CN114157408A - Digital image encryption method, digital image decryption method and digital image decryption system based on chaotic system - Google Patents
Digital image encryption method, digital image decryption method and digital image decryption system based on chaotic system Download PDFInfo
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Abstract
The invention discloses a digital image encryption method, a digital image decryption method and a digital image encryption system based on a chaotic system, which belong to the field of chaotic image encryption and comprise the following steps: taking the one-dimensional chaotic mapping as seed mapping, introducing a multiplication operator and a modulus operator, constructing a strong-power chaotic mapping, and initializing control parameters of the strong-power chaotic mapping by using a hash value of a digital image to be encrypted and an encryption key; performing multiple iterations on the strong-power chaotic mapping, extracting bits with preset lengths from chaotic state values obtained by each iteration to form corresponding pseudo-random sequences, and performing diffusion processing on image pixels of the digital image to be encrypted by using the pseudo-random sequences; and iterating the strong power chaotic mapping for multiple times again, converting the chaotic state value obtained by each iteration into integer values in a set interval until a set number of different integer values are obtained, and scrambling the image pixels after diffusion processing to obtain a final encrypted image. And the digital image is encrypted safely and effectively.
Description
Technical Field
The invention belongs to the field of chaotic image encryption, and particularly relates to a digital image encryption method, a digital image decryption method and a digital image decryption system based on a chaotic system.
Background
With the rapid development of information technology, the internet has produced a large number of digital images and has spread to all over the world through various networks. Many digital images involve private or confidential information that, once used maliciously, can be severely compromised. Therefore, before storing and transmitting the image data, the image data should be protected, wherein the image encryption is the most direct and effective scheme. However, due to the characteristics of data redundancy, large pixel correlation and the like, the digital image cannot be well processed by the traditional text information encryption technology. Therefore, various theories have entered the field of researchers, and the chaos theory is widely concerned because its inherent characteristics such as pseudo-randomness, non-linearity, long-term unpredictability, etc. are highly consistent with the requirements of digital image encryption. The digital image encryption method designed by using the chaotic system is regarded as a novel and promising technical scheme.
The chaotic mapping is of great importance in an image encryption method based on a chaotic system, and the performance of an encryption scheme greatly depends on the dynamic property of the chaotic mapping. The classic chaotic mapping has the defects of low chaotic complexity, small chaotic range and the like, and potential safety hazards are caused to a chaotic image encryption method constructed based on the classic chaotic mapping. In recent years, the dynamics of various novel chaotic maps provided by researchers have certain superiority on the whole, but the defects of not complex chaotic behaviors, not large chaotic intervals, not uniform statistical distribution, not sensitive to initial conditions and the like still exist. In addition, most chaos complexity of the newly proposed chaos mapping can only be verified through simulation experiments, and no mathematical analysis and proof exists, so that the chaos performance of the chaos mapping is lack of theoretical guarantee. Therefore, the digital image encryption scheme using the newly proposed chaotic system design often needs to use additional processing, such as embedding multiple chaotic maps, increasing encryption rounds, introducing complex scrambling or diffusion operations, and the like, so as to improve the encryption performance of the digital image encryption scheme. These additional processes will have a large impact on the efficiency of the overall encryption algorithm operation, thereby greatly limiting its usefulness. Therefore, how to construct a chaotic map with complex behaviors and simple structure and strong dynamic property and design an image encryption scheme with good performance by utilizing the strong dynamic property has important research significance and application value.
Disclosure of Invention
Aiming at the defects and the improvement requirements of the prior art, the invention provides a digital image encryption method, a digital image decryption method and a digital image encryption system based on a chaotic system, and aims to carry out diffusion and scrambling operations on pixels of a plaintext image by constructing the chaotic system with strong dynamic property so as to improve the security of image data encryption.
To achieve the above object, according to an aspect of the present invention, there is provided a digital image encryption method based on a chaotic system, including: s1, taking the one-dimensional chaotic map as a seed map, introducing a multiplication operator and a module operator to construct a strong-power chaotic map, and initializing control parameters of the strong-power chaotic map by using a hash value of a digital image to be encrypted and a randomly set encryption key; s2, performing multiple iterations on the strong power chaotic map, wherein the iteration times are determined by the size of the digital image to be encrypted, extracting bits with preset length from the chaotic state value obtained by each iteration to form a corresponding pseudo-random sequence, and performing diffusion processing on image pixels of the digital image to be encrypted by using the pseudo-random sequence; s3, iterating the strong power chaotic mapping for multiple times, and converting the chaotic state value obtained by each iteration into integer values in a set interval according to a preset conversion relation until a set number of different integer values are obtained; and S4, scrambling the image pixels after the diffusion processing by using the set number of different integer values to obtain a final encrypted image.
Further, the strong power chaos map constructed in S1 is:
xi+1＝sF(μ，xi)modR
wherein x isiFor the chaotic state value, x, obtained for the i-1 st iterationi+1Is the chaos state value obtained by the ith iteration, F (mu, x)i) The method is one-dimensional chaotic mapping, s is a first control parameter, mu is a second control parameter, modR is a modulo operator for limiting the chaotic state value to be between 0 and R, and R is a preset integer.
