Multi-image optical phase truncation asymmetric secure compression method

Abstract

The application relates to a multi-image optical phase truncation asymmetric security compression method, relates to the field of image encryption technology, and solves the problems of insufficient nonlinear characteristics, low key security and poor transmission efficiency in the existing optical image encryption process. In the phase truncation asymmetric security compression method, the initial key is encrypted through an elliptic curve algorithm and a hash algorithm, the truncated private key is subjected to class type permutation and scrambling, and the private key is processed as an initial value for generating a composite secondary chaotic phase mask, so that the security of the encryption process is greatly improved; and the method of multi-image encryption solves the problem of low transmission efficiency, and greatly improves the transmission efficiency.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of image encryption technology, and particularly relates to a multi-image optical phase truncation asymmetric secure compression method. BACKGROUND

[0002] With the continuous development of information globalization, the rapid development of network technology and communication technology, people are in an era of information explosion, and have to face a large amount of information from all aspects at all times. The development of science and technology has brought a lot of convenience to people's life, but at the same time, people also face the threat of private information being stolen, interfered and destroyed, and how to ensure the security of these information has become a serious problem. With the continuous development of science and technology, people have created many new encryption methods in the field of computer, communication and other fields. Among them, optical and optoelectronic information encryption and anti-counterfeiting technology has the characteristics of fast processing speed, multiple attribute dimensions and parallel operation, so it has good application prospect in the field of real-time communication, confidential file encryption and other fields, and shows its unique advantages. The use of optical method of information security has been widely studied, so various optical cipher systems have been proposed. Due to the linear characteristic, the symmetric cipher system is vulnerable to various types of attacks. There is a obvious defect in optical encryption, that is, the problem of insufficient nonlinear characteristics, which leads to the effect of encryption is not very good, for example, by traditional double random phase encoding to encrypt the image. In addition to the nonlinear characteristics, the management and protection of the key also become a problem to be solved. SUMMARY

[0003] The present application provides a multi-image optical phase truncation asymmetric secure compression method to solve the problems of insufficient nonlinear characteristics, low key security and poor transmission efficiency in the existing optical image encryption process.

[0004] The multi-image optical phase truncation asymmetric secure compression method is realized by the following steps:

[0005] Step one, select 2^n gray images with a size of MxN as original images, perform bitwise XOR operation on each two original images to obtain 2^(n-1) XOR images, and simultaneously perform complex encoding on each two original images to obtain 2^(n-1) combined images;

[0006] Step two, generate 2^(n-1) groups of message digests from the 2^(n-1) XOR images obtained in step one, and calculate 2^(n-1) groups of initial keys through the 2^(n-1) groups of message digests;

[0007] Step three, encrypt the 2^(n-1) groups of initial keys to obtain 2^(n-1) groups of secure keys, and send the secure keys to the receiving party;

[0008] Step four, taking the 2^(n-1) groups of initial keys in step three as initial values respectively, iterating the chaotic system to generate 2^(n-1) chaotic random sequences, and performing matrix transformation on the chaotic random sequences to generate 2^(n-1) composite first-level chaotic phase masks;

[0009] Step five, modulating the combined image in step one by the composite first-level chaotic phase mask in step four respectively to obtain 2^(n-1) first-level modulated combined images;

[0010] Performing phase truncation and phase reservation operations on the first-level modulated combined images to obtain 2^(n-1) first-level modulated combined image phase components and 2^(n-1) first-level modulated combined ciphertext images respectively;

[0011] Step six, performing key update operation on the 2^(n-1) groups of initial keys in step two by using user control parameter u1 to obtain 2^(n-1) groups of initial updated keys;

[0012] Step seven, taking the 2^(n-1) groups of initial updated keys in step six as initial values respectively, iterating the chaotic system to generate 2^(n-1) updated chaotic random sequences;

[0013] Performing fractal scrambling operation on the 2^(n-1) first-level modulated combined image phase components in step five by using the 2^(n-1) updated chaotic random sequences respectively to obtain 2^(n-1) first-level phase private keys;

[0014] Step eight, taking the 2^(n-1) first-level modulated combined ciphertext images in step five two by two to form a group to perform composite encoding to obtain 2^(n-2) second-level combined images;

[0015] Performing key combination update operation on the 2^(n-1) groups of initial keys in step two by using user control parameter u2 to obtain 2^(n-2) groups of initial updated keys;

