Quantum image encryption method based on quantum long short-term memory network and chaotic system

Abstract

The present invention discloses a quantum image encryption method based on a quantum long short-term memory network and a chaotic system, comprising the following steps: S1 uses a quantum long short-term memory network to improve a chaotic sequence generated by a hyperchaotic Lorenz system; S2 controls the three-level radial diffusion through the improved chaotic sequence to change the grayscale value of the quantum image; S3 controls the quantum Arnold transformation through the improved chaotic sequence to disrupt the position of the quantum image. The present invention combines a quantum long short-term memory network with a chaotic system for quantum image encryption for the first time, and by virtue of the characteristics of quantum mechanics itself, including entanglement and superposition, and the non-periodicity and unpredictability of chaotic sequences, not only the security of encryption is improved, but the combination of the two can better destroy the strong correlation between adjacent pixels, and at the same time, the key is concise and the decryption process is simple, which greatly reduces the technical content and time required for decryption, and effectively ensures the security of image information.

Description

Technical Field

[0001] The present invention relates to the field of image encryption, in particular to a quantum image encryption method based on a quantum long short-term memory network and a chaotic system. Background Art

[0002] In recent years, with the rapid development of multimedia and computer network communication technologies, information transmission through networks has become increasingly frequent, and information security has received extensive attention. Since attackers can intercept information or change the data of information to achieve the purpose of destroying data transmission, it poses a huge threat to information transmission. As the main carrier of information transmission, digital images are involved in various information security systems, and it is very important to find a practical image encryption algorithm.

[0003] With the rapid development of quantum computing and quantum computers, quantum image processing has received increasing attention. Due to reasons such as classical encrypted images being relatively easy to be attacked and cracked, with a very large computational amount, insufficient key space, and being easily cracked, researchers must explore new methods to develop encryption algorithms. Because of the superposition principle of quantum mechanics, quantum image processing has parallelism, with an exponential improvement in processing time and an exponential increase in the amount of data processed, achieving speed and space advantages relative to classical computers. Therefore, this technology has attracted much attention from researchers. Combining the advantages of quantum information processing, quantum image encryption will be a possible method to solve the shortcomings of traditional image encryption algorithms. At the same time, the no-cloning theorem of quantum computing makes the quantum image encryption algorithm more secure. Summary of the Invention

[0004] In order to overcome the above problems existing in the prior art, the present invention proposes a quantum image encryption method based on a quantum long short-term memory network and a chaotic system.

[0005] The technical solution adopted by the present invention to solve its technical problems is: a quantum image encryption method based on a quantum long short-term memory network and a chaotic system, including the following steps:

[0006] S1. Using a quantum long short-term memory network to improve the chaotic sequence generated by the hyperchaotic Lorenz system;

[0007] S2. Controlling the three-level radial diffusion through the improved chaotic sequence to change the gray value of the quantum image;

[0008] S3. Controlling the quantum Arnold transform through the improved chaotic sequence to scramble the position of the quantum image.

[0009] For the above-mentioned quantum image encryption method based on a quantum long short-term memory network and a chaotic system, in step S1, the specific method includes the following steps:

[0010] S11. Set the parameters and initial values of the hyperchaotic Lorenz system to generate a hyperchaotic sequence. Let \(K = \{x 0 ,y 0 ,z 0 ,w 0 ,r 1 ,r 2 \}\) be the secret key, where \(\{x 0 ,y 0 ,z 0 ,w 0 \}\) is the initial value, and \(\{r 1 ,r 2 \}\) are integer random numbers with a value range of \([0, 255]\);

[0011] S12. Substitute \(\{x 0 ,y 0 ,z 0 ,w 0 \}\) in the secret key \(K\) into the hyperchaotic Lorenz system to obtain four pseudo-random sequences, denoted as \(\{l 1 \},\ \{l 2 \},\ \{l 3 \},\ \{l 4 \}\) respectively;

[0012] S13. Intercept part of the pseudo-random sequences and input them into the quantum long short-term memory network to obtain the improved new sequences \(\{l' 1 \},\ \{l' 2 \},\ \{l' 3 \},\ \{l' 4 \}\);

[0013] S14. Use the following equations to convert the four hyperchaotic sequences \(\{l' 1 \},\ \{l' 2 \},\ \{l' 3 \},\ \{l' 4 \}\) into four integer sequences \(\{L' 1 \},\ \{L' 2 \},\ \{L' 3 \},\ \{L' 4 \}\).

