brings the initial value that step 1 calculates into hyperchaotic system and is iterated, generating four length is
(height*width) pseudorandom sequence X, sequence Y, sequence Z and sequence W.
Chaos phenomenon is that a kind of there is a phenomenon where in the pseudorandom irregular movement determined in system.This motion process was both
No periodic is not restrained again, and very sensitive to the parameter of system, and the minor alteration of system parameter can cause the pole of tracks
Big difference.The characteristic and cryptography of chaos system are overlapped the requirement height of key and key stream, and chaos system is in cryptography
It is widely used.The chaos system initial value and system parameter of low-dimensional are few, and track can short-term forecast.The chaos of higher-dimension
System is more compared to Low-dimensional Chaotic Systems initial value and system parameter, and track is increasingly complex, so, in recent ten years, chaos
System just develops towards higher dimension.
The present invention realized using the new hyperchaotic system that Zhang Na et al. is proposed to the scramble of plaintext image pixel and
Replacement operator.Shown in the definition of hyperchaotic system such as formula (2):
Wherein,It is the inverse of state variable x, y, z, w respectively, a, b, c, d, e, f, g is hyperchaotic system
Parameter；Work as a=1.55, b=1.24, c=0.25, d=0.05, e=2.6, when f=0.21, g=0.48, the hyperchaos system
System is in hyperchaos state.The hyperchaotic system has positive number Lyapunov coefficient, and meets the requirement of NIST test, has pole
High safety.Take step-length 0.002 using Runge-Kutta method to hyperchaotic system iteration, phase rail figure such as Fig. 2 of hyperchaotic system
It is shown.Hyperchaotic system track is increasingly complex as shown in Figure 2, and system is safer.
The pseudorandom sequence X, sequence Y, sequence Z and sequence W are hyperchaotic system respectively with initial value x1、y1、z1With
w1The iterative value of the state variable x, y, z and w chosen after being iterated 1000 times.After obtaining initial value, to hyperchaotic system
The value for being iterated, and giving up preceding 1000 iteration can remove the transient effect of hyperchaotic system.Four pseudorandom sequences
X, sequence Y, sequence Z and sequence W can be used for carrying out scramble and replacement operator to pixel.
Step 3: sequence X is converted to the matrix X of height*width1, utilize matrix X1In every a line sequence conduct
Key is input to variable step Joseph's function and obtains index sequence and utilize every a line in index sequence scramble original image, obtains
To encrypted image I1。
The matrix X that sequence X is converted to height*width1Method are as follows:
Wherein, X (:) is the element in sequence X,To be rounded symbol downwards, mod () is MOD function.
Reshape (,) indicating recombination functions, reshape (a1, b1, c1) indicates the sequence that array a1 is preferential by column
It is rearranged into the array that size is b1 × c1.
Joseph's problem is a searching loop problem, and source is that famous Jewish history scholar Josephus is experienced
Story.After Roman captures Qiao Tapate, 39 Jews and Josephus and his friend hide into a hole, and 39 still
Too people determines also not caught by enemy extremely, then determines a suicide mode, and 41 people line up a circle, by the
1 people starts count off, and every count off must just commit suiside to the 3rd people the people, then again by next count off again, until owner all
Until committing suicide and die.However, Josephus and his friend do not want to die.Most latter two quilt could somewhere be become by standing
The people being recycled to? Josephus wants his friend first to pretend to defer to, he by friend with oneself be arranged in the 16th and the 31st position
It sets, has then escaped from this dead game.By calculating Joseph's problem, a kind of sequence of pseudo-random transformation can be imitated out,
And it is used in the operation of location of pixels scramble and location of pixels unrest.
Joseph's problem can be described as: M element formed a circle, this circle is looped through in order, is deleted
Except n-th element, and this operation is continued to execute since the N+1 element, until choosing the last one element from circle.