[0016] Step nine, taking the 2^(n-2) groups of initial updated keys in step eight as initial values respectively, iterating the chaotic system to generate 2^(n-2) combined updated chaotic random sequences;

[0017] Step ten, performing matrix transformation on the combined updated chaotic random sequences in step nine to generate 2^(n-2) composite second-level chaotic phase masks; modulating the second-level combined images in step eight by the composite second-level chaotic phase masks respectively to obtain 2^(n-2) second-level modulated combined images;

[0018] Step eleven, performing phase truncation and phase reservation operation on the secondary modulation combined image of step ten, respectively obtaining 2^(n-2) secondary modulation combined image phase components and 2^(n-2) secondary modulation combined ciphertext images;

[0019] Step twelve, performing complex encoding on the 2^(n-2) secondary modulation combined ciphertext images of step eleven, obtaining a tertiary combined image;

[0020] Step thirteen, performing fractal scrambling operation on the 2^(n-2) secondary modulation combined image phase components of step eleven by using the updated chaotic random sequence of step seven, obtaining 2^(n-2) secondary phase private keys;

[0021] Step fourteen, combining the 2^(n-1) primary phase private keys of step seven with the 2^(n-2) secondary phase private keys obtained in step thirteen, obtaining a plaintext related user private key set Priv;

[0022] Step fifteen, performing fractal scrambling operation on the tertiary combined image of step twelve by using chaosSeq(userkey3)' in the updated chaotic random sequence of step seven, wherein userkey3 is a user control key, obtaining a final ciphertext image EnImage.

[0023] The method of the present application encrypts the initial key through elliptic curve algorithm and hash algorithm, and performs class fractal scrambling on the truncated private key, and processes the private key as the initial value for generating a composite secondary chaotic phase mask, greatly improving the security of the encryption process. The method of multi-image encryption solves the problem of low transmission efficiency, greatly improving the transmission efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0024] Figure 1 The encryption process flow chart in the multi-image optical phase truncation asymmetric security compression method of the present application;

[0025] Figure 2 The decryption process flow chart in the multi-image optical phase truncation asymmetric security compression method of the present application;

[0026] Figure 3 The effect diagram for encrypting and decrypting by using the multi-image optical phase truncation asymmetric security compression method of the present application: wherein Figure 3 (a) is the original image of "man", Figure 3 (b) is the original image of "snow mountain", Figure 3 (c) is the original image of "David", Figure 3 (d) is the original image of "hills", Figure 3(e) is an encrypted image of (a) (b) (c) (d), Figure 3 (f) is a decrypted image of (a), Figure 3 (g) is a decrypted image of (b), Figure 3 (h) is a decrypted image of (c), Figure 3 (l) is a decrypted image of (d). DETAILED DESCRIPTION

[0027] DETAILED DESCRIPTION Figure 1 and Figure 2 The present embodiment is to illustrate a multi-image optical phase truncation asymmetric secure compression method, which is realized by the following steps:

[0028] Step 1: Select 2^n gray images with a size of MxN as original images Image1, Image2, Image3, Image4, … Image2^n;

[0029] Step 2: Perform complex encoding on each pair of original images to obtain combined images C_imag1, C_imag2, C_imag2^(n-1);

[0030] Step 3: Perform bitwise XOR operation on each pair of original images to obtain 2^(n-1) XOR images Xor_image1, …, Xor_image2^(n-1);

[0031] Step 4: Use the XOR images Xor_image1, …, Xor_image2^(n-1) obtained in Step 3 to respectively calculate 2^(n-1) groups of message digests Info1, …, Info2^(n-1);

[0032] Step 5: Calculate 2^(n-1) groups of initial keys chaoskey1, …, chaoskey2^(n-1) from the message digests Info1, …, Info2^(n-1);

[0033] Step 6: Perform encryption operation on the 2^(n-1) groups of initial keys chaoskey1, …, chaoskey2^(n-1) obtained in Step 5 to obtain 2^(n-1) groups of secure keys Enchaoskey1, …, Enchaoskey2^(n-1), and send the secure keys to the receiver;

[0034] Step 7: Use the initial keys chaoskey1, …, chaoskey2^(n-1) generated in Step 5 as initial values to iterate the chaotic system and generate 2^(n-1) chaotic random sequences chaosSeq1, …, chaosSeq2^(n-1);