[0014]

[0015] For the above quantum image encryption method based on the quantum long short-term memory network and the chaotic system, in step S2, the specific method includes the following steps:

[0016] S21. Represent the original image using the NCQI quantum representation method:

[0017]

[0018] Among them, |M> represents the original image, n represents the number of qubits, represents the color information of the original image, and |yx> represents the position information of the original image, represents the grayscale value of the red channel of the original image, represents the grayscale value of the green channel of the original image, represents the grayscale value of the blue channel of the original image;

[0019] S22. The radial diffusion has three modes: two - bit radial diffusion, four - bit radial diffusion, and eight - bit radial diffusion. The arrangement order rule of the three - level radial diffusion is determined by the chaotic sequence {L′ 1};

[0020] S23. The chaotic sequences {L′ 2}, {L′ 3}, {L′ 4} are used as elements in the XOR operation, and the XOR operation is performed on the grayscale values of the image in sequence and changes according to the arrangement order rule of the three - level radial diffusion to obtain the image |M 2 >;

[0021] For the above - mentioned quantum image encryption method based on the quantum long - short - term memory network and the chaotic system, the arrangement order rules in S22 and S23 are as follows: when , the arrangement order is two - bit, four - bit, and eight - bit radial diffusion; when , the arrangement order is two - bit, eight - bit, and four - bit three - level radial diffusion; when , the arrangement order is four - bit, two - bit, and eight - bit three - level radial diffusion; when , the arrangement order is four - bit, eight - bit, and two - bit three - level radial diffusion; when , the arrangement order is eight - bit, two - bit, and four - bit three - level radial diffusion; when , the arrangement order is eight - bit, four - bit, and two - bit three - level radial diffusion. Among them, is the i - th number in the first chaotic sequence.

[0022] For the above - mentioned quantum image encryption method based on the quantum long - short - term memory network and the chaotic system, the specific method in S3 includes the following steps:

[0023] S31. According to the generalized Arnold transformation formula, its quantum representation is:

[0024]

[0025] Among them, |x′> represents the horizontal coordinate position of the image after the generalized Arnold transform, |y′> represents the vertical coordinate position of the image after the generalized Arnold transform, u represents the generalized Arnold transform coefficient, m represents the generalized Arnold transform coefficient, x represents the horizontal coordinate position of the image before the generalized Arnold transform, and y represents the vertical coordinate position of the image before the generalized Arnold transform;

[0026] S32. Apply to |M 2 >.

[0027]

[0028] Among them, |yx> represents the coordinate position of the image before the generalized Arnold transform, represents the generalized Arnold transform, |x> represents the horizontal coordinate position of the image before the generalized Arnold transform, |y> represents the horizontal coordinate position of the image before the generalized Arnold transform, j represents an integer, m represents the m-th number of the sequence {L′ 3}, n represents the number of qubits, |g(y, x)> represents the color information of the image after the radial transform, |y′x′> represents the coordinate position of the image after the generalized Arnold transform, |x′> represents the horizontal coordinate position of the image after the generalized Arnold transform, |x′> = |(x + my) mod 2 n >, |y′> represents the vertical coordinate position of the image after the generalized Arnold transform, |y′> = |[ux + (mu + 1)y] mod 2 n >, |M 3 > represents the final encrypted image.

[0029] In the above quantum image encryption method based on the quantum long short-term memory network and the chaotic system, in S31, the quantum Arnold transform coefficients m and u are respectively controlled by the chaotic sequences {L′ 1}, {L′ 2}, and the number of iterations of the quantum Arnold transform is controlled by the chaotic sequence {L′ 3}.

[0030] The beneficial effects of the present invention are as follows. In view of the limitations of traditional encryption schemes in the field of image encryption, the present application combines a quantum long short-term memory network with a chaotic system, and proposes a quantum image encryption scheme that combines a quantum long short-term memory network with a chaotic system. By improving the chaotic sequence through the quantum long short-term memory network and combining three-level radial diffusion and quantum Arnold transform scrambling, excellent anti-noise performance is generated for image encryption. Each level result of the three-level radial diffusion is related to the previous level, making decryption more difficult and improving the security of the algorithm; the chaotic sequence improved by the quantum long short-term memory network has better chaotic performance and is more difficult to predict, so the encryption security is higher. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] The present invention will be further described below with reference to the drawings and embodiments.