By one function representation of Joseph's problem, i.e. f (M, N).For example, the solution of function f (8,25) is by 1,2,3,4,5,6,7,8
These elements form a circle, and then loop through in order and delete the 25th element, in this reducing subspaces successively
Deleted element is respectively as follows: 1,5,6,4,7,8,2,3.For this there are also the solution of another, still it is with f (8,25)
Element 1,2,3,4,5,6,7,8 is formed an one-dimensional sequence by example, first calculating mod (25,8)=1, i.e. first time quilt
It chooses and what is deleted is the 1st element, i.e. element 1.Form new sequence 2 with remaining element, 3,4,5,6,7,8, then count
It calculates mod (25,7)=4, i.e., second element that is selected and deleting is the 4th element, i.e. element 5 in new sequence.With remaining
Element forms new sequence 6, and 7,8,2,3,4, mod (25,6)=1 then are calculated, i.e., third time is selected and the element deleted is
1st element, i.e. element 6 in new sequence.And so on cracking can solve the problems, such as Joseph.
In order to expand to Joseph's problem, increase its content and form, Xiang Desheng et al. draws in Joseph's problem
Enter a new rule, i.e., starting point S has been added on the basis of original rule, has been f (M, N, S) by Joseph's function extension, this
Kind method can choose the starting point in reducing subspaces, and Joseph's problem is made to have more interest.In Xiang Desheng et al. in order to about plucked instrument
On the basis of the expansion that husband's problem carries out, Guo Yi et al. joined loop direction and count off interval again for Joseph's problem, will about
Plucked instrument husband's function extension is f (M, N, S, D, L), wherein parameter D is loop direction, indicates right-hand circular as D=1, works as D=-
Left-hand circular is indicated when 1；Parameter L is count off interval.This method significantly increases the diversity of Josephus traversing.
The present invention it is above-mentioned be directed to Joseph's problem extending method on the basis of continue to improve, put forward a kind of changes and walk
Long searching loop method.By Joseph's problem in conjunction with chaos system picture, the parameter N in Joseph's problem, which is expanded, becomes one
Pseudo-random sequence N ' (N '1,N′2,N′3…N′M), when traversing to reducing subspaces, parameter N=is used in i-th circulation
N′iIt is recycled as step-length.Because of sequence N ' (N '1,N′2,N′3…N′M) in number be pseudo random number, can infinitely expand,
So the method that Joseph loops through is significantly increased again.For example, when working as N '=(1,2,3,4,5,6,7,8), Xie Han
Number f (8, (1,2,3,4,5,6,7,8), 1,1,0), result 1,3,6,4,5,2,7,8.Simultaneously, it is possible to use this method is to report
Number interval L is expanded, and is repeated no more herein.
Variable step Joseph's function is f (M, N, D, L), wherein parameter D is loop direction, indicates clockwise as D=1
Circulation, indicates left-hand circular as D=-1；Parameter L is circulation step-length；Parameter N is the pseudo-random sequence N ' containing M element
(N′1,N′2,N′3…N′M), i-th loop parameter N=N ' (i) when traversal, wherein M is the element number of pseudo-random sequence N '.
Scramble method is a kind of common method for changing position, the position that it can be upset with certain specific rule, with
This effect to play encryption.The scramble method that the present invention uses is will to need the position of element and isometric sequence in the sequence of scramble
The position for arranging element in s is corresponding, then by sequence s { s1,s2,s3,s4,snWith certain regular scramble at sequence s ' { s '1,s
′2,s′3,s′4,s′n, and by former sequence according to the sequence of this regular scramble Cheng Xin, the sequence after scramble is obtained with this.Scramble
The flow chart of method is as shown in figure 3, the decrypting process of pixel permutation method is the inverse process of ciphering process, therefore repeats no more.
Utilize matrix X1In every a line sequence to original image carry out scramble method be to be set to the position of pixel
Disorderly operation, the method using index sequence scramble image is the scramble of location of pixels, i.e., by matrix X1In every a line sequence make
For pseudo-random sequence N ' input variable step Joseph's function, index sequence s ' is obtained, by the pixel sequence of the row composition of original image
Column s { 1,2,3,4 ... M } → s ' { s '1,s′2,s′3,s′4…s′MRegular scramble, here the value of M be height.