[0035] Step eight, matrix transformation is performed on the chaotic random sequence in step seven to generate 2^(n-1) composite first-level chaotic phase masks CRPM1_1,…,CRPM1_2^(n-1);

[0036] Step nine, the combined images C_imag1,…,C_imag2^(n-1) in step two are respectively modulated by the composite first-level chaotic phase masks CRPM1_1,…,CRPM1_2^(n-1) to obtain 2^(n-1) first-level modulated combined images M1C_imag1,…,M1C_imag2^(n-1);

[0037] Step ten, phase truncation and phase reservation operations are performed on the first-level modulated combined images M1C_imag1,…,M1C_imag2^(n-1) in step nine to respectively obtain 2^(n-1) first-level modulated combined image phase components P M1C_imag1 ,…,P M1C_imag2^(n-1) and 2^(n-1) first-level modulated combined ciphertext images EnImg M1C_imag1 ,…,EnImg M1C_imag2^(n-1) ;

[0038] Step eleven, the 2^(n-1) groups of initial keys chaoskey1,…,chaoskey2^(n-1) in step four are subjected to a key update operation using a user control parameter u1 to obtain initial updated keys chaoskey1’,…,chaoskey2^(n-1)';

[0039] Step twelve, the initial updated keys chaoskey1’,…,chaoskey2^(n-1)' generated in step eleven are respectively used as initial values to iterate a chaotic system to generate 2^(n-1) updated chaotic random sequences chaosSeq1’,…,chaosSeq2^(n-1)';

[0040] Step thirteen, the 2^(n-1) first-level modulated combined image phase components P M1C_imag1 ,…,P M1C_imag2^(n-1) in step ten are respectively subjected to a fractal scrambling operation using the updated chaotic random sequences chaosSeq1’,…,chaosSeq2^(n-1)' in step twelve to obtain 2^(n-1) first-level phase private keys P' M1C_imag1 ,…,P' M1C_imag2^(n-1) ;

[0041] Step fourteen, the 2^(n-1) first-level modulated combined ciphertext images EnImg M1C_imag1 ,…,EnImg M1C_imag2^(n-1)Each group is composed and coded to obtain 2^(n-2) secondary combined images Img M1C_imag1 , …, Img M1C_imag2^(n-2) ;

[0042] Step fifteen, using user control parameter u2, performing key composition update operation on the 2^(n-1) groups of initial keys chaoskey1, …, chaoskey2^(n-1) described in step five to obtain 2^(n-2) groups of initial update keys chaoskey1*, …, chaoskey2^(n-2)*;

[0043] Step sixteen, using the initial update keys chaoskey1*, …, chaoskey2^(n-2)* generated in step fifteen as initial values respectively, iterating the chaotic system to generate 2^(n-2) groups of combined update chaotic random sequences chaosSeq1*, …, chaosSeq2^(n-1)*;

[0044] Step seventeen, performing matrix transformation on the combined update chaotic random sequences described in step sixteen to generate 2^(n-2) composite secondary chaotic phase masks CRPM2_1, …, CRPM2_2^(n-2);

[0045] Step eighteen, modulating the secondary combined images Img M1C_imag1 , …, EnImg M1C_imag2^(n-2) described in step fourteen through the composite secondary chaotic phase masks CRPM2_1, …, CRPM2_2^(n-2) respectively to obtain 2^(n-2) secondary modulation combined images M2C_imag1, …, M2C_imag2^(n-2);

[0046] Step nineteen, performing phase truncation and phase reservation operation on the secondary modulation combined images M2C_imag1, …, M2C_imag2^(n-2) described in step eighteen to obtain 2^(n-2) secondary modulation combined image phase components P M2C_imag1 , …, P M2C_imag2^(n-2) and 2^(n-2) secondary modulation combined ciphertext images EnImg M2C_imag1 , …, EnImg M2C_imag2^(n-2) respectively;

[0047] Step twenty, composing and coding the 2^(n-2) secondary modulation combined ciphertext images EnImg M2C_imag1 , …, EnImg M2C_imag2^(n-2) described in step nineteen to obtain a tertiary combined image Img M3C_imag ;