[0032] Figure 1 Schematic diagram of the quantum representation method of NCQI in the embodiment of the present invention;

[0033] Figure 2 Schematic diagram of three kinds of radial diffusion in the embodiment of the present invention;

[0034] Figure 3 Recurrent unit structure of the quantum long short-term memory network in the embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0035] To enable those skilled in the art to better understand the technical solutions of the present invention, the present invention will be described in detail below with reference to the drawings and specific embodiments.

[0036] This embodiment discloses a quantum image encryption scheme based on a quantum long short-term memory network and a chaotic system, including the following steps:

[0037] S1. Improve the chaotic sequence generated by the hyperchaotic Lorenz system using a quantum long short-term memory network;

[0038] S11. Set the parameters and initial values of the hyperchaotic Lorenz system to generate a hyperchaotic sequence. Let \(K = \{x 0 ,y 0 ,z 0 ,w 0 ,r 1 ,r 2 \}\) be the key, where \(\{x 0 ,y 0 ,z 0 ,w 0 \}\) is the initial value, and \(\{r 1 ,r 2 \}\) are integer random numbers with a value range of \([0, 255]\);

[0039] S12. Take the \(\{x0 , y 0 , z 0 , w 0} Substitute into the hyperchaotic Lorenz system to obtain four pseudo-random sequences, denoted as {l 1}, {l 2}, {l 3}, {l 4};

[0040] S13. Intercept part of the pseudo-random sequence and input it into the quantum long short-term memory network to obtain the improved new sequence {l′ 1}, {l′ 2}, {l′ 3}, {l′ 4};

[0041] S14. Use the following equations to convert the four hyperchaotic sequences {l′ 1}, {l′ 2}, {l′ 3}, {l′ 4} into four integer sequences {L′ 1}, {L′ 2}, {L′ 3}, {L′ 4}.

[0042] {L′ 1} = mod((l′ 1 - floor(l′ 1 )) × 10 14 , 256)

[0043] {L′ 2} = mod((l′ 2 - floor(l′ 2 )) × 10 14 , 256)

[0044] {L′ 3} = mod((l′ 3 - floor(l′ 3 )) × 10 14 , 256)

[0045] {L′ 4} = mod((l′ 4 - floor(l′ 4 )) × 10 14 , 256)

[0046] S2. Change the gray value of the quantum image by controlling the three-level radial diffusion through the improved chaotic sequence;

[0047] S21. Represent the original image using the NCQI quantum representation method (as Figure 1 shown):

[0048]

[0049] where |M> represents the original image, n represents the number of qubits, represents the color information of the original image, and |yx> represents the position information of the original image, represents the grayscale value of the red channel of the original image, represents the grayscale value of the green channel of the original image, represents the grayscale value of the blue channel of the original image;

[0050] S22. There are three ways of radial diffusion: two - dimensional radial diffusion, four - dimensional radial diffusion, and eight - dimensional radial diffusion. Determine the arrangement order rule of the three - level radial diffusion through the chaotic sequence {L′ 1}, and the rule is as follows: when , the arrangement order is two - dimensional, four - dimensional, and eight - dimensional radial diffusion; when , the arrangement order is two - dimensional, eight - dimensional, and four - dimensional three - level radial diffusion; when , the arrangement order is four - dimensional, two - dimensional, and eight - dimensional three - level radial diffusion; when , the arrangement order is four - dimensional, eight - dimensional, and two - dimensional three - level radial diffusion; when , the arrangement order is eight - dimensional, two - dimensional, and four - dimensional three - level radial diffusion; when , the arrangement order is eight - dimensional, four - dimensional, and two - dimensional three - level radial diffusion. Among them, is the i - th number in the first chaotic sequence.

[0051] S23. The chaotic sequences {L′ 2}, {L′ 3}, {L′ 4} are used as elements in the exclusive - or operation, and perform exclusive - or operations on the grayscale values of the image in sequence and change according to the arrangement order rule of the three - level radial diffusion.

[0052] Taking the order of two - dimensional, four - dimensional, and eight - dimensional radial diffusion as an example, obtain the image |M 2 >, as Figure 2 shown, where Figure 2 in (a) is eight - dimensional radial diffusion; Figure 2 in (b) is four - dimensional radial diffusion; Figure 2 in (c) is two - dimensional radial diffusion.

