Multi-image hierarchical encryption method based on fingerprint key and off-axis digital holography

Abstract

The invention discloses a multi-image grading encryption method based on a fingerprint key and off-axis digital holography, which comprises the following encryption steps: firstly, grading an encryption user and a plaintext image to be encrypted, then collecting an encryption fingerprint of the encryption user and generating a fingerprint chaos phase mask; performing hierarchical encryption on a plurality of plaintext images by using improved double random phase coding and off-axis digital holographic coding, and finally generating an amplitude type ciphertext; and a decryption step: firstly, authenticating a decryption fingerprint by using a fingerprint column code authentication technology, generating a fingerprint chaos conjugate phase mask for decryption after the authentication succeeds, and then performing hierarchical decryption on the ciphertext by using improved off-axis digital holographic decoding and improved double random phase decoding so as to obtain a plurality of decryption images. The multi-image hierarchical encryption method provided by the invention has the advantages of high security level, strong fingerprint key robustness, high digital key sensitivity, high decryption quality and differentiated authorization of users.

Description

Technical Field

[0001] The present invention relates to the field of information security technology, and in particular to a multi-image hierarchical encryption method based on fingerprint keys and off-axis digital holography. Background Art

[0002] Since Refregier and Javidi proposed an image encryption method based on double random phase encoding in 1995, optical image encryption technology has received widespread attention. Later, related technologies such as optical interference, diffraction imaging, computational ghost imaging, digital holography, and metasurfaces were gradually introduced into optical image encryption technology, and a variety of novel optical image encryption schemes emerged, which accelerated the practical application of optical image encryption technology. However, the current optical image encryption technology often has the problem of high key complexity, especially the phase mask key is usually difficult for the user to remember or carry, and the key and the user lack a connection, which leads to the possibility of attackers stealing the user's key, thus seriously threatening the security of the encryption system. Biometric keys, especially fingerprint keys, are an effective solution to the above problems because fingerprints are unique, immutable, and convenient. In recent years, researchers have begun to study optical image encryption methods based on fingerprint keys. For example, Tashima et al. proposed a binary image encryption method based on fingerprint keys and double random phase encoding. Zhao et al. proposed a grayscale image encryption method based on fingerprint keys, phase recovery algorithms, and RSA public key algorithms. Su et al. proposed a color image encryption method based on fingerprint key and phase-shift digital holography. However, most of the existing optical image encryption methods based on fingerprint key encrypt a single plaintext image, resulting in low encryption efficiency. In order to meet the demand for high encryption efficiency, some researchers have conducted beneficial research on dual-image / multi-image encryption methods based on fingerprint key. For example, Li et al. proposed a dual-image encryption method based on fingerprint key and Gyrator domain dual random phase encoding. Later, Wang et al. from the same group proposed a multi-image encryption method based on chaotic fingerprint phase mask and multi-layer diffraction imaging.

[0003] However, in the above-mentioned dual-image / multi-image encryption scheme based on fingerprint key, the encryption level of all images is the same, and the access rights of all users are also the same, which cannot meet the requirements of different sensitivity information being given different protection levels, and the security system cannot classify and identify the decryption users in a refined manner, thus severely limiting the scope of application of such schemes. In order to solve the above problems, it is necessary to introduce the idea of ​​hierarchical encryption in the dual-image / multi-image encryption scheme based on fingerprint key, set different encryption levels according to the sensitivity and importance of the image information, and assign different access rights according to the identity of the user, so as to ensure that only authorized users can access the information of the corresponding level. However, the dual-image / multi-image hierarchical encryption scheme based on fingerprint key has not been reported yet. In view of this situation, the present invention proposes a multi-image hierarchical encryption method of fingerprint key and off-axis digital holography, aiming to achieve multi-image hierarchical encryption with high security level, strong robustness of fingerprint key, high encryption efficiency, no crosstalk in decryption, and differentiated authorization of users. Summary of the invention

[0004] The purpose of the present invention is to provide a multi-image hierarchical encryption method based on fingerprint key and off-axis digital holography. The present invention uses the fingerprint of the encryption user as the key, and utilizes the improved double random phase encoding technology and off-axis digital holographic encoding technology to hierarchically encrypt multiple plaintext images, which has the advantages of large key space, strong fingerprint key robustness, high digital key sensitivity, high encryption efficiency, high decryption quality, and small number of ciphertexts.

