CN108021814B - A kind of image encryption method of the bionical cellular automata based on balance rule - Google Patents
A kind of image encryption method of the bionical cellular automata based on balance rule Download PDFInfo
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Abstract
The invention discloses a kind of image encryption methods of bionical cellular automata based on balance rule, steps of the method are: random number is dosed at plaintext image end first with digital filling technique, it is set to be converted into the identical binary system square matrices of two sizes, respectively as two original states of bionical cellular automata, then the balance rule of a bionical cellular automata is chosen as key, is encrypted using bionical cellular automata number of iterations wheel.The method of the present invention has biggish key space, can resist various attacks, be very suitable to image encryption.
Description
Technical field
The present invention relates to a kind of image encryption methods of bionical cellular automata based on balance rule, belong to information security
Image security technology in field.
Background technique
Today's society, with the development of information age, more and more digital pictures are in transmission over networks, in cloud platform
Storage is shared in mobile terminal.The problems such as these images are directed not only to individual privacy, are more likely to concerning national security.Therefore,
Attention of the safety problem of digital picture increasingly by society and academia.Add in recent years, there is many about image
Close algorithm, wherein cellular automata because its to the sensibility of initial value, the randomness of dynamic behaviour and evolution can not be pre-
The property surveyed, is widely used in image encryption.
Cellular automata is a discrete dynamical system.Its structure is simple, and interaction part, behavior is random, and information
Highly-parallel is handled, is allowed to that there is unique advantage in image encryption field.Cellular automata is introduced into close by Wolfram earliest
Code learns field, proposes a kind of stream secrete key based on cellular automata, which is to be changed using original state as key with rule 30
Algebra time generates random sequence.Just occur many encryption technologies using cellular automata later, opens cryptography research
Uncharted field.Faraoun et al. proposes the resume image using reversible cellular automata.It is automatic using one-dimensional cellular
Machine encrypts piece image simultaneously to obtain concurrency by multiple processors.Yang et al. is proposed using One-dimensional Quantum cellular certainly
The novel quantum image encryption of motivation.But since evolutionary process is in one-dimensional level, applicable rule space is small, and diffusion is low.
Evolutionary process from One-Dimensional Extended to two dimension, is improved disadvantages mentioned above by two dimensional cellular automaton, can be generated preferably
Avalanche effect improves encryption/decryption speed.Wang et al., using be referred to as " Life of Game's " two dimensional cellular automaton to image into
Line shuffle operation.But scrambling effect is bad, there are obvious textures.Wang et al. is proposed automatic based on chaos and reversible cellular
The resume image of machine.Two original states of cellular automata are generated by the Gao Siwei of image and chaos system respectively.Though
The right algorithm can save encryption times, but additional memory space is needed to record the iteration result of last two-wheeled, to guarantee to solve
When close, also gather around there are two original state.Souyah et al. proposes a kind of image encryption of combination chaos-memory cellular automata
The diffusion part of scheme, the program is divided into two stages, successively changes pixel value in order first with chaos system, secondly uses
The further diffusion image of two-dimensional quadravalence cellular automata combination quadtree decomposition strategy.Above-mentioned several documents are all to use
While any regular is developed, cellular automata still has reversible capacity, so that rule space becomes larger.But cellular is certainly
The different local rule of motivation, generated evolution properties are different, and some shows certain and fixes or the structure of preiodic type,
Some then shows random or chaos Non-periodic Type behavior.So needing further consideration to the selection of local rule.
Summary of the invention
Aiming at the problems existing in the prior art, the present invention provides a kind of bionical cellular automata based on balance rule
Image encryption method.