[0053] (1) Two - dimensional radial diffusion:

[0054]

[0055] (2) Four - bit radial diffusion:

[0056]

[0057] (3) Eight - bit radial diffusion:

[0058]

[0059] Among them, represents the 8th qubit of the pixel value of the image after eight - bit radial diffusion, represents the 1st qubit of the pixel value of the image after four - bit radial diffusion, represents the 5th qubit of the pixel value of the image after two - bit radial diffusion, and so on, represents the 7th qubit of the pixel value of the image after eight - bit radial diffusion ……, represents the 2nd qubit of the pixel value of the image after four - bit radial diffusion ……, represents the 6th qubit of the pixel value of the image after two - bit radial diffusion ……; represents the 1st number of the sequence {L′ 4}, represents the 5th number of the sequence {L′ 3}, represents the 7th number of the sequence {L′ 2}, and so on, represents the 2nd number of the sequence {L′ 4}……, represents the 6th number of the sequence {L′ 3}……, represents the 8th number of the sequence {L′ 2}……

[0060] S3. Shuffle the position of the quantum image by controlling the quantum Arnold transform with the improved chaotic sequence.

[0061] S31. According to the classical generalized Arnold transform formula, its quantum representation is:

[0062]

[0063] Among them, |x′> represents the horizontal coordinate position of the image after the generalized Arnold transform, |y′> represents the vertical coordinate position of the image after the generalized Arnold transform, u represents the generalized Arnold transform coefficient, m represents the generalized Arnold transform coefficient, x represents the horizontal coordinate position of the image before the generalized Arnold transform, and y represents the vertical coordinate position of the image before the generalized Arnold transform;

[0064] The Arnold transform coefficients m, u are respectively determined by the chaotic sequence {L′1 , {L′ 2} Controlled, the number of iterations of the Arnold transform is determined by the chaotic sequence {L′ 3}.

[0065] S32. Apply to |M 2 >,

[0066]

[0067] where |x′> = |(x + my) mod 2 n >, |y′> = |[ux + (mu + 1)y] mod 2 n >.

[0068] Among them, |yx> represents the coordinate position of the image before the generalized Arnold transform, represents the generalized Arnold transform, |x> represents the horizontal coordinate position of the image before the generalized Arnold transform, |y> represents the horizontal coordinate position of the image before the generalized Arnold transform, j represents an integer, m represents the m-th number of the sequence {L′ 3}, n represents the number of qubits, |g(y, x)> represents the color information of the image after the radial transform, |y′x′> represents the coordinate position of the image after the generalized Arnold transform, |x′> represents the horizontal coordinate position of the image after the generalized Arnold transform, |x′> = |(x + my) mod 2 n >, |y′> represents the vertical coordinate position of the image after the generalized Arnold transform, |y′> = |[ux + (mu + 1)y] mod 2 n >, |M 3 > represents the final encrypted image.

[0069] Decrypt the image. The decryption process is the inverse of the encryption process. Specifically,

[0070] S41. According to the above scheme, obtain four integer sequences {L′ 1}, {L′ 2}, {L′ 3}, {L′ 4}.

[0071] S42. Perform the inverse Arnold transform on the ciphertext image |M 3 > to obtain |M 2 >.

[0072]

[0073]

[0074] S43. Perform a three - level inverse radial diffusion on |M 2 > to obtain the original image |M>. First, the permutation order is determined by {L′ 1}, and secondly, the chaotic sequences {L′ 4}, {L′ 3}, {L′ 2} are used as elements in the exclusive - or operation to participate in decryption.

[0075] The permutation order rule of the three - level inverse radial diffusion is determined by the chaotic sequence {L′ 1} as follows: When holds, the permutation order is radial diffusion of eight - bit, four - bit, and two - bit; when holds, the permutation order is three - level radial diffusion of four - bit, eight - bit, and two - bit; when holds, the permutation order is three - level radial diffusion of eight - bit, two - bit, and four - bit; when holds, the permutation order is three - level radial diffusion of two - bit, eight - bit, and four - bit; when holds, the permutation order is three - level radial diffusion of four - bit, two - bit, and eight - bit; when holds, the permutation order is three - level radial diffusion of two - bit, four - bit, and eight - bit. Among them, is the i - th number in the first chaotic sequence.

[0076] In this embodiment, Figure 3 is the recurrent unit structure of the quantum long - short - term memory network. The input values are the external state H t-1 at the previous moment and the input value X t at the current moment. After passing through four VQC blocks and two linear layers, a new external state H t and an internal state C t are obtained.