[0005] To achieve the above-mentioned invention object, the technical solution provided by the present invention is as follows: a multi-image hierarchical encryption method based on fingerprint key and off-axis digital holography, characterized in that it includes encryption steps:

[0006] S1: Encryption level classification: N encryption users and corresponding N plaintext images P to be encrypted n (n=1,2,...,N) is divided into 1~N levels;

[0007] S2: Generation of fingerprint chaotic phase mask: First, collect the encrypted fingerprint original image Z of the nth (n=1, 2, ..., N) level encrypted user n (n=1,2,...,N), and then use fingerprint image processing technology and fingerprint column coding technology to obtain the encrypted fingerprint column code average of each encrypted user and ridge frequency And store it in the encryption database; then, the chaotic initial value mapping is performed on the encrypted fingerprint column code mean and ridge frequency of each encrypted user, and the mapping result is input into the chaotic matrix generation program as the chaotic initial value, thereby generating the first fingerprint chaotic phase mask FCPM required in the n-level encryption process 1,n and the second fingerprint chaotic phase mask FCPM2,n .

[0008] S3: Multi-image hierarchical encryption based on off-axis digital holographic encoding:

[0009] (i) First-level encryption: First, the first-level plaintext image P1 is subjected to improved double random phase encoding, and the encoding result is padded with zeros to obtain the first-level encrypted object light wave g 1,o . After that, the first level encrypted object light wave g 1,o Off-axis digital holographic encoding is performed to generate the first level encrypted hologram I1:

[0010] I1=ODHE(ZP(MDRPE(P1)))

[0011] Where MDRPE(·) and ODHE(·) represent the improved dual random phase encoding and off-axis digital holographic encoding operations, respectively, and ZP(·) represents the zero-filling operation.

[0012] (ii) Encryption at the nth level (n = 2:1:N): First, the plaintext image P to be encrypted at the nth level is n Perform zero-filling operation to obtain zero-filling result Then, the n-1th level encrypted hologram I n-1 and zero-filled result As amplitude and phase respectively, the complex amplitude synthesis technology is used to generate the n-th level encrypted complex amplitude G n After that, the complex amplitude G is encrypted at the nth level. n Improved double random phase encoding is performed, and zero padding is performed on the encoding result to obtain the nth level encrypted light wave g n,o Finally, for the nth level encrypted object light wave g n,o Off-axis digital holographic encoding is performed to generate the nth level encrypted hologram I n :

[0013]

[0014] In the formula, exp(·) represents exponential operation, j is an imaginary unit, and n=2:1:N represents a step length of 1 from 2 to N, that is, the above steps start from the second level of encryption and end after the Nth level of encryption is completed, and finally the Nth level encrypted hologram I is generated. N , and the output is the final multi-image encrypted ciphertext.

[0015] At this point, the encryption step is completed.

[0016] Decryption steps:

[0017] J1: Decrypted fingerprint authentication: First, collect the original decrypted fingerprint image of the nth (n=1,2,...,N) decryption user, and then use the fingerprint image processing technology and fingerprint column code authentication technology to calculate the global similarity GS of the decrypted fingerprint of the nth (n=1,2,...,N) decryption user and the encrypted fingerprint of the nth (n=1,2,...,N) encryption user n , if the global similarity GS n If it is greater than the preset threshold δ, the authentication is successful, and the encrypted fingerprint column code mean of the nth (n=1, 2, ..., N) encrypted user stored in the encryption database is output and ridge frequency As decrypted data and enter the next decryption step; otherwise, the authentication fails and the decryption is terminated.

[0018] J2: Generation of fingerprint chaotic conjugate phase mask: First, the decrypted data output from the previous decryption step, that is, the average encrypted fingerprint column code of the nth (n = 1, 2, ..., N) encrypted user and ridge frequency Perform chaos initial value mapping, and input the mapping result as chaos initial value into the chaos matrix generation program to generate the first fingerprint chaos phase mask FCPM 1,n and the second fingerprint chaotic phase mask FCPM 2,n ; Afterwards, the generated fingerprint chaotic phase mask is conjugated to generate the first fingerprint chaotic conjugate phase mask required in the n-th level decryption process and the second fingerprint chaotic conjugate phase mask

[0019] J3: Multi-image hierarchical decryption based on off-axis digital holographic reconstruction:

[0020] (i) Nth level decryption: First, encrypt the multi-image ciphertext, i.e., the Nth level encrypted hologram I N Perform off-axis digital holographic reconstruction to obtain the Nth level decryption object light wave Afterwards, the Nth level decryption object light wave Perform improved double random phase decoding to obtain the Nth level decrypted complex amplitude Afterwards, the amplitude extraction and phase extraction operations are performed on the N-th level decrypted complex amplitude, thereby obtaining the N-th level decryption result and the N-1 level decrypted hologram

[0021]

[0022]

[0023] Where MDRPD(·) and ODHR(·) represent the improved dual random phase decoding and off-axis digital holographic decoding operations, respectively, and arg(·) represents the phase extraction operation.