The present invention uses following technical scheme to solve above-mentioned technical problem:
The present invention provides a kind of image encryption method of bionical cellular automata based on balance rule, the encryption method packet
Include following steps:
Step 1, the picture element matrix I of plaintext image is extractedm×n, wherein m is the height of plaintext image, and n is plaintext image
Width；
Step 2, by the picture element matrix I of plaintext imagem×nIt is converted into the one-dimensional sequence that length is m × n, it is then one-dimensional at this
Fill pseudo random number, the length for the pseudo random number filled in sequence endOne after the completion of filling
Tieing up sequence length is
Step 3, the one-dimensional sequence after the completion of filling is converted into binary sequence, which isThen the binary sequence is converted into two binary system square matrices Ia′×aWith matrix Ia″×a, wherein
A is the side length of binary system square matrices, is worth and is
Step 4, by binary system square matrices Ia′×aAnd Ia″×aRespectively as two initial shapes of bionical cellular automata
State C0And C1, wherein C0Indicate the state of t=0 moment bionical cellular automata, C1Indicate t=1 moment bionical cellular automata
State；
Step 5, balance rule F is chosen from bionical rule as key, and determines the number d of iteration；
Step 6, it according to balance rule F, calculatesWherein, CtIndicate that the bionical cellular of t moment is automatic
The state of machine, Ct-1Indicate the state of t-1 moment bionical cellular automata, Ct+1Indicate the shape of t+1 moment bionical cellular automata
State；
Step 7, step 6 is repeated, bionical cellular automata iteration d times, obtains two final shapes of bionical cellular automata
State CdAnd Cd+1, by CdAnd Cd+1Matrix after mergingBeing converted into length isOne-dimensional binary sequence,
The one-dimensional binary sequence, which is converted to side length, again later isDecimal system picture element matrix, the decimal system pixel
Matrix is ciphertext image.
As further technical solution of the present invention, the bionical cellular automata in step 4 has a × a cellular, Mei Geyuan
Born of the same parents have raw and dead two states, are indicated respectively with 1 and 0, each cellular and its cellular group up and down and on diagonal line
At one 3 × 3 Moore neighborhood；Preiodic type BORDER PROCESSING: the 0th row member is carried out to the borderline cellular of bionical cellular automata
The state value of born of the same parents is equal to the state value of a row cellular, and the state value of a+1 row cellular is equal to the state value of the 1st row cellular, and the 0th
The state value of column cellular is equal to the state value of a column cellular, and the state value of a+1 column cellular is equal to the state value of the 1st column cellular.
As further technical solution of the present invention, rule F=Bx/Dy is balanced in step 5, wherein B expression is lived again, D table
Show death；It is dead that Bx indicates current cellular, if must occur cellular quantity of surviving as defined in rule x in its neighborhood, that
In subsequent time, which lives again, and is still death otherwise；Dy indicates current cellular survival, if must go out in its neighborhood
Survival cellular quantity as defined in existing rule y, then the cellular is dead, otherwise, it will continue to survive in subsequent time.
As further technical solution of the present invention, the number d of iteration is determined by plaintext image size in step 5.
As further technical solution of the present invention, the number of iteration
The invention adopts the above technical scheme compared with prior art, has following technical effect that the present invention is based on balances
The image encryption method of the bionical cellular automata of rule can change simultaneously firstly, scramble and diffusion are carried out in bit levels
Become location of pixels and pixel value, improves safety and encryption efficiency.Secondly, the selected balance rule of algorithm, can make cellular certainly
The 0 of motivation and 1 is in equilibrium state, that is to say, that and it is substantially uniform in 0 and 1 quantity in cellular space, in distribution relatively
Weighing apparatus, can generate more preferably scramble and diffusion effect.
Detailed description of the invention
Fig. 1 is flow chart of the method for the present invention；
Fig. 2 is the plaintext image in the embodiment of the present invention；
Fig. 3 is the ciphertext image in the embodiment of the present invention；
Fig. 4 is the histogram of plaintext image in the embodiment of the present invention；
Fig. 5 is the histogram of ciphertext image in the embodiment of the present invention.
Specific embodiment
Technical solution of the present invention is described in further detail with reference to the accompanying drawing:
The present invention provides a kind of image encryption method of bionical cellular automata based on balance rule, as shown in Figure 1, packet
Include following steps:
Step 1, the picture element matrix I of plaintext image is extractedm×n, m is the height of plaintext image, and n is the width of plaintext image,
In pixels；
Step 2, by the picture element matrix I of plaintext imagem×nIt is converted into the one-dimensional sequence that length is m × n, is then calculated one
Tie up the length of sequence end filling pseudo random numberIf len=0, without filling, filling is completed
One-dimensional sequence length afterwards is
Step 3, the one-dimensional sequence conversion binary sequence that will have been filled, the binary sequence length are
Then binary sequence is converted into two binary system square matrices I 'a×aWith matrix I "a×a, a is matrix side length, is worth and is
Step 4, by binary matrix I "a×aWith I "a×aRespectively as two original state C of bionical cellular automata0With
C1, wherein C0Indicate the state of t=0 moment bionical cellular automata, C1Indicate the state of t=1 moment bionical cellular automata；
Step 5, balance rule F is chosen from bionical rule as key, and determines the number d of iteration；
Step 6, it according to balance rule F, calculates:CtIndicate the bionical cellular automata of t moment
State, Ct-1Indicate the state of t-1 moment bionical cellular automata, Ct+1Indicate the state of t+1 moment bionical cellular automata；
Step 7, step 6 is repeated, bionical cellular automata iteration d times, obtains two final shapes of bionical cellular automata
State CdAnd Cd+1, CdAnd Cd+1It merges into up and downAnd it is converted into length and isOne-dimensional binary sequence, it
After be reconverted into side length and beDecimal number picture element matrix, as ciphertext image
Wherein, bionical cellular automata has a × a cellular in step 4, and each cellular has raw and dead two states, point
It is not indicated with 1 and 0, the Moore neighborhood of each cellular and its cellular composition one 3 × 3 up and down and on diagonal line；It is right
The bionical borderline cellular of cellular automata carries out preiodic type BORDER PROCESSING: the state value of the 0th row cellular is equal to a row cellular
State value, the state value of a+1 row cellular are equal to the state value of the 1st row cellular, and the state value of the 0th column cellular is equal to a column member
The state value of born of the same parents, the state value of a+1 column cellular are equal to the state value of the 1st column cellular.