Step 4: sequence Y is converted to the matrix Y for the height*width that all elements are respectively positioned in section [1,30]1,
To image I1In each pixel use matrix Y1In element corresponding with its position carry out as key based on reducing subspaces
Location of pixels disorderly operates, and obtains encrypted image I2。
Sequence Y is converted to the matrix Y for the height*width that all elements are respectively positioned in section [1,30]1Method
Are as follows:
The all elements of matrix Y1 are respectively positioned on section [1,30].Location of pixels in the step 4 based on reducing subspaces is random
The method of operation are as follows: by matrix Y1Middle position is that the value of (h1, g1) obtains index sequence s ' as key input Joseph's function
=f (8, Y1(h1,g1),L)；By image I1Middle position is that the pixel of (h1, g1) is converted to 8 bits；The position of pixel is used
s{1,2,3,4…8}→s′{s′1,s′2,s′3,s′4…s′8Regular scramble；Wherein, 1≤h1≤height, 1≤g1≤
Width, L are circulation step-length.
Step 5: sequence Z is converted to the matrix Z of height*width1, utilize matrix Z1In each column sequence conduct
Key is input to variable step Joseph's function and obtains index sequence using index sequence scramble image I2Each column, encrypted
Image I afterwards3。
Sequence Z is converted to the matrix Z of height*width1Method are as follows:
Method using index sequence scramble image is the scramble of location of pixels, i.e., by matrix Z1In each column sequence make
For pseudo-random sequence N ' input variable step Joseph's function, index sequence s ' is obtained, by image I2Column composition pixel sequence
With s { 1,2,3,4 ... M } → s ' { s '1,s′2,s′3,s′4…s′MRegular scramble, here the value of M be width.
Step 6: sequence W is converted to the matrix for the height*width that all elements are respectively positioned in section [0,255]
W1, use image I3In each pixel and matrix W1The element of corresponding position carries out two binary additions or subtraction pair
Pixel is replaced, and encrypted ciphertext image C is obtained.
Sequence W is converted to the matrix W for the height*width that all elements are respectively positioned in section [0,255]1Method
Are as follows:
The all elements of matrix W 1 are respectively positioned on section [0,255].
The present invention carries out replacement operator to pixel using two bit binary number addition and subtractions.In two binary digits
In, there is a kind of special addition and subtraction rules.Two binary additions or subtraction do not consider addition or subtraction mistake
Carry in journey and the case where borrowing, only retain last two bit binary number in operation result.For example, ' 10 '+' 11 '=
' 01 ', ' 01 '-' 10 '=' 11 '.When using this addition and subtraction rule, 32 kinds of possible situations are shared, this 32 kinds of situations such as table 1
It is shown.
32 kinds of situations of 1. liang of bit binary number addition and subtractions of table
| + | 00 | 01 | 10 | 11 | - | 00 | 01 | 10 | 11 |
| 00 | 00 | 01 | 10 | 11 | 00 | 00 | 11 | 10 | 01 |
| 01 | 01 | 10 | 11 | 00 | 01 | 01 | 00 | 11 | 10 |
| 10 | 10 | 11 | 00 | 01 | 10 | 10 | 01 | 00 | 11 |
| 11 | 11 | 00 | 01 | 10 | 11 | 11 | 10 | 01 | 00 |
The method for carrying out pixel replacement using two binary additions or subtraction in the step 6 are as follows: by image I3
The pixel of middle position (h1, g1) is converted to 8 bit binary numbers, this 8 bit binary number is then split into 4 two two
Binary digits, then 4 two bit binary numbers and matrix W1The value of position (h1, g1) be equally split into 4 two two into
The key of system number carries out two binary additions or subtraction, wherein 1≤h1≤height, 1≤g1≤width.Example
Such as, using 225 and 108 carry out two bit binary number signed magnitude arithmetic(al)s, 225 and 101 should be respectively converted into first 8 two into
Then the two numbers are split into two bit binary numbers and carry out addition fortune by system number ' 11100001 ' and ' 01101100 '
It calculates, acquired results are ' 00001101 '.This number is converted into ten's digit, result 13.Two binary add subtractions
Operation is reciprocal process.
The decrypting process of encryption method of the present invention is the inverse process of ciphering process, therefore repeats no more.
The present invention can be used to encrypt the digital picture of arbitrary size, the original image encrypted using the present invention and ciphertext graph
As shown in Figure 4, wherein the Hash sequence for being used as initial key is generated by original image, and part of key in addition is a=
1.55, b=1.24, c=0.25, d=0.05, e=2.6, f=0.21, g=0.48, S=1, D=1, L=0, x '1=0, y '1
=0, z '1=0, w '1=0.By Fig. 4 (e)-(h) it is found that the example for the ciphertext image listed loses original image completely
Feature, encryption method of the present invention work well.Also, encryption method be it is lossless, decrypted image and original image are completely the same.