[0024] (ii) nth level decryption (n = N-1:-1:2): First, the nth level decryption hologram Perform off-axis digital holographic reconstruction to obtain the nth level decryption object light wave Afterwards, the nth level decryption object light wave Perform improved double random phase decoding to obtain the nth level decrypted complex amplitude Afterwards, the amplitude extraction and phase extraction operations are performed on the n-th level decrypted complex amplitude, thereby obtaining the n-th level decryption result and the n-1th level decrypted hologram

[0025]

[0026]

[0027] In the formula, n = N-1:-1:2 means taking -1 as the step length, from N-1 to 2, that is, the above steps start from the N-1th level decryption and end after the second level decryption is completed, and finally generate the second level decryption result and Level 1 Decrypted Hologram

[0028] (iii) Generation of the first-level decryption result: First, the first-level decryption hologram Perform off-axis digital holographic reconstruction to obtain the first-level decryption light wave Afterwards, the first level decryption object light wave Perform improved dual random phase decoding and perform amplitude extraction on the decoding result to obtain the first level decryption result

[0029]

[0030] At this point, the decryption step is completed.

[0031] The above-mentioned multi-image hierarchical encryption method based on fingerprint key and off-axis digital holography, the improved double random phase encoding in the encryption step S3 is characterized by: first, the input signal S in Perform the first chaotic phase fractional Fourier transform and compare the result with the first fingerprint chaotic phase mask FCPM 1,n The phase distribution is multiplied by the second chaotic phase fractional Fourier transform, and the result of this transformation is combined with the second fingerprint chaotic phase mask FCPM 2,nThe phase distribution of the input signal S is multiplied by the phase distribution of the input signal S, and then the product is subjected to the third chaotic phase fractional Fourier transform to obtain the input signal S in The output signal S generated after improved double random phase encoding out for:

[0032]

[0033] In the formula, Indicates that the wavelength is λ and the fractional order is a i , focal length is f i Fractional Fourier transform operation of chaotic phase.

[0034] The above-mentioned multi-image hierarchical encryption method based on fingerprint key and off-axis digital holography, the off-axis digital holographic encoding in the encryption step S3 is characterized in that: the n-th level encryption object light wave g n,o (n=1,2,…,N) propagates vertically to the holographic recording plane through Fresnel diffraction, and at the same time introduces a reference light wave g which is not coaxial with the object light wave n,r (n=1,2,...,N), interferes with the object light wave on the holographic recording plane, thereby generating the nth level encrypted hologram I n (n=1,2,...,N):

[0035] I n =ODHE(g n,o )=FRT λ,d (g n,o )+g n,r 2 (n=1:1:N)

[0036] Where, FRT λ,d (·) represents the Fresnel diffraction operation with a wavelength of λ and a distance of d, |·| represents the amplitude extraction operation, and n=1:1:N represents the step size from 1 to N.

[0037] In the above-mentioned multi-image hierarchical encryption method based on fingerprint key and off-axis digital holography, the off-axis digital holographic reconstruction in the decryption step J3 is characterized in that: the reference light wave is used as the reconstructed light wave to illuminate the Nth level encrypted hologram I N or the nth level decrypted hologram Diffraction occurs on the surface, and then bandpass filtering is performed on the reconstruction plane to obtain the nth order decryption object light wave

[0038]

[0039] In the formula, The wavelength is Distance is BPF(·) represents the inverse Fresnel diffraction operation, and n=1:1:N-1 represents the step size from 1 to N-1.

[0040] The above-mentioned multi-image hierarchical encryption method based on fingerprint key and off-axis digital holography, the improved double random phase decoding in the decryption step J3 is characterized by: first, the input signal Perform the first chaotic phase fractional Fourier inverse transform and combine the inverse transform result with the second fingerprint chaotic conjugate phase mask The phase distribution of the first fingerprint is multiplied by the second chaotic phase fractional Fourier inverse transform, and the inverse transform result is combined with the first fingerprint chaotic conjugate phase mask. The phase distribution of the input signal is multiplied by the chaotic phase fractional Fourier transform. Output signal generated after improved double random phase encoding for:

[0041]

[0042] In the formula, The wavelength is The fractional order is The focal length is The inverse fractional Fourier transform operation of the chaotic phase.