Wherein, rule is balanced in step 5 be given by definition:
Firstly, by formulaIn formula, ai∈ { 0,1 }, indicating whether to choose in cellular Moore type neighborhood has i
A cellular survival, if choosing ai=1, otherwise ai=0.And r is referred to as rule number, it is specified that when cellular subsequent time state changes,
The survival cellular quantity that can occur in its neighborhood；
Bionical rule uses two rules number, respectively as cellular survival and it is dead when, condition that state changes.It is fixed
Justice is F=Bx/Dy, and B expression is lived again, and D indicates dead.Bx indicates that current cellular is dead, if must advise in its neighborhood
Then survival cellular quantity as defined in number x, then the cellular is lived again in subsequent time, it is still death otherwise；Dy indicates current member
Born of the same parents' survival, if must occur cellular quantity of surviving as defined in rule y in its neighborhood, in subsequent time, the cellular
Death, otherwise, it will continue to survive；
Rule number defines the cellular quantity for occurring one or more survivals in neighborhood, each amount of survival is again different
Cellular distribution situation.In order to calculate the quantity summation for the neighborhood cellular distribution that a rule number is included, rule are first calculated
Binary number a then number0a1a2a3a4a5a6a7a8, it reuses following formula and obtains,In formula, ai∈{0,
1 }, indicate whether there be i cellular survival in cellular neighborhood, if there is ai=1, otherwise ai=0.Indicate i occur in cellular neighborhood
When a survival cellular, the quantity of cellular distribution situation in corresponding neighborhood.And sum is called state summation, if cellular is in
The state summation sum of rule number x when deadxThe state summation sum of rule number y when in survivalyIt is equal, i.e. sumx=sumy,
So the rule-like is referred to as balance rule.
Wherein, the number of iterations d in step 5 is determined by the size of plaintext image.The neighborhood of bionical cellular automata is
Moore type, iteration can only all influence eight cellulars around current cellular each time.It meanwhile and being using preiodic type boundary, institute
It can be determined as with the number of iterations
Technical solution of the present invention is described in further detail combined with specific embodiments below:
This specific embodiment is emulated using Matlab software, and original image selects the standard that size is 256 × 256 to survey
Gray level image is tried, each pixel of image is made of 8 bits, as shown in Figure 2.
Original-gray image is encrypted, detailed process is as follows:
Step 1: extracting the picture element matrix I of plaintext image256×256, the height of image is 256 pixels, and the width of image is
256 pixels.
Step 2, by plaintext image I256×256The one-dimensional sequence that length is 256 × 256 is lined up, calculates and needs in one-dimensional sequence
The length of end filling, len=0, so without filling, so, one-dimensional sequence length is
Step 3, by one-dimensional sequence conversion binary sequence, length isReconvert at
Two binary system square matrices I '512×512With matrix I "512×512。
Step 4, by binary matrix I '512×512With I "512×512Respectively as two initial shapes of bionical cellular automata
State C0And C1.The state of cellular is life or death, is indicated respectively with 1 and 0.The neighborhood of cellular be Moore type, by its up and down and
This 8 cellular compositions of diagonally opposing corner.Boundary uses preiodic type BORDER PROCESSING, and boundary connects up and down, and left and right connects, and diagonally opposing corner connects,
I.e. the state value of the 0th row cellular is equal to the state value of the 256th row cellular, and the state value of the 257th row cellular is equal to the 1st row cellular
State value, the state value of the 0th column cellular are equal to the state value of the 256th column cellular, and the state value of the 257th column cellular is equal to the 1st column
The state value of cellular.