Histogram is the index of the value of each pixel of statistics, embodies the quantity situation of each pixel in image.It is arranged in Fig. 5
The histogram of original image and ciphertext image is lifted.It can by the pixel histogram comparative analysis of original image and ciphertext image
Know, the pixel Distribution value of original image is more concentrated, and has certain statistical property, does not have resistivity to exhaustive attack.And
The uniform and dispersion that the pixel of ciphertext image is then distributed, has broken the regularity of distribution of pixel, has not had statistical property, attacker
It cannot restore the original information of image using statistical property, therefore Statistical Analysis Attacks can be resisted well.
For original image, because the value between the adjacent pixel of most of region is all very close, image is adjacent
The correlation of the value of pixel between position is very strong.And break the strong correlation between pixel, have to Statistical Analysis Attacks are resisted
Very big significance.Between adjacent pixel shown in the calculation method of related coefficient such as formula (7):
Wherein, xiIndicate the value of chosen pixel, yiExpression and xiAdjacent pixel value, N indicates chosen picture
The sum of element, E (x) are the average value of chosen pixel, and E (y) is the average value of the pixel adjacent with chosen pixel, D
(x) variance of chosen pixel, the variance of pixel D (y) adjacent with chosen pixel are indicated, cov (x, y) indicates x, y
Between covariance, rxyIndicate the covariance between x, y.
5000 pairs of pixels are randomly selected, to the horizontal direction of original image and ciphertext image, vertical direction and diagonal
Related coefficient on line direction is counted, and statistical result is as shown in table 2.
The related coefficient of 2. original image of table and ciphertext image all directions
The statistical result of table 2 shows that in original image, the pixel interdependence randomly selected is very strong, and in ciphertext
In image, related coefficient between pixel is close to 0.The present invention can preferably upset the correlation between pixel, therefore can
Preferably to resist Statistical Analysis Attacks.
Differential attack analysis, which refers to do original image, small variations and then to be encrypted, and ciphertext image then pair carries out
Analysis, analyzes its sensitivity to plaintext.Measure resist differential attack ability index difference NPCR (pixel rate of change) and
UACI (pixel averagely changes intensity), shown in calculation such as formula (8).
Wherein, P1(i, j) and P2(i, j) respectively indicates correct decrypted image and adding when minor alteration occurs for plaintext
Pixel value of the close image at position (i, j), height, width respectively indicate the height and width of image.
NPCR and UACI theoretical eapectation is respectively 100% and 33.4635%.Original image is listed in table 3
The value of the NPCR and UACI between ciphertext image and former ciphertext image when 1bit changes, the data in table 3 are all close to theory
Value, this reflects using the ciphertext image of the invention encrypted and there is very strong relevances between original image, even if original
The minor alteration of 1bit occurs for image, and ciphertext image will occur thoroughly to change, and the present invention can effectively resist differential attack.
The value of NPCR and UACI when minor alteration occurs for 3. original image of table
| Image | NPCR | UACI |
| Camera 128*128 | 99.6216 | 33.2842 |
| Camera 256*256 | 99.6109 | 33.3735 |
| Camera 512*512 | 99.5941 | 33.4795 |
| Brain 128*128 | 99.5544 | 33.3126 |
| Brain 256*256 | 99.5789 | 33.3460 |
| Brain 512*512 | 99.6094 | 33.4677 |
| White 128*128 | 99.6033 | 33.7762 |
| White 256*256 | 99.6506 | 33.4553 |
| White 512*512 | 99.6109 | 33.5130 |
Comentropy be to the concept to information quantization and measurement, can with its measure image in pixel randomness and
Even distributed degrees.If the pixel distribution of image is visibly homogeneous and random, image will have good comentropy.Otherwise such as
Pixel distribution is more regular in fruit image, then its comentropy is with regard to poor.For a gray level image, each pixel may
It will appear 256 kinds of states, therefore the probability that every kind of state of pixel has 1/256 occurs.One completely random is distributed
Image, desirable information entropy should be 8.And if the gray value of all pixels is all equal in a gray level image, comentropy
It is 0.Shown in the calculation method of comentropy H (s) such as formula (9).Wherein, p (m) indicates the probability that every kind of pixel m occurs, and m's takes
Being worth range is [0,255], and n is the number that pixel m occurs.