[0043] The beneficial effects of the present invention are as follows: (1) The present invention implements multi-image encryption by hierarchical encryption, and all plaintext image encryption levels and decryption user access rights are different, which can meet the needs of different sensitivity information being assigned different protection levels, and the security system can also accurately identify the decryption user during decryption; (2) The fingerprint key in the present invention is easy to carry, the digital key is easy to remember, and there is no random phase mask key, thereby effectively reducing the complexity of the key; (3) The present invention uses fingerprint column code authentication technology to perform security authentication on the decryption fingerprint key, which effectively improves the robustness of the fingerprint key; (4) The present invention adopts an improved dual random phase encoding technology in the encryption process, thereby effectively improving the sensitivity of the digital key and significantly improving the security of the encryption method; (5) The encryption process and decryption process of each level in the present invention are independent, thereby avoiding the crosstalk problem commonly existing in the existing multi-image encryption scheme and ensuring the high quality of the decrypted image; (6) The present invention finally encrypts multiple plaintext images into an amplitude-type ciphertext based on off-axis digital holography technology, which is convenient for storage and transmission. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1The present invention is a flow chart of encryption steps in a multi-image hierarchical encryption method based on fingerprint key and off-axis digital holography.

[0045] Figure 2 The flowchart for generating the chaotic phase mask of the fingerprint of the nth level encrypted user in the encryption step S2, where Z n The original encrypted fingerprint image of the nth level encrypted user; and are the encrypted fingerprint column code mean and ridge frequency of the nth level encrypted user respectively; CIVM and CMG represent the chaotic initial value mapping and chaotic matrix generation operations; and Two sets of output results of chaotic initial value mapping; FCPM 1,n and FCPM 2,n They are respectively the first fingerprint chaotic phase mask and the second fingerprint chaotic phase mask required in the n-th level encryption process.

[0046] Figure 3 is a flowchart of the implementation of the encryption step S3, wherein P1, P2, P3, ..., P N They are the first level, second level, third level, ..., and Nth level plaintext images to be encrypted respectively; They are P2, P3, ..., P N The zero-filling result of G2, G3, ..., G N are the encrypted complex amplitudes of the 2nd, 3rd, …, Nth levels respectively; g 1,o ,g 2,o ,g 3,o ,...,g N,o They are the 1st level, 2nd level, 3rd level, ..., Nth level encrypted light waves; I1, I2, I3, ..., I N-1 ,I N They are the 1st level, 2nd level, 3rd level, …, N-1th level, and Nth level encrypted holograms respectively; MDRPE and ODHE represent improved dual random phase encoding and off-axis digital holographic encoding operations respectively; ZP and CAS represent zero-filling and complex amplitude synthesis operations respectively.

[0047] Figure 4 is a flowchart of the implementation of the improved double random phase encoding in the encryption step S3, wherein S in and S out are the input signal and output signal in the improved double random phase encoding process respectively; Indicates that the wavelength is λ and the fractional order is a i , focal length is f i Fractional Fourier transform operation of chaotic phase.

[0048] Figure 5is a flowchart for implementing off-axis digital holographic encoding in the encryption step S3, wherein g n,o and g n,r are the nth level encrypted object light wave and the reference light wave respectively; n Encrypted hologram for level n; FRT λ,d Represents the Fresnel diffraction operation with wavelength λ and distance d.

[0049] Figure 6 The present invention is a flow chart of the decryption steps in a multi-image hierarchical encryption method based on fingerprint key and off-axis digital holography.

[0050] Figure 7 This is the decryption fingerprint authentication flow chart of the nth level decryption user in the decryption step J1, where Decrypted fingerprint original image for the nth level decryption user; GS n Decryption fingerprint for the nth decryption user and the encrypted fingerprint Z of the nth encrypted user n The global similarity of ; δ is the preset threshold.

[0051] Figure 8 A flow chart is generated for the chaotic conjugate phase mask of the fingerprint of the nth level decryption user in the decryption step J2, where and They are respectively the first fingerprint chaotic conjugate phase mask and the second fingerprint chaotic conjugate phase mask required in the n-th level decryption process.

[0052] Fig. 9 This is a flowchart of multi-image hierarchical decryption based on off-axis digital holographic reconstruction in decryption step J3, where The decrypted holograms are respectively level N-1, level N-2, ..., level 2, and level 1; They are respectively the Nth level, the N-1th level, ..., the 2nd level, and the 1st level decryption material light waves; The decrypted complex amplitudes are respectively the Nth level, the N-1th level, …, the 2nd level, and the 1st level; They are the decryption results of level N, level N-1,…, level 2, and level 1 respectively; ODHR and MDRPD represent improved dual random phase decoding and off-axis digital holographic decoding operations respectively; AE and PE represent amplitude extraction operation and phase extraction operation respectively.

[0053] Fig.10 is a flowchart for implementing off-axis digital holographic reconstruction in decryption step J3, where g N,r and They are the Nth level reference light wave and the decryption object light wave respectively; Decrypt the hologram for level n; g n,r and They are the nth level reference light wave and the decryption object light wave respectively; The wavelength