Further, the control parameters initialized in S1 are:
s＝(a+h(P))modk
μ＝(b+h(P))modk
wherein s is a first control parameter, μ is a second control parameter, a is a first encryption key, b is a second encryption key, k is a third encryption key, P is the digital image to be encrypted, h (-) is a hash function, and modk is a modulo operator defining the control parameter between 0 and k.
Further, the pseudo random sequence formed in S2 is:
M[32(i-1)+1]∶32i＝T(bin(xi))1∶32
wherein M is[32(i-1)+1]∶32iIs xiCorresponding pseudo-random sequence, xiH W/4 for the chaos state value obtained from the i-1 th iteration, i ═ 1,2,3.. H and W are the length and width of the digital image to be encrypted, respectively, and bin (·) is a function for converting the chaos state value into a binary bit stream, T (·)1∶32Is a function of extracting the first 32 bits of the binary bit stream.
Further, the image pixels after the diffusion processing in S2 are:
Pd(j)＝(P(j)+dec(M8(j-1)+1∶8j))mod 256
wherein, Pd(j) Is the jth image pixel in the digital image to be encrypted after diffusion processing, P (j) is the jth image pixel in the digital image to be encrypted before diffusion processing, dec (-) is a function for converting binary bits into decimal integers, M8(j-1)+1∶8jThe 8(j-1) +1 to 8j bits, j 1,2,3.. H × W, mod256, which are combined in sequence for each pseudorandom sequence, are modulo operators that define image pixels between 0 and 256.
Further, the setting interval is [0, 255], and the preset conversion relationship is:
Ii＝floor(xi×2n)
wherein, IiIs xiConverted integer value, xiFor the chaotic state value, flo, obtained for the i-1 st iterationor (-) is a function of the largest integer with output no greater than a given value, and n is the number of pixel bits.
Further, the scrambling operation in S4 is:
C(j)＝N[Pd(j)]
wherein C (j) is the j encrypted image pixel obtained after the scrambling operation, Pd(j) And j is 1,2, 3.H × W, and N is a sequence composed of the set number of different integer values, for the jth image pixel in the digital image to be encrypted after the diffusion processing.
According to another aspect of the present invention, there is provided a chaotic system based digital image decryption method for decrypting an encrypted image obtained by the chaotic system based digital image encryption method, the decryption operation being:
D(j)＝(index(N，Pd(j))-dec(M8(j-1)+1∶8j))mod 256
wherein D (j) is the j-th decrypted image pixel obtained after decryption, and index (-) is used for outputting Pd(j) Indexing a function of values in N, N being a sequence of a set number of different integer values, Pd(j) For the jth image pixel in the digital image to be encrypted after diffusion processing, dec (-) is a function for converting binary bits into decimal integers, M8(j-1)+1∶8jThe 8(j-1) +1 to 8j bits, j 1,2,3.. H × W, mod256, which are combined in sequence for each pseudorandom sequence, are modulo operators that define image pixels between 0 and 256.
According to another aspect of the present invention, there is provided a digital image encryption system based on a chaotic system, comprising: the construction and initialization module is used for taking the one-dimensional chaotic mapping as seed mapping, introducing a multiplication operator and a module operator to construct a strong power chaotic mapping, and initializing control parameters of the strong power chaotic mapping by utilizing a hash value of a digital image to be encrypted and a randomly set encryption key; the iteration and diffusion processing module is used for carrying out multiple iterations on the strong power chaotic mapping, the iteration times are determined by the size of the digital image to be encrypted, bits with preset lengths are extracted from chaotic state values obtained by each iteration to form corresponding pseudo-random sequences, and the pseudo-random sequences are used for carrying out diffusion processing on image pixels of the digital image to be encrypted; the second iteration module is used for carrying out multiple iterations on the strong power chaotic mapping again, and converting the chaotic state value obtained by each iteration into an integer value in a set interval according to a preset conversion relation until a set number of different integer values are obtained; and the scrambling encryption module is used for scrambling the image pixels subjected to the diffusion processing by using the set number of different integer values to obtain a final encrypted image.
According to another aspect of the present invention, there is provided a digital image decryption system based on a chaotic system, comprising: the decryption module is used for decrypting the encrypted image obtained by the digital image encryption method based on the chaotic system, and the decryption operation is as follows:
D(j)＝(index(N，Pd(j))-dec(M8(j-1)+1∶8j))mod 256
wherein D (j) is the j-th decrypted image pixel obtained after decryption, and index (-) is used for outputting Pd(j) Indexing a function of values in N, N being a sequence of a set number of different integer values, Pd(j) For the jth image pixel in the digital image to be encrypted after diffusion processing, dec (-) is a function for converting binary bits into decimal integers, M8(j-1)+1∶8jThe 8(j-1) +1 to 8j bits, j 1,2,3.. H × W, mod256, which are combined in sequence for each pseudorandom sequence, are modulo operators that define image pixels between 0 and 256.