[0048] Step twenty-one, update chaosSeq1', chaosSeq2^(n-2)' in the chaos random sequence in step twelve to the 2^(n-2) two-level modulation combination image phase components P M2C_imag1 , …, P M2C_imag2^(n-2) respectively to obtain 2^(n-2) two-level phase private keys P* M1C_imag1 , …, P* M1C_imag2^(n-2) ;

[0049] Step twenty-two, combine the 2^(n-1) one-level phase private keys P' M1C_imag1 , …, P' M1C_imag2^(n-1) obtained in step thirteen with the 2^(n-2) two-level phase private keys P* M1C_imag1 , …, P* M1C_imag2^(n-2) obtained in step twenty-one to obtain a plaintext related user private key set Priv.

[0050] Step twenty-three, perform a fractal scrambling operation on the three-level combination image Img M3C_imag in step twenty using chaosSeq(userkey3)' in the chaos random sequence in step twelve, where userkey3 is a user control key, to obtain a final ciphertext image EnImage.

[0051] Specific implementation method two, in combination Figures 1 to 3 with the above-mentioned specific implementation method one, the present embodiment is an embodiment of the multi-image optical phase truncation asymmetric security compression method described in specific implementation method one: taking four images as an example, the method is implemented by the following steps:

[0052] Step one, take four images with a size of 256x256 as original images Image1 and Image2, Image3, Image4, respectively as Figure 3 (a), (b), (c) and (d).

[0053] Step two, composite encode the original images in pairs according to formula (1) to obtain C_imag1 and C_imag2.

[0054]

[0055] where Image1 is the real part and i*Image2 is the imaginary part, and i is an imaginary number, i^2=-1.

[0056] Step three, perform a bitwise XOR operation on the original images in pairs according to formula (2) to obtain two XOR images Xor_image1 and Xor_image2.

[0057]

[0058] wherein bitxor() represents a bitwise XOR operation.

[0059] Step four, according to formula (3), two groups of message digests Info1, Info2 are generated by using the XOR images Xor_image1, Xor_image2 of step three, and Info1, Info2 are grouped as shown in formula (4) (5):

[0060]

[0061]

[0062]

[0063] wherein h represents that Info1 is divided into 64 bits, H represents that h is divided into 16 groups of four bits each, g represents that Info2 is divided into 64 bits, and G represents that g is divided into 16 groups of four bits each.

[0064] Step five, two groups of initial keys chaoskey1, chaoskey2 are generated according to formula (6) (7) by using the message digests Info1, Info2:

[0065]

[0066]

[0067] wherein x0, y0 are initial values of the chaotic system, ω, is a control parameter of the chaotic system, and α0, β0, γ0, δ0 are fixed parameters, which are set to (0.5, 0.7, 2.4, 3.2). hex2dec() represents conversion from hexadecimal number to decimal number.

[0068] Step six, the initial keys chaoskey1, chaoskey2 generated in step five are used as initial values to iterate the 2D chaotic system, and random sequences chaosSeq1, chaosSeq2 are generated. The state equation of the 2D chaotic system is shown in formula (8):

[0069]

[0070] wherein ω, is a control parameter of the chaotic system, and two pseudo-random sequences chaosSeq1, chaosSeq2 with lengths of 256x256 are generated as shown in formula (9):

[0071]

[0072] Step seven, the chaotic random sequence described in step six is subjected to matrix transformation, and two composite first-level chaotic phase masks CRPM1_1, CRPM1_2 are generated according to formula (10).

[0073]

[0074] In the formula, reshape() is a matrix transformation function, and reshape(A, m, n) represents returning an m*n matrix.

[0075] Step eight, the combined images C_imag1 and C_imag2 described in step two are modulated by the composite first-level chaotic phase masks CRPM1_1 and CRPM1_2 to obtain two first-level modulated combined images M1C_imag1 and M1C_imag2, as shown in formula (11):

[0076]

[0077] Step nine, the first-level modulated combined images M1C_imag1 and M1C_imag2 described in step eight are subjected to phase truncation and phase reservation operations to obtain two first-level modulated combined image phase components P MIC_imag1 , P MIC_imag2 , and two first-level modulated combined ciphertext images EnImg MIC_imag1 , EnImg MIC_imag2 , as shown in formula (12).