The comentropy that some images encrypted using the present invention are listed in table 4, by comparing it is found that the ciphertext graph obtained
As having good comentropy, it is closer to ideal value 8, ciphertext image has good randomness.
The comentropy of table 4. original image and ciphertext image
Loss of data attack refers to the attack pattern that partial data is intercepted and deleted to ciphertext image.Ciphertext image quilt
A certain number of loss of data are produced after attack, if the recovery capability effect of decipherment algorithm is limited, lose information
The decrypted image of ciphertext image afterwards just cannot provide enough effective informations.The analysis of loss of data attack test refers to ciphertext
Image portion pixels are deleted, and are compared point by corresponding decipherment algorithm, and then to obtained decrypted image and original image
Analysis, counts its recovery extent.Fig. 6 is the ciphertext image and corresponding decrypted image after loss of data is attacked.
In order to analyze the ability that the present invention resists loss of data, between the decrypted image and original image after analysis is attacked
Correlation, on the basis of the indexs such as NPCR, UACI, also use MSE (mean square deviation) and PSNR (Y-PSNR) two fingers
Mark goes to measure the similarity degree of two images.Shown in the calculation of MSE and PSNR such as formula (10) and formula (11).It is general next
It says, as MSE≤30dB, two images do not have marked difference, and as MSE > 30, the value of MSE is closer to 30, two images difference
It is smaller.PSNR has reacted the size of image fault, and PSNR is bigger, and image fault is smaller.
The indices of the decrypted image after Cameraman image is attacked by loss of data are listed in table 5.By right
Than can be seen that the present invention when attacking by loss of data with certain recovery capability, have one to loss of data attack
Fixed resistivity.
The indices of decrypted image after 5. Cameraman image of table is attacked by loss of data
The present invention is proposed a kind of based on hyperchaotic system and variable step by means of the analysis and improvement to Joseph's problem
The image encryption method of reducing subspaces, the pseudorandom chaos sequence that hyperchaotic system is generated increase in conjunction with Joseph's problem
The rule of traversal reducing subspaces, while the method that increases location of pixels scramble.The experimental results showed that the present invention is with larger
Key space attacked the various classics such as to resist exhaustive attack, while statistical attack, differential attack, shearing attack can also be resisted
It hits, can be widely applied to the encryption and transmission of image information.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all in essence of the invention
Within mind and principle, any modification, equivalent replacement, improvement and so on be should all be included in the protection scope of the present invention.
Claims (10)
1. a kind of image encryption method based on hyperchaotic system and variable step Joseph's problem, which is characterized in that its step is such as
Under:
Step 1: the original image that size is height*width being input in Key generation functions and generates binary sequence,
The initial value of hyperchaotic system is calculated by binary sequence；
Step 2: bringing the initial value that step 1 calculates into hyperchaotic system and be iterated, and generating four length is (height*
Width pseudorandom sequence X, sequence Y, sequence Z and sequence W)；
Step 3: sequence X is converted to the matrix X of height*width1, utilize matrix X1In every a line sequence as key
It is input to variable step Joseph's function to obtain index sequence and utilize every a line in index sequence scramble original image, be added
Image I after close1；
Step 4: sequence Y is converted to the matrix Y for the height*width that all elements are respectively positioned in section [1,30]1, to figure
As I1In each pixel use matrix Y1In element corresponding with its position as key carry out the pixel based on reducing subspaces
Position shuffle operation, obtains encrypted image I2；
Step 5: sequence Z is converted to the matrix Z of height*width1, utilize matrix Z1In each column sequence as key
It is input to variable step Joseph's function and obtains index sequence using index sequence scramble image I2Each column, obtain encrypted
Image I3；
Step 6: sequence W is converted to the matrix W for the height*width that all elements are respectively positioned in section [0,255]1, use
Image I3In each pixel and matrix W1The element of corresponding position carries out two binary additions or subtraction and carries out to pixel
Displacement, obtains encrypted ciphertext image C.
2. the image encryption method according to claim 1 based on hyperchaotic system and variable step Joseph's problem, special
Sign is that the Key generation functions are SHA-256 functions, and SHA-256 function converts original image to 256 binary systems
Hash sequence H.