Generally, by the above technical solution conceived by the present invention, the following beneficial effects can be obtained:
(1) the multiplicative operator and the modular operator are introduced, the multiplicative operator can further expand the state values of all chaotic mappings, and the modular operator can bring more distant values back to the phase space, so that the constructed chaotic system has stronger dynamic property, and the corresponding strong-power chaotic mapping has the advantages of high complexity, large chaotic interval, strong pseudo-randomness, high sensitivity to initial conditions and the like, thereby laying a good foundation for the design of the whole algorithm and effectively improving the encryption performance of the algorithm;
(2) furthermore, the image encryption method fully utilizes the strong dynamic property of chaotic mapping, can effectively encrypt the image without introducing additional complex operation, greatly improves the running speed of the algorithm on the basis of ensuring the encryption performance, and improves the practicability of the encryption method;
(3) any one of the existing one-dimensional chaotic maps can be used as a seed map to be input into the chaotic system to generate a new strong power chaotic map, so that the flexibility of the whole encryption algorithm is greatly improved, meanwhile, an attacker is prevented from attacking the algorithm by guessing the seed chaotic map, and the encryption safety is improved;
(4) in addition, the plaintext image information is closely associated with the control parameters of the strong-power chaotic mapping, any tiny change of the plaintext image can cause the finally output encrypted image to be completely different, and the encryption method has enough capacity of resisting typical attacks such as differential analysis and the like.
Drawings
Fig. 1 is a flowchart of a digital image encryption method based on a chaotic system according to an embodiment of the present invention;
fig. 2A is an iteration function diagram of Logistic mapping according to an embodiment of the present invention;
fig. 2B is an iteration function diagram of the SLM with strong-power chaotic mapping, which is constructed after the multiplicative operator and the modular operator are introduced according to the embodiment of the present invention;
fig. 3 is a bifurcation diagram of the strong power chaotic map provided by the embodiment of the present invention;
FIG. 4 is a Lyapunov exponent diagram of the strong power chaos mapping provided by the embodiment of the invention;
fig. 5A is a state value statistical distribution diagram of the strong power chaotic map provided by the embodiment of the present invention under different first control parameter values;
fig. 5B is a state value statistical distribution diagram of the strong power chaotic map provided by the embodiment of the present invention under different second control parameter values;
FIG. 6 is an initial condition sensitivity graph of a strong power chaotic map provided by an embodiment of the present invention;
fig. 7A, fig. 7B and fig. 7C are a plaintext diagram, an encryption diagram and a decryption diagram provided in the embodiment of the present invention in sequence;
fig. 8A, 8B and 8C are the statistical histograms of the plaintext diagram, the encrypted diagram and the decrypted diagram provided by the embodiment of the present invention in sequence;
FIGS. 9A-9D are the original plaintext image and the secret key K provided by the embodiment of the invention in sequence1Encrypted ciphertext image C1Secret key K2Encrypted ciphertext image C2、C1And C2Absolute difference image therebetween;
FIGS. 9E-9H are diagrams illustrating a key K according to an embodiment of the present invention1Decrypting ciphertext image C1The resulting decrypted image D1Secret key K2Decrypting ciphertext image C1The resulting decrypted image D2Secret key K3Decrypting ciphertext image C1The resulting decrypted image D3、D2And D3Absolute difference image therebetween;
fig. 10 is a block diagram of a digital image encryption system based on a chaotic system according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
In the present application, the terms "first," "second," and the like (if any) in the description and the drawings are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order.
Fig. 1 is a flowchart of a digital image encryption method based on a chaotic system according to an embodiment of the present invention. Referring to fig. 1, with reference to fig. 2A to 9H, the digital image encryption method based on the chaotic system according to the present embodiment will be described in detail, and the method includes operations S1 to S4.
And operation S1, taking the one-dimensional chaotic map as a seed map, introducing a multiplication operator and a module operator to construct a strong-power chaotic map, and initializing control parameters of the strong-power chaotic map by using the hash value of the digital image to be encrypted and a randomly set encryption key.
In one embodiment, operation S1 includes a sub-operation S11-sub-operation S12.
In the sub-operation S11, a multiplication operator and a modulo operator are introduced to construct a chaotic system with strong dynamic properties, and any one existing one-dimensional chaotic map is used as a seed map and input into the constructed chaotic system, thereby generating a new strong dynamic chaotic map. The constructed strong power chaos is mapped as follows:
xi+1＝sF(μ，xi)modR
wherein x isiFor the chaotic state value, x, obtained for the i-1 st iterationi+1Is the chaos state value obtained by the ith iteration, F (mu, x)i) The method is one-dimensional chaotic mapping, s is a first control parameter, mu is a second control parameter, modR is a modulo operator for limiting the chaotic state value to be between 0 and R, and R is a preset integer.
It should be noted that any one of the existing one-dimensional chaotic maps (e.g., Logistic map, Tent map, Sine map) can be used as a seed map and input into the chaotic system to generate a new chaotic map with strong dynamic properties. Taking the Logistic mapping as the seed mapping as an example, the constructed strong power chaotic mapping SLM is:
xn+1＝(s(μxn(1-xn)))mod1
in the field of chaos research, the Lyapunov exponent is an important index for measuring the complexity of chaos mapping. The Lyapunov exponent is positive, which indicates that the chaotic mapping can show chaotic behaviors under the current parameter configuration, and the greater the Lyapunov exponent value is, the stronger the chaotic complexity of the mapping is. Based on mathematical analysis of the lyapunov exponent, the embodiment proves that any new chaotic map generated by the chaotic system is stronger than the complexity of the corresponding seed chaotic map, and a detailed proving process is described below.