[0077] This application improves the chaotic sequence through a quantum long - short - term memory network, combines three - level radial diffusion and quantum Arnold transform scrambling, and generates excellent anti - noise performance for image encryption. The chaotic sequence improved by the quantum long - short - term memory network has better chaotic performance and is more difficult to predict, so the encryption security is higher. Moreover, each level result of the three - level radial diffusion is related to the previous level, making decryption more difficult and further improving the security of the algorithm.

[0078] The above embodiments are only exemplary embodiments of the present invention and are not used to limit the present invention. The protection scope of the present invention is defined by the claims. Those skilled in the art can make various modifications or equivalent substitutions within the essence and protection scope of the present invention, and such modifications or equivalent substitutions should also be regarded as falling within the protection scope of the present invention.

Claims

1. A quantum image encryption method based on quantum long short-term memory network and chaotic system, characterized in that: The steps include: S1. Improve the chaotic sequence generated by the hyperchaotic Lorenz system using quantum long short-term memory network; S2. The gray value of the quantum image is changed by controlling the three-level radial diffusion through the improved chaotic sequence; S3. Control the quantum Arnold transform through the improved chaotic sequence to disrupt the position of the quantum image; In S1, the specific method includes the following steps: S11, set the parameters and initial values ​​of the hyperchaotic Lorenz system to generate a hyperchaotic sequence. is the key, where is the initial value, The value range is An integer random number; S12, the key In Substituting into the hyperchaotic Lorenz system, we get four pseudo-random sequences, which are respectively denoted as ; S13. Extract part of the pseudo-random sequence and input it into the quantum long short-term memory network to obtain an improved new sequence. ; S14, using the following equations, the four hyperchaotic sequences are Convert to a sequence of 4 integers : ； In S2, the specific method includes the following steps: S21. The original image is represented using the NCQI quantum representation method: ； in, represents the original image, n represents the number of qubits, Represents the color information of the original image. Indicates the location information of the original image. Represents the grayscale value of the red channel of the original image, Represents the grayscale value of the green channel of the original image, Represents the grayscale value of the blue channel of the original image; S22, radial diffusion has three modes: two-bit radial diffusion, four-bit radial diffusion, eight-bit radial diffusion, through chaotic sequence The rules for determining the order of arrangement of the three-level radial diffusion; S23, Chaos Sequence As the element in the XOR operation, the grayscale values ​​of the image are XORed in turn, and the arrangement order of the three-level radial diffusion is changed according to the rule to obtain the image .

2. The quantum image encryption method based on quantum long short-term memory network and chaotic system according to claim 1 is characterized in that: The arrangement order rules in S22 and S23 are as follows: When , the order of arrangement is radial diffusion of two, four, and eight positions; when When , the arrangement order is two, eight, and four three-level radial diffusion; when When , the arrangement order is four, two, and eight three-level radial diffusion; when When , the arrangement order is four, eight, and two three-level radial diffusion; when When , the arrangement order is eight, two, and four three-level radial diffusion; when When , the arrangement order is eight, four, and two three-level radial diffusion; among them, is the first chaotic sequence Number.

3. The quantum image encryption method based on quantum long short-term memory network and chaotic system according to claim 1 is characterized in that: The specific method in S3 comprises the following steps: S31. According to the generalized Arnold transformation formula, its quantum representation is: ； in, Represents the horizontal coordinate position of the image after generalized Arnold transformation, represents the vertical coordinate position of the image after generalized Arnold transformation, represents the generalized Arnold transform coefficients, represents the generalized Arnold transform coefficients, represents the horizontal coordinate position of the image before the generalized Arnold transformation, Indicates the vertical coordinate position of the image before generalized Arnold transformation; S32, Apply to , ； in, represents the coordinate position of the image before the generalized Arnold transformation, represents the generalized Arnold transform, represents the horizontal coordinate position of the image before the generalized Arnold transformation, Represents the vertical coordinate position of the image before the generalized Arnold transform, j represents an integer, and m represents a sequence The mth number of , n represents the number of qubits, Represents the color information of the image after radial transformation, represents the coordinate position of the image after generalized Arnold transformation, Represents the horizontal coordinate position of the image after generalized Arnold transformation, , Represents the vertical coordinate position of the image after generalized Arnold transformation, , Represents the final encrypted image.

4. The quantum image encryption method based on quantum long short-term memory network and chaotic system according to claim 3 is characterized in that: The quantum Arnold transformation coefficients in S31 Chaotic sequence Control, the number of iterations of quantum Arnold transform is determined by the chaotic sequence control.

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