3. the image encryption method according to claim 2 based on hyperchaotic system and variable step Joseph's problem, special
Sign is, the method for the initial value that hyperchaotic system is calculated by binary sequence are as follows: by 256 binary system Hash sequences
Column H is divided into 8 binary sequence h of 32 parts of equal lengths1, h2, h3…h32, calculate the initial value x of hyperchaotic system1、y1、z1
And w1:
Wherein,For XOR operation, x '1、y′1、z′1With w '1Indicate given initial parameter value.
4. the image encryption method according to claim 1 or 3 based on hyperchaotic system and variable step Joseph's problem,
It is characterized in that, the hyperchaotic system are as follows:
Wherein,z、It is the inverse of state variable x, y, z, w respectively, a, b, c, d, e, f, g is the parameter of hyperchaotic system；
Work as a=1.55, b=1.24, c=0.25, d=0.05, e=2.6, when f=0.21, g=0.48, which is in super
Chaos state.
5. the image encryption method according to claim 4 based on hyperchaotic system and variable step Joseph's problem, special
Sign is that the pseudorandom sequence X, sequence Y, sequence Z and sequence W are hyperchaotic system respectively with initial value x1、y1、z1With
w1The iterative value of the state variable x, y, z and w chosen after being iterated 1000 times.
6. the image encryption method according to claim 1 based on hyperchaotic system and variable step Joseph's problem, special
Sign is, the matrix X that sequence X is converted to height*width1Method are as follows:
Sequence Y is converted to the matrix Y for the height*width that all elements are respectively positioned in section [1,30]1Method are as follows:
Sequence Z is converted to the matrix Z of height*width1Method are as follows:
Sequence W is converted to the matrix W for the height*width that all elements are respectively positioned in section [0,255]1Method are as follows:
Wherein,To be rounded symbol downwards, mod () is MOD function, and recombination functions reshape (a1, b1, c1) is indicated
Array a1 is rearranged into the array that size is b1 × c1 by preferential sequence is arranged.
7. the image encryption method according to claim 6 based on hyperchaotic system and variable step Joseph's problem, special
Sign is that variable step Joseph function is f (M, N, D, L) in the step 3 and step 5, wherein parameter D is loop direction,
Right-hand circular is indicated as D=1, indicates left-hand circular as D=-1；Parameter L is circulation step-length；Parameter N is containing M
The pseudo-random sequence N ' (N ' of element1,N′2,N′3…N′M), i-th loop parameter N=N ' (i) when traversal, wherein M be it is pseudo- with
The element number of machine sequence N '.
8. the image encryption method according to claim 7 based on hyperchaotic system and variable step Joseph's problem, special
Sign is, is the scramble of location of pixels using the method for index sequence scramble image in the step 3 and step 5, i.e., by square
Battle array X1In every a line sequence or matrix Z1In each column sequence as pseudo-random sequence N ' input variable step Joseph's function,
Index sequence s ' is obtained, by the row of original image or image I2Column composition pixel sequence with sequence s { 1,2,3,4 ... M } →
s′{s′1,s′2,s′3,s′4…s′MRegular scramble.
9. the image encryption method according to claim 7 based on hyperchaotic system and variable step Joseph's problem, special
Sign is, the method that the location of pixels in the step 4 based on reducing subspaces disorderly operates are as follows: by matrix Y1Middle position be (h1,
G1 value) obtains index sequence s '=f (8, Y as key input Joseph's function1(h1,g1),L)；By image I1Middle position is
The pixel of (h1, g1) is converted to 8 bits；By the position of pixel sequence s { 1,2,3,4 ... 8 } → s ' { s '1,s′2,s′3,
s′4…s′8Regular scramble；Wherein, 1≤h1≤height, 1≤g1≤width, L are circulation step-length.