Since the mathematical definition of the Lyapunov exponent is derived from the concept of the track slope of the chaotic system, the track slope is not affected by the modular operation. Therefore, in the process of analyzing the lyapunov exponent, the modular operation is omitted, and the constructed chaotic map can be rewritten as:
xn+1＝s(xn)＝sF(μ，xn)
suppose y0And x0Are two very close initial values, then after the first iteration y1And x1The difference between them is:
furthermore, because:
therefore, | y1-x1| can be rewritten as:
similarly, after the second iteration, y2And x2The difference between them is:
after the nth (n → ∞) iteration, ynAnd xnThe difference between them is:
thus, the average divergence Δ after n iterationss(x)Comprises the following steps:
by definition, the Lyapunov exponent lambda of the chaotic systems(x)Comprises the following steps:
wherein λ isF(μ，x)The lyapunov exponent is mapped for the corresponding seed.
The above theoretical analysis shows that: compared with seed chaotic mapping, the new chaotic mapping generated by the chaotic system constructed in the embodiment has better chaotic complexity, and provides theoretical guarantee for the encryption performance of a digital image encryption method based on the strong power chaotic mapping design.
The strong dynamic property of the chaotic system constructed in the embodiment is verified through simulation experiments, and the simulation results are shown in fig. 2A-6.
Fig. 2A and 2B graphically illustrate the mechanism of action of the multiplicative and modulo operators introduced in the SLM. Comparing fig. 2A and fig. 2B, it can be seen that, on the basis of Logistic chaotic mapping, the multiplication operator of the SLM can further expand the state value of Logistic chaotic mapping, and the modulo operator can bring a farther value back into the phase space again, which means that the separation rate between the chaotic tracks of the SLM is faster and more unstable than that of Logistic mapping. In addition, it can be observed in fig. 2B that the slope of point a is identical to the slope of the end' point, and therefore the first derivative of these two points is also identical. This indicates that although the chaotic orbits that exceed the phase space are brought back into the phase space, the increasing effect of the rate of separation and instability of the chaotic orbits caused by the multiplicative and modulo operators will be preserved unaffected. The action mechanism is completely different from many typical chaotic maps (such as Logistic map, Tent map and the like), and has a unique translation effect.
Based on this, the role of the multiplier and the modulus operator introduced in the strong dynamics chaotic system constructed in the embodiment is not only the same as that of the stretching and folding operation used in the typical chaotic mapping, but also has stronger effect. The new chaotic map generated by the chaotic system is actually based on the seed chaotic map at the bottom layer, and an enhanced stretching and folding operation is executed, which is the root cause for the chaotic map to have strong dynamic property.
The present embodiment also provides a bifurcation diagram, Lyapunov exponent, state value statistical distribution diagram, and initial condition sensitivity diagram of the SLM when s, μ ∈ [500, 600], as shown in FIGS. 3, 4, 5A, 5B, and 6, respectively. Referring to fig. 3, 4, 5A, 5B and 6, it can be seen that the SLM has high chaotic complexity, large chaotic interval, strong pseudo-randomness and high sensitivity to initial conditions, which lays a good foundation for the design of digital image encryption algorithm.
In sub-operation S22, the hash value of the digital image to be encrypted and the randomly set initial encryption key are associated to initialize the control parameters of the strong power chaotic map, where the initialized control parameters are:
s＝(a+h(P))modk
μ＝(b+h(P))modk
wherein s is a first control parameter, μ is a second control parameter, a is a first encryption key, b is a second encryption key, k is a third encryption key, P is a digital image to be encrypted, h (-) is a hash function, modk is a modulo operator defining the control parameter between 0 and k, a, b, k belongs to R+. Specifically, h (·) is, for example, an MD5 hash function. Since the SLM can show complex chaotic behaviors in a huge control parameter space, the method of coupling the hash value of the plaintext image and the secret key together for setting the control parameters fully utilizes the dynamic property of the SLM, and greatly improves the sensitivity of the whole encryption scheme to the plaintext and the secret key.
And operation S2, performing multiple iterations on the strong-power chaotic map, wherein the iteration times are determined by the size of the digital image to be encrypted, extracting bits with preset lengths from the chaotic state value obtained by each iteration to form a corresponding pseudo-random sequence, and performing diffusion processing on image pixels of the digital image to be encrypted by using the pseudo-random sequence.
Operation S2 includes sub-operation S21-sub-operation S22, according to an embodiment of the invention.
In sub-operation S21, the strong-power chaotic map is iterated many times, and bits with a preset length are extracted from the chaotic state value obtained in each iteration to form a corresponding pseudorandom sequence:
M[32(i-1)+1]∶32i＝T(bin(xi))1∶32
wherein M is[32(i-1)+1]∶32iIs xiCorresponding pseudo-random sequence, xiH W/4 for the chaotic state values obtained for the i-1 th iteration, i ═ 1,2,3.. H and W are the length and width, respectively, of the digital image to be encrypted, bin (·) is a function that converts the chaotic state values into a binary bitstream according to the IEEE754 standard, T (·)1∶32Is a function of extracting the first 32 bits of the binary bit stream.