[0078]

[0079] Where F α represents fractional Fourier transform, and a represents the order of fractional Fourier transform. PR{} and PT{} represent phase reservation and phase truncation operations, respectively.

[0080] Step ten, the two sets of initial keys chaoskey1 and chaoskey2 described in step four are subjected to key update operations using a user control parameter u1 to obtain initial updated keys chaoskey1' and chaoskey2'.

[0081] Step eleven, the initial updated keys chaoskey1' and chaoskey2' generated in step ten are used as initial values to iterate the chaotic system to generate two updated chaotic random sequences chaosSeq1' and chaosSeq2', as shown in formula (13):

[0082]

[0083] Step twelve, update the chaos random sequence chaosSeq1', chaosSeq2' described in step eleven to the two first-level modulation combined image phase components P M1C_imag1 , P M1C_imag2 , respectively, to obtain two first-level phase private keys P' M1C_imag1 , P' M1C_imag2 , and the scrambling method is shown in the following formula.

[0084]

[0085] wherein r1=rand(), r2=rand(), rand() is a function of generating a random number between 0 and 1. The random initial point s in the pixel matrix is generated by r1 and r2, the coordinates are (s1, s2), and d is the key. (u1, v1) is the initial value of the first iteration, (u n+1 , v n+1 ) is the result of iteration n+1 times, R is a randomly selected matrix of base points, B is a two-dimensional array containing the coordinates of the base points of the chaos game, B[R n ][1] is a specific value in the two-dimensional array matrix, and P' represents the chaos sequence. When scrambling the phase component P M1C_imag1 , chaosSeq1' represents the chaos sequence; when scrambling the phase component P M1C_imag2 , chaosSeq2' represents the chaos sequence.

[0086] Step thirteen, composite encode the two first-level modulation combined ciphertext images EnImg M1C_imag1 , EnImg M1C_imag2 described in step nine to obtain a second-level combined image

[0087] wherein EnImg M1C_imag1 is the real part, i*(EnImg M1C_imag2 ) is the imaginary part, i is an imaginary number, and i^2=-1.

[0088] Step fourteen, use the user control parameter u2 to perform a key combination update operation on the two sets of initial keys chaoskey1, chaoskey2 described in step five to obtain a set of initial updated keys chaoskey1*.

[0089] Step fifteen, use the initial updated key chaoskey1* generated in step fourteen as the initial value to iterate the chaos system to generate a combined updated chaos random sequence chaosSeq1*.

[0090] Step 16: Perform matrix transformation on the combined updated chaotic random sequence chaosSeq1* described in Step 15 to generate a composite second-order chaotic phase mask CRPM2_1, as shown in formula (16):

[0091] CRPM2_1=reshape(chaosSeq1*,256,256) (16)

[0092] Step 17: Combine the secondary composite image Img described in Step 13. M1C_imag Modulation is performed using a composite second-order chaotic phase mask CRPM2_1, and the second-order modulated combined image M2C is obtained according to formula (17). _imag .

[0093]

[0094] Step 18: Perform phase truncation and phase preservation operations on the second-level modulated combined image M2C_imag described in Step 17 to obtain a second-level modulated combined image phase component P. M2C_imag A second-level modulation combined ciphertext image EnImg M2C_imag As shown in formula (18):

[0095]

[0096] Where F β Let denot , where β represents the order of the fractional Fourier transform, and PR{} and PT{} represent the phase preservation and phase truncation operations, respectively.

[0097] Step 19: Using the chaosSeq1' updated in the chaotic random sequence described in Step 11, adjust the phase component P of the second-level modulation combination image described in Step 18 according to formula (19). M2C_imag Perform a fractal scrambling operation to obtain a two-level phase private key P*. M1C_imag .

[0098]

[0099] Step 20: Transfer the two first-level phase private keys P' described in Step 12. M1C_imag1 , P' M1C_imag2 Combine the secondary phase private key P*M1C_imag obtained in step nineteen to obtain the plaintext-related user private key set Priv.

[0100] Step 21: Use the chaosSeq2' in the updated chaotic random sequence described in Step 11 to update the second-level modulation and combination ciphertext image EnImg described in Step 18. M2C_imag Perform a scrambling operation to obtain the final encrypted image EnImage.

[0101]

[0102] As Figure 2 shown, in the embodiment, an image decryption method is also included, which is realized by the following steps:

[0103] Step twenty-two, performing inverse fractal scrambling on the final ciphertext image EnImage to obtain ciphertext image EnImg M2C_imag .