10. the image encryption method according to claim 6 based on hyperchaotic system and variable step Joseph's problem, special
Sign is, two binary additions or the method for subtraction progress pixel replacement is utilized in the step 6 are as follows: by image I3
The pixel of middle position (h1, g1) is converted to 8 bit binary numbers, this 8 bit binary number is then split into 4 two two
Binary digits, then 4 two bit binary numbers and matrix W1The value of position (h1, g1) be equally split into 4 two two into
The key of system number carries out two binary additions or subtraction, wherein 1≤h1≤height, 1≤g1≤width；It is described
The case where two binary additions or subtraction do not consider carry during addition or subtraction and borrow, only retains fortune
Last two bit binary number in result is calculated, 32 kinds of situations are shared are as follows:
。
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111105339A (en) * | 2019-12-23 | 2020-05-05 | 郑州轻工业大学 | Image encryption method based on multidimensional chaotic system and Joseph scrambling |
| CN112422266A (en) * | 2020-10-28 | 2021-02-26 | 郑州轻工业大学 | Hyperchaotic encryption method based on Joseph traversal and bit plane reconstruction |
| CN112543093A (en) * | 2020-11-27 | 2021-03-23 | 长沙理工大学 | Image encryption method, device and storage medium based on double-entropy source hyperchaotic system |
| CN114389787A (en) * | 2021-12-06 | 2022-04-22 | 中南大学 | Carrier-free information hiding method and system based on chaotic system and computer storage medium |
| CN115719300A (en) * | 2023-01-09 | 2023-02-28 | 浙江出海云技术有限公司 | Personnel information management method for big data |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103929563A (en) * | 2014-04-11 | 2014-07-16 | 陕西师范大学 | Image encryption and decryption method based on improved Joseph traversal and generalized Henon mapping |
| CN107659751A (en) * | 2017-09-19 | 2018-02-02 | 中国矿业大学 | More image encryption methods based on DNA encoding and chaos |
| CN108366181A (en) * | 2018-01-23 | 2018-08-03 | 西南财经大学 | A kind of image encryption method based on hyperchaotic system and multistage scramble |
| CN108650434A (en) * | 2018-05-08 | 2018-10-12 | 吉林大学 | A kind of method of image encryption |
| AU2018102042A4 (en) * | 2018-12-10 | 2019-01-17 | Li, Lili MISS | A color image encryption based on optical chaos and secure sharing in cloud |
-
2019
- 2019-04-28 CN CN201910349398.2A patent/CN110086600B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103929563A (en) * | 2014-04-11 | 2014-07-16 | 陕西师范大学 | Image encryption and decryption method based on improved Joseph traversal and generalized Henon mapping |
| CN107659751A (en) * | 2017-09-19 | 2018-02-02 | 中国矿业大学 | More image encryption methods based on DNA encoding and chaos |
| CN108366181A (en) * | 2018-01-23 | 2018-08-03 | 西南财经大学 | A kind of image encryption method based on hyperchaotic system and multistage scramble |
| CN108650434A (en) * | 2018-05-08 | 2018-10-12 | 吉林大学 | A kind of method of image encryption |
| AU2018102042A4 (en) * | 2018-12-10 | 2019-01-17 | Li, Lili MISS | A color image encryption based on optical chaos and secure sharing in cloud |
Non-Patent Citations (2)
| Title |
|---|
| 郭毅,邵利平,杨 璐: "基于约瑟夫和Henon映射的比特位图像加密算法", 《计 算 机 应 用 研 究》 * |
| 马欣: "基于动态约瑟夫环和比特双重置乱的图像加密", 《电脑知识与技术》 * |
Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111105339A (en) * | 2019-12-23 | 2020-05-05 | 郑州轻工业大学 | Image encryption method based on multidimensional chaotic system and Joseph scrambling |
| CN112422266A (en) * | 2020-10-28 | 2021-02-26 | 郑州轻工业大学 | Hyperchaotic encryption method based on Joseph traversal and bit plane reconstruction |
| CN112543093A (en) * | 2020-11-27 | 2021-03-23 | 长沙理工大学 | Image encryption method, device and storage medium based on double-entropy source hyperchaotic system |
| CN112543093B (en) * | 2020-11-27 | 2022-06-10 | 长沙理工大学 | Image encryption method, device and storage medium based on double-entropy source hyperchaotic system |
| CN114389787A (en) * | 2021-12-06 | 2022-04-22 | 中南大学 | Carrier-free information hiding method and system based on chaotic system and computer storage medium |
| CN114389787B (en) * | 2021-12-06 | 2024-05-07 | 中南大学 | Carrier-free information hiding method and system based on chaotic system and computer storage medium |
| CN115719300A (en) * | 2023-01-09 | 2023-02-28 | 浙江出海云技术有限公司 | Personnel information management method for big data |
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