It should be noted that most existing chaotic mapping dynamics are not strong enough, and most schemes only extract one-digit bits from one state value in order to ensure that the generated pseudo-random sequence can pass the randomness test. The dynamic nature of the chaotic map constructed in this embodiment is strong enough that the first 32 bits can be extracted from each chaotic state value to form a high quality pseudorandom sequence required to perform the diffusion operation. Therefore, for the gray-scale image encryption, the pseudo-random array which is enough for subsequent use can be generated only by iterating the strong-power chaotic mapping H × W/4 times in the sub-operation S21, and the operation efficiency of the encryption scheme is greatly improved.
In sub-operation S22, the pixels of the digital image P to be encrypted are recombined in order into a bit array, and the image pixels of the digital image P to be encrypted are subjected to diffusion processing using a pseudorandom sequence. The recombination order is, for example, from left to right, from top to bottom, and the image pixels after diffusion processing are:
Pd(j)＝(P(j)+dec(M8(j-1)+1∶8j))mod 256
wherein, Pd(j) Is added after diffusion treatmentJ image pixel in the digital image, P (j) is j image pixel in the digital image to be encrypted before diffusion processing, dec (-) is a function for converting binary bit into decimal integer, M8(j-1)+1∶8jThe 8(j-1) +1 to 8j bits, j 1,2,3.. H × W, mod256, which are combined in sequence for each pseudorandom sequence, are modulo operators that define image pixels between 0 and 256.
In operation S3, the strong-power chaotic map is iterated again for multiple times, and the chaotic state value obtained in each iteration is converted into an integer value in the set interval according to the preset conversion relationship until a set number of different integer values are obtained.
Specifically, operation S3 includes sub-operation S31-sub-operation S34.
In sub-operation S31, a null sequence N of length equal to the set number is defined for storing the integer value to be generated. The set number is 256, for example. It is understood that the set number may have other values.
In sub-operation S32, the strong-power chaotic map is iterated once, and the current chaotic state value is converted into an integer value within a set interval according to a preset conversion relationship.
According to the embodiment of the present invention, the setting interval is [0, 255], and the preset conversion relationship is:
Ii＝floor(xi×2n)
wherein, IiIs xiConverted integer value, xiFor the chaotic state value obtained by the i-1 iteration, floor (.) is a function of the maximum integer which is not more than a given value, and n is the pixel bit number. In this embodiment, n is 8.
In suboperation S33, it is determined whether an integer value I already exists in the sequence NiIf present, discarding the integer value IiIf not, the integer value IiInserted into the sequence N.
In sub-operation S34, the above sub-operations S32 and S33 are repeatedly performed until the sequence N is filled.
In operation S4, the diffusion-processed image pixels are scrambled using a set number of different integer values to obtain a final encrypted image.
According to the embodiment of the present invention, the scrambling operation in operation S4 is:
C(j)＝N[Pd(j)]
wherein C (j) is the j encrypted image pixel obtained after the scrambling operation, Pd(j) J is 1,2,3.. H.W.N is a sequence formed by setting different integer values in number, and an image C formed by combining encrypted image pixels C (j) is a final ciphertext image.
In order to evaluate the overall performance of the digital image encryption method based on the chaotic system in the embodiment, the digital image encryption method is evaluated in the following five aspects of simulation results, statistical histograms, key sensitivity, correlation analysis and differential attack resistance analysis.
(1) Simulation result
A well-designed image encryption method should have the ability to convert a plaintext image into an unrecognizable ciphertext image, while only using the correct key can completely restore the ciphertext image to the original plaintext image. In this embodiment, a classical image Lena is selected from a standard image database to simulate the encryption and decryption process of the set algorithm. The key is randomly set to a 120, b 150, p 800, x00.123. The experimental results are shown in fig. 7A, 7B and 7C. Referring to fig. 7A and 7B, it can be seen that after the plaintext image in fig. 7A is encrypted, a ciphertext image similar to random noise is output as shown in fig. 7B, and no visual information is observed by a human. After decryption using the same key, a decrypted image as shown in fig. 7C is obtained, which completely coincides with the original plaintext image shown in fig. 7A. The simulation result verifies the correctness and the effectiveness of the digital image encryption method based on the chaotic system designed by the embodiment.
(2) Statistical histogram
A statistical histogram of an image can intuitively reflect the distribution of image pixels, and thus an attacker generally analyzes the relationship between a plaintext image and a ciphertext image using the statistical histogram. A well-designed image encryption method should have a uniform distribution of the statistical histogram of the ciphertext. Fig. 8A, 8B, and 8C show the statistical histograms of the plaintext image, the ciphertext image, and the decrypted image of Lena, respectively. Referring to fig. 8A, it can be seen that the statistical histogram of the plaintext image exhibits a distinct distribution pattern, and thus a large amount of image information can be inferred. Referring to fig. 8B, it can be seen that the histogram of the ciphertext image is uniformly distributed, and thus, it is difficult for an attacker to obtain the original information from the ciphertext image. Experiments show that the digital image encryption method based on the chaotic system designed by the embodiment has better capability of resisting the histogram attack.