[0104] Step twenty-three, performing inverse fractal scrambling on the phase private key P M1C_imag to obtain P M2C_imag , multiplying the ciphertext image EnImg M2C_imag of step twenty-two by the decryption key P M2C_imag , and then performing inverse fractional Fourier transform with order β. The transformed image is multiplied by the conjugate value [CRPM2_1] -1 of CRPM2_1 to obtain two first-level modulation combined ciphertext images EnImg M1C_imag1 , EnImg M1C_imag2 , as shown in equation (21):

[0105]

[0106] where real{} represents taking the real part of a complex function, imag{} represents taking the imaginary part of a complex function, F -β is inverse fractional Fourier transform with order β, and [CRPM2_1] -1 is the conjugate of CRPM2_1.

[0107] Step twenty-four, performing inverse fractal scrambling on the phase private key P M1C_imag1 to obtain P M1C_imag1 , multiplying the EnImg M1C_imag1 of step twenty-three by the decryption key P M1C_imag1 , and then performing inverse fractional Fourier transform with order α. The transformed image is multiplied by the conjugate value [CRPM1_1] -1 of CRPM1_1 to obtain two decrypted original images Image1 and Image2, as shown in equation (22):

[0108]

[0109] where real{} represents taking the real part of a complex function, imag{} represents taking the imaginary part of a complex function, F -α is inverse fractional Fourier transform with order α, and [CRPM1_1] -1 is the conjugate of CRPM1_1.

[0110] Step twenty-five, the phase private key P' M1C_imag2 Step twenty-six, inverse fractal scrambling is performed on P' M1C_imag2 Step twenty-seven, EnImg M1C_imag2 Step twenty-eight, multiply EnImg M1C_imag2 Step twenty-nine, inverse fractional Fourier transform is performed on the product of step twenty-eight with order α. The transformed image is multiplied by the conjugate value of CRPM1_2[CRPM1_2] -1 Step thirty, two decrypted original images Image3, Image4 are obtained as shown in equation (23):

[0111]

[0112] Where real{} represents taking the real part of a complex function, imag{} represents taking the imaginary part of a complex function, F -α is inverse fractional Fourier transform with order α, and [CRPM1_2] -1 is the conjugate of CRPM1_2.

[0113] The technical features of the above-described embodiments can be combined in any manner. To make the description concise, all possible combinations of the technical features in the above-described embodiments are not described, but as long as the combinations of the technical features do not contradict, they should be considered within the scope of the present disclosure.

[0114] The above-described embodiments only express several implementation manners of the present disclosure, and the description is relatively specific and detailed, but it should not be understood as a limitation on the scope of the patent. It should be pointed out that for ordinary skilled persons in the art, several modifications and improvements can be made without departing from the concept of the present disclosure, and these are within the protection scope of the present disclosure. Therefore, the protection scope of the patent of the present disclosure should be subject to the appended claims.