Step 5, balance rule F is chosen from bionical rule as key.It is assumed that the balance rule selected is B298/
D484, indicates if current cellular is dead, must occur as defined in regular number 298 0 or 3 or 5 or 7 in its neighborhood and deposit
Cellular living, then in subsequent time, which can just live again, and be still death otherwise；If current cellular survival, its neighbour
Must occur 0 or 2 or 5 or 6 or 7 survival cellular as defined in regular number 484 in domain, then in subsequent time, which just can be dead
It dies, otherwise, it will continue to survive.And the state summation of rule number 298 is advised for 121 with when being in survival when cellular is in dead
Then the state summation of number 484 is 121 equal.No matter cellular is in dead or survival, and the probability of their states transformation is equal, institute
With during iteration, the 0 of cellular automata and 1 is gradually in equilibrium state.Because the neighborhood of bionical cellular automata is
Moore type, so iteration can only influence eight cellulars around current cellular each time.It meanwhile and being using preiodic type boundary.
When image is 256 × 256 size, the number of iterations is calculated as d=256.
Step 6, it according to balance rule F, calculates:
Step 7, repetition step 6, bionical cellular automata iteration 256 times, two for obtaining bionical cellular automata are final
State C512And C513, 256 × 256 decimal number picture element matrix, as ciphertext image are switched to after merging, as shown in Figure 3.
Performance evaluation is carried out to embodiment with reference to the accompanying drawing:
1, histogram analysis
The histogram of digital picture is the quantity or probability that each pixel occurs in statistical picture, can react point of image pixel
Cloth situation.In general, the pixel distribution of plaintext image changes with apparent peak valley, the letter of plaintext image can be therefrom found out
Breath.And Statistical Analysis Attacks can crack image information in the case where grasping small part information, such as histogram.So encryption
Ciphertext image afterwards, it should tend to be uniformly distributed as far as possible, effectively to cover original image information.Fig. 4 is the straight of plaintext gray level image Fig. 2
Fang Tu, Fig. 5 are the histograms using the method for the present invention ciphertext image Fig. 3 after encrypted, it can be seen that ciphertext image of the invention
Histogram distribution is relatively uniform, and fluctuation range is smaller, can resist stronger Statistical Analysis Attacks.
2, correlation analysis
Adjacent pixel correlation refers to the degree of correlation of pixel value between adjacent pixel in digital picture.Plaintext image phase
Between adjacent pixel value relatively, redundancy is high, and correlation is high.In order to cover image information, need to reduce the correlation of image.
In order to measure the image encrypted using the present invention, in horizontal, vertical, these three directions of diagonally opposing corner correlation, respectively from plain text
Image and ciphertext image are drawn up 20000 pairs of adjacent pixels in each side, their correlation is calculated according to following formula, carry out
Compare.
Wherein, x and y respectively indicates the pixel value of two neighboring pixel in image, γxyIndicate the phase of two adjacent pixels
Relationship number.
Table 1 lists the correlation of original image with ciphertext image adjacent pixel on horizontal, vertical and diagonal three directions.It can
Adjacent pixel related coefficient to find out plaintext image illustrates that its correlation is very high close to 1, and the adjacent pixel phase of ciphertext image
Relationship number illustrates that the present invention effectively reduces the relative coefficient of image close to 0.
The correlation of 1 original image of table and ciphertext image adjacent pixel on horizontal, vertical and diagonal three directions
| Correlation | Horizontal direction | Vertical direction | Diagonal direction |
| Plaintext image | 0.9771 | 0.9895 | 0.9669 |
| Ciphertext image | -0.0016 | 0.0022 | 0.0006 |
3, difference analysis
Difference analysis refers to that attacker using same key, modifies certain place value in specific plaintext image,
And influence caused by corresponding ciphertext image is observed, by comparing the relationship between the two, to obtain most probable add
Key.So needing algorithm that there is comparable sensibility to plaintext image, i.e., when plaintext image when resisting difference analysis
In any one pixel occur minor change when, this difference can be influenced into rapidly entire figure during image encryption
Picture finally makes ciphertext image that huge change occur.Usually we use change ratio of pixel (number of pixels change
Rate, NPCR) and normalization pixel value averagely change intensity (unified average changing intensity, UACI)
Two indexs are measured.