(3) Key sensitivity
The sensitivity to the key means that small changes of the key can cause encryption and decryption to produce completely different results, and is one of the basic characteristics that a well-designed image encryption method should have. If the key sensitivity of the algorithm is weak, it means that the original image can be successfully restored using the wrong key, which makes the actual key space much smaller than the theoretical key space and thus greatly reduces the security of the algorithm. In the digital image encryption method design of the present embodiment, the encryption key is highly coupled with the control parameters of the SLM, and since SLM mapping has strong initial condition sensitivity, the encryption method is naturally highly sensitive to the key as well. Referring to fig. 9A to 9H, a key sensitivity test analysis process of the digital image encryption method designed in the present embodiment is visually illustrated.
FIG. 9A shows an original plaintext image P, and FIG. 9B shows a key K1Ciphertext image C obtained by encrypting image P1FIG. 9C shows the use of a secret key K2Ciphertext image C obtained by encrypting image P2Secret key K1And a secret key K2With a slight difference therebetween, FIG. 9D shows a ciphertext image C1And ciphertext image C2Absolute difference image | C between1-C2L. Referring to the test results shown in fig. 9A-9D, it can be seen that the results of the ciphertext images output by encrypting the same plaintext with the key having a small difference are completely different, and the difference rate of the pixels reaches about 99.6%.
FIG. 9E shows a secret key K1Decrypting ciphertext image C1The resulting decrypted image D1FIG. 9F shows the use of a secret key K2Decrypting ciphertext image C1The resulting decrypted image D2FIG. 9G shows a use and key K1Key K with minor differences3Decrypting ciphertext image C1The resulting decrypted image D3FIG. 9H is a decrypted image D2And decrypting the image D3Absolute difference image | D of2-D3L. Referring to the test results shown in fig. 9E-9H, it can be seen that the original image can be successfully decrypted from the ciphertext image only by using the encryption key, and the decryption results of other keys are unidentifiable and have about 99.6% pixel difference. Therefore, the image encryption method designed by the embodiment has good key sensitivity in the encryption and decryption stages.
(4) Correlation analysis
The image acts as a carrier of visual information, with neighboring pixels having strong correlation in various directions. This correlation needs to be eliminated as much as possible in the encryption process so that there is no relationship between the original image and its ciphertext image, thereby defending against the correlation analyzer attack. Table 1 shows correlation coefficients of Lena plaintext image and its ciphertext image in horizontal direction, vertical direction, and diagonal direction, where 2000 pairs of adjacent pixels are selected in each direction.
TABLE 1
| Pixel point | Plaintext image correlation | Ciphertext image correlation |
| Horizontally adjacent pixel points | 0.9888 | 0.0060 |
| Vertically adjacent pixel points | 0.9735 | 0.0020 |
| Diagonally adjacent pixel points | 0.9613 | 0.0022 |
As can be seen from table 1, the correlation of the plaintext image in three directions is very high, and after the digital image encryption method designed in this embodiment is used for encryption, the correlation coefficient of the ciphertext image in three directions is close to 0. This shows that the digital image encryption method in the present embodiment can efficiently decorrelate high correlation of the plaintext image.
(5) Analysis against differential attacks
The differential attack is a typical cryptoanalysis method, and an attacker tries to establish a relationship between a plaintext image and a ciphertext image by analyzing the influence of the change of plaintext image information on an encryption result. Therefore, for a good image encryption method, even if the difference between two plaintext images is only one bit, there should not be any potential relationship between the generated ciphertext images after being encrypted using the same key. In engineering, the capability of an image encryption algorithm to resist differential attacks is generally evaluated by using two indexes, namely a pixel change ratio NPCR and a uniform average change degree UACI. The pixel change ratio NPCR is a ratio of the number of pixels that change in the corresponding ciphertext to the total number of pixels when a pixel value of the plaintext image changes; the unified average change degree UACI reflects the degree of change of the corresponding pixel point value. The ideal values of NPCR and UACI are 99.6094% and 33.4635%, respectively, and the closer the calculated values are to the ideal values, the stronger the image encryption algorithm is against attacks.
In the test, firstly, the digital image encryption method in the embodiment is used for encrypting the plaintext image Lena to obtain the ciphertext image thereof, then, one bit of the plaintext image is randomly changed and encrypted by using the same secret key to obtain another ciphertext image, and finally, the NPCR and UACI values between the two ciphertext images are calculated. The above test was repeated 200 times, and the obtained average NPCR and UACI reached 99.6094% and 33.4633%, respectively, which were extremely close to the ideal values. Based on this, the digital image encryption method in the embodiment has strong capability of resisting differential attack.
According to the above all test analysis results, the digital image encryption method based on the chaotic system in the embodiment makes full use of the strong dynamic property of the constructed new chaotic mapping, can safely and effectively encrypt the digital image, and is particularly suitable for the safe transmission of the digital image in the broadband open environment.