Claims

1. A multi-image optical phase truncation asymmetric secure compression method, characterized in that: The compression method is realized by the following steps: Step one, selecting 2^n gray images with the size of M*N as original images, performing bitwise XOR operation on each pair of original images to obtain 2^(n-1) XOR images, and performing composite encoding on each pair of original images to obtain 2^(n-1) composite images; Step two, generating 2^(n-1) groups of message digests from the 2^(n-1) XOR images obtained in step one, and calculating 2^(n-1) groups of initial keys through the 2^(n-1) groups of message digests; Step three, performing encryption operation on the 2^(n-1) groups of initial keys in step two to obtain 2^(n-1) groups of secure keys, and sending the secure keys to the receiving party; Step four, iterating the chaotic system with the 2^(n-1) groups of initial keys in step three as initial values to generate 2^(n-1) chaotic random sequences, and performing matrix transformation on the chaotic random sequences to generate 2^(n-1) composite first-level chaotic phase masks; Step five, modulating the composite images in step one through the composite first-level chaotic phase masks in step four to obtain 2^(n-1) first-level modulated composite images; Performing phase truncation and phase reservation operations on the first-level modulated composite images to obtain 2^(n-1) first-level modulated composite image phase components and 2^(n-1) first-level modulated composite ciphertext images, respectively; Step six, performing key update operation on the 2^(n-1) groups of initial keys in step two using user control parameter u1 to obtain 2^(n-1) groups of initial updated keys; Step seven, iterating the chaotic system with the 2^(n-1) groups of initial updated keys in step six as initial values to generate 2^(n-1) updated chaotic random sequences; Performing fractal scrambling operation on the 2^(n-1) first-level modulated composite image phase components in step five using the 2^(n-1) updated chaotic random sequences to obtain 2^(n-1) first-level phase private keys; Step eight, performing composite encoding on each pair of the 2^(n-1) first-level modulated composite ciphertext images in step five to obtain 2^(n-2) second-level composite images; Performing key combination update operation on the 2^(n-1) groups of initial keys in step two using user control parameter u2 to obtain 2^(n-2) groups of initial updated keys; Step nine, iterating the chaotic system with the 2^(n-2) groups of initial updated keys in step eight as initial values to generate 2^(n-2) combined updated chaotic random sequences; Step ten, performing matrix transformation on the combined updated chaotic random sequences in step nine to generate 2^(n-2) composite second-level chaotic phase masks, and modulating the second-level composite images in step eight through the composite second-level chaotic phase masks to obtain 2^(n-2) second-level modulated composite images; Step eleven, performing phase truncation and phase reservation operation on the secondary modulation combined image of step ten, respectively obtaining 2^(n-2) secondary modulation combined image phase components and 2^(n-2) secondary modulation combined ciphertext images; Step twelve, performing complex encoding on the 2^(n-2) secondary modulation combined ciphertext images of step eleven, obtaining a tertiary combined image; Step thirteen, performing fractal scrambling operation on the 2^(n-2) secondary modulation combined image phase components of step eleven respectively by using the updated chaos random sequence of step seven, obtaining 2^(n-2) secondary phase private keys; Step fourteen, combining the 2^(n-1) primary phase private keys of step seven with the 2^(n-2) secondary phase private keys obtained in step thirteen, obtaining a plaintext related user private key set Priv; Step fifteen, performing fractal scrambling operation on the tertiary combined image of step twelve by using chaosSeq(userkey3)' in the updated chaos random sequence of step seven, wherein userkey3 is a user control key, obtaining a final ciphertext image EnImage.

2. The multi-image optical phase truncation asymmetric security compression method according to claim 1, characterized in that: In step five, phase truncation and phase reservation operations are performed on the first-level modulation combined image M1C_imag1, M1C_imag2, to obtain two first-level modulation combined image phase components P MIC_imag1 , P MIC_imag2 , and two first-level modulation combined ciphertext images EnImg MIC_imag1 , EnImg MIC_imag2 , which are expressed by the following formula: In the formula, F α denotes the fractional Fourier transform, a denotes the order of the fractional Fourier transform, and PR{} and PT{} denote the phase preserving and phase truncating operations, respectively.

3. The multi-image optical phase truncation asymmetric security compression method of claim 1, wherein: In step seven, the chaos random sequence chaosSeq1', chaosSeq2' is used to update the phase components P MIC_imag1 , P MIC_imag2 of the two first-level modulation combined images in step five, respectively, to obtain two first-level phase private keys P M1C_imag1 , P' M1C_imag2 , and the scrambling formula is as follows: wherein, r1=rand(), r2=rand(), rand() is a function of generating a random number between 0 and 1; the random initial point s in the pixel matrix is generated by r1 and r2, the coordinates are (s1, s2), d is a key, R is a random selection matrix of base points; (u1, v1) is the initial value of the first iteration, (u n+1 , v n+1 ) is the result of the n+1th iteration, B is a two-dimensional array containing the coordinates of the chaotic game base points, B[R n ][1] is the value in the two-dimensional array matrix, and P' is a chaotic sequence.

4. The multi-image optical phase truncation asymmetric security compression method of claim 1, wherein: In step eleven, a phase truncation and phase reservation operation is performed on the second modulated combined image M2C_imag described in step ten to obtain a second modulated combined image phase component P M2C_imag and a second modulated combined ciphertext image EnImg M2C_imag which is expressed by the following formula: In the formula, F β denotes the fractional Fourier transform, β denotes the order of the fractional Fourier transform, and PR{} and PT{} denote the phase preserving and phase truncating operations, respectively.

Images