NPCR is for calculating when position a certain in plaintext image pixel value changes, and ciphertext image changes
The ratio of the total pixel of pixel quantity Zhan.For NPCR closer to 100%, algorithm implementation effect is better.UACI is to calculate to modify preceding ciphertext
The mean intensity of ciphertext image is poor after image and modification.UACI is higher, and resistance differential attack is better.Calculation formula is to set two
It is C that width, which differs only by the ciphertext image after the plaintext image encryption an of pixel,1, C2, then
Wherein, m and n indicates the width and height of image.C1(i, j), C2(i, j) is respectively ciphertext image C1, C2Middle pixel
The gray value of (i, j).
200 pixels randomly selected at different location in plaintext image graph 1 are chosen in experiment, modify the value of 1 bit, then press
It is calculated according to formula (5) and (6), obtains average value.Experimental result is as shown in table 2, and the NPCR and UACI of the method for the present invention are equal
Very close ideal desired value, this shows the method for the present invention to very sensitive in plain text.
The average value of table 2NPCR and UACI
| NPCR average value | UACI average value |
| 99.6563 | 33.4919 |
The above, the only specific embodiment in the present invention, but scope of protection of the present invention is not limited thereto, appoints
What is familiar with the people of the technology within the technical scope disclosed by the invention, it will be appreciated that expects transforms or replaces, and should all cover
Within scope of the invention, therefore, the scope of protection of the invention shall be subject to the scope of protection specified in the patent claim.
Claims (2)
1. a kind of image encryption method of the bionical cellular automata based on balance rule, which is characterized in that the encryption method packet
Include following steps:
Step 1, the picture element matrix I of plaintext image is extractedm×n, wherein m is the height of plaintext image, and n is the width of plaintext image；
Step 2, by the picture element matrix I of plaintext imagem×nIt is converted into the one-dimensional sequence that length is m × n, then in the one-dimensional sequence
Fill pseudo random number, the length for the pseudo random number filled in endOne-dimensional sequence after the completion of filling
Column length is
Step 3, the one-dimensional sequence after the completion of filling is converted into binary sequence, which isThen the binary sequence is converted into two binary system square matrices I 'a×aWith matrix I "a×a, wherein
A is the side length of binary system square matrices, is worth and is
Step 4, by binary system square matrices I 'a×aWith I "a×aRespectively as two original state C of bionical cellular automata0
And C1, wherein C0Indicate the state of t=0 moment bionical cellular automata, C1Indicate the shape of t=1 moment bionical cellular automata
State；
Step 5, balance rule F is chosen from bionical rule as key, and determines the number d of iteration；Balance rule F=Bx/
Dy, wherein B expression is lived again, and D indicates dead；Bx indicates that current cellular is dead, if must occur rule x in its neighborhood
Defined survival cellular quantity, then the cellular is lived again in subsequent time, it is still death otherwise；Dy indicates that current cellular is deposited
Living, if must occur cellular quantity of surviving as defined in rule y in its neighborhood, in subsequent time, the cellular is dead,
Otherwise, it will continue to survive；
Step 6, it according to balance rule F, calculatesWherein, CtIndicate the bionical cellular automata of t moment
State, Ct-1Indicate the state of t-1 moment bionical cellular automata, Ct+1Indicate the state of t+1 moment bionical cellular automata；
Step 7, step 6 is repeated, bionical cellular automata iteration d times, obtains two end-state C of bionical cellular automatadWith
Cd+1, by CdAnd Cd+1Matrix after mergingBeing converted into length isOne-dimensional binary sequence, Zhi Houzai
The one-dimensional binary sequence, which is converted to side length, isDecimal system picture element matrix, which is
Ciphertext image；The number d of iteration determines by plaintext image size,
2. a kind of image encryption method of bionical cellular automata based on balance rule according to claim 1, special
Sign is that the bionical cellular automata in step 4 has a × a cellular, and each cellular has raw and dead two states, respectively with 1
It is indicated with 0, the Moore neighborhood of each cellular and its cellular composition one 3 × 3 up and down and on diagonal line；To bionical
The borderline cellular of cellular automata carries out preiodic type BORDER PROCESSING: the state value of the 0th row cellular is equal to the state of a row cellular
Value, the state value of a+1 row cellular are equal to the state value of the 1st row cellular, and the state value of the 0th column cellular is equal to a column cellular
State value, the state value of a+1 column cellular are equal to the state value of the 1st column cellular.
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| CN111597574B (en) * | 2020-04-16 | 2021-03-23 | 南通职业大学 | Parallel image encryption system and method based on spatial diffusion structure |
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