Fig. 10 is a block diagram of a digital image encryption system based on a chaotic system according to an embodiment of the present invention. Referring to fig. 10, the chaotic system based digital image encryption system 100 includes a construction and initialization module 110, an iteration and diffusion processing module 120, a second iteration module 130, and a scrambling encryption module 140.
The constructing and initializing module 110, for example, performs operation S1, and is configured to use the one-dimensional chaotic map as a seed map, introduce a multiplication operator and a modulo operator to construct a strong-power chaotic map, and initialize control parameters of the strong-power chaotic map by using the hash value of the digital image to be encrypted and the randomly set encryption key.
The iteration and diffusion processing module 120, for example, performs operation S2, and is configured to perform multiple iterations on the strong-power chaotic map, where the iteration number is determined by the size of the digital image to be encrypted, extract bits with a preset length from the chaotic state value obtained in each iteration to form a corresponding pseudorandom sequence, and perform diffusion processing on image pixels of the digital image to be encrypted by using the pseudorandom sequence.
The second iteration module 130, for example, performs operation S3, to perform multiple iterations on the strong power chaotic map again, and convert the chaotic state value obtained by each iteration into an integer value in a set interval according to a preset conversion relation until a set number of different integer values are obtained.
The scramble encryption module 140 performs, for example, operation S4 to perform a scrambling operation on the diffusion-processed image pixels with a set number of different integer values to obtain a final encrypted image.
The chaotic system based digital image encryption system 100 is used to perform the chaotic system based digital image encryption method in the embodiments shown in fig. 1-9H. For details, please refer to the digital image encryption method based on the chaotic system in the embodiments shown in fig. 1 to fig. 9H, which will not be described herein again.
The embodiment of the invention also provides a digital image decryption method based on the chaotic system, which is used for decrypting the encrypted image obtained by the digital image encryption method based on the chaotic system in the embodiment shown in the figures 1-9H. The specific decryption operation is as follows:
D(j)＝(index(N，Pd(j))-dec(M8(j-1)+1∶8j))mod 256
wherein D (j) is the j-th decrypted image pixel obtained after decryption, and index (-) is used for outputting Pd(j) Indexing a function of values in N, N being a sequence of a set number of different integer values, Pd(j) For the jth image pixel in the digital image to be encrypted after diffusion processing, dec (-) is a function for converting binary bits into decimal integers, M8(j-1)+1∶8jThe 8(j-1) +1 to 8j bits, j 1,2,3.. H × W, mod256, which are combined in sequence for each pseudorandom sequence, are modulo operators that define image pixels between 0 and 256.
For details, please refer to the digital image encryption method based on the chaotic system in the embodiments shown in fig. 1 to fig. 9H, which will not be described herein again.
The embodiment of the invention also provides a digital image decryption system based on the chaotic system, which comprises a decryption module. The decryption module is used for decrypting the encrypted image obtained by the digital image encryption method based on the chaotic system in the embodiments shown in fig. 1-9H. The specific decryption operation is as follows:
D(j)＝(index(N，Pd(j))-dec(M8(j-1)+1∶8j))mod 256
wherein D (j) is the j-th decrypted image pixel obtained after decryption, and index (-) is used for outputting Pd(j) Indexing a function of values in N, N being a sequence of a set number of different integer values, Pd(j) For the jth image pixel in the digital image to be encrypted after diffusion processing, dec (-) is a function for converting binary bits into decimal integers, M8(j-1)+1∶8jThe 8(j-1) +1 to 8j bits, j 1,2,3.. H × W, mod256, which are combined in sequence for each pseudorandom sequence, are modulo operators that define image pixels between 0 and 256.
For details, please refer to the digital image encryption method based on the chaotic system in the embodiments shown in fig. 1 to fig. 9H, which will not be described herein again.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (10)
1. A digital image encryption method based on a chaotic system is characterized by comprising the following steps:
s1, taking the one-dimensional chaotic map as a seed map, introducing a multiplication operator and a module operator to construct a strong-power chaotic map, and initializing control parameters of the strong-power chaotic map by using a hash value of a digital image to be encrypted and a randomly set encryption key;
s2, performing multiple iterations on the strong power chaotic map, wherein the iteration times are determined by the size of the digital image to be encrypted, extracting bits with preset length from the chaotic state value obtained by each iteration to form a corresponding pseudo-random sequence, and performing diffusion processing on image pixels of the digital image to be encrypted by using the pseudo-random sequence;
s3, iterating the strong power chaotic mapping for multiple times, and converting the chaotic state value obtained by each iteration into integer values in a set interval according to a preset conversion relation until a set number of different integer values are obtained;
and S4, scrambling the image pixels after the diffusion processing by using the set number of different integer values to obtain a final encrypted image.
2. The chaotic system-based digital image encryption method according to claim 1, wherein the strong power chaotic map constructed in S1 is:
xi+1＝sF(m,xi)mod R
wherein x isiFor the chaotic state value, x, obtained for the i-1 st iterationi+1Is the chaos state value obtained by the ith iteration, F (mu, x)i) The method is one-dimensional chaotic mapping, s is a first control parameter, mu is a second control parameter, mod R is a modulo operator limiting the chaotic state value to be between 0 and R, and R is a preset integer.
3. The chaotic system-based digital image encryption method according to claim 1, wherein the control parameters initialized in S1 are:
s＝(a+h(P))mod k
μ＝(b+h(P))mod k
wherein s is a first control parameter, μ is a second control parameter, a is a first encryption key, b is a second encryption key, k is a third encryption key, P is the digital image to be encrypted, h (-) is a hash function, mod k is a modulo operator defining the control parameter between 0 and k.
4. The chaotic system-based digital image encryption method according to claim 1, wherein the pseudo random sequence formed in S2 is:
M[32(i-1)+1]:32i＝T(bin(xi))1:32
wherein M is[32(i-1)+1]:32iIs xiCorresponding pseudo-random sequence，xiH W/4 for the chaos state value obtained from the i-1 th iteration, i ═ 1,2,3.. H and W are the length and width of the digital image to be encrypted, respectively, and bin (·) is a function for converting the chaos state value into a binary bit stream, T (·)1:32Is a function of extracting the first 32 bits of the binary bit stream.
5. The chaotic system-based digital image encryption method according to claim 4, wherein the image pixels subjected to the diffusion processing in S2 are:
Pd(j)＝(P(j)+dec(M8(j-1)+1:8j))mod256
wherein, Pd(j) Is the jth image pixel in the digital image to be encrypted after diffusion processing, P (j) is the jth image pixel in the digital image to be encrypted before diffusion processing, dec (-) is a function for converting binary bits into decimal integers, M8(j-1)+1:8jThe 8(j-1) +1 to 8j bits, j 1,2,3.. H × W, mod256, which are combined in sequence for each pseudorandom sequence, are modulo operators that define image pixels between 0 and 256.
6. The chaotic system-based digital image encryption method according to claim 1, wherein the setting interval is [0, 255], and the preset transformation relationship is:
Ii＝floor(xi×2n)
wherein, IiIs xiConverted integer value, xiFor the chaos state value obtained by the i-1 st iteration, floor (·) is a function of the maximum integer with the output not greater than a given value, and n is the pixel bit number.
7. The chaotic system-based digital image encryption method according to any one of claims 1-6, wherein the scrambling operation in S4 is:
C(j)＝N[Pd(j)]
wherein C (j) is the j encrypted image pixel obtained after the scrambling operation, Pd(j) For the digital image to be encrypted after diffusion processingJ ═ 1,2,3.. H × W, N is a sequence of the set number of different integer values.
8. A chaotic system based digital image decryption method, for decrypting an encrypted image obtained by the chaotic system based digital image encryption method according to any one of claims 1 to 7, the decryption operation being:
D(j)＝(index(N,Pd(j))-dec(M8(j-1)+1:8j))mod256
wherein D (j) is the j-th decrypted image pixel obtained after decryption, and index (-) is used for outputting Pd(j) Indexing a function of values in N, N being a sequence of a set number of different integer values, Pd(j) For the jth image pixel in the digital image to be encrypted after diffusion processing, dec (-) is a function for converting binary bits into decimal integers, M8(j-1)+1:8jThe 8(j-1) +1 to 8j bits, j 1,2,3.. H × W, mod256, which are combined in sequence for each pseudorandom sequence, are modulo operators that define image pixels between 0 and 256.
9. A digital image encryption system based on a chaotic system is characterized by comprising:
the construction and initialization module is used for taking the one-dimensional chaotic mapping as seed mapping, introducing a multiplication operator and a module operator to construct a strong power chaotic mapping, and initializing control parameters of the strong power chaotic mapping by utilizing a hash value of a digital image to be encrypted and a randomly set encryption key;
the iteration and diffusion processing module is used for carrying out multiple iterations on the strong power chaotic mapping, the iteration times are determined by the size of the digital image to be encrypted, bits with preset lengths are extracted from chaotic state values obtained by each iteration to form corresponding pseudo-random sequences, and the pseudo-random sequences are used for carrying out diffusion processing on image pixels of the digital image to be encrypted;
the second iteration module is used for carrying out multiple iterations on the strong power chaotic mapping again, and converting the chaotic state value obtained by each iteration into an integer value in a set interval according to a preset conversion relation until a set number of different integer values are obtained;
and the scrambling encryption module is used for scrambling the image pixels subjected to the diffusion processing by using the set number of different integer values to obtain a final encrypted image.
10. A digital image decryption system based on a chaotic system, comprising:
a decryption module, configured to decrypt the encrypted image obtained by the chaotic system based digital image encryption method according to any one of claims 1 to 7, wherein the decryption operation is:
D(j)＝(index(N,Pd(j))-dec(M8(j-1)+1:8j))mod256
wherein D (j) is the j-th decrypted image pixel obtained after decryption, and index (-) is used for outputting Pd(j) Indexing a function of values in N, N being a sequence of a set number of different integer values, Pd(j) For the jth image pixel in the digital image to be encrypted after diffusion processing, dec (-) is a function for converting binary bits into decimal integers, M8(j-1)+1:8jThe 8(j-1) +1 to 8j bits, j 1,2,3.. H × W, mod256, which are combined in sequence for each pseudorandom sequence, are modulo operators that define image pixels between 0 and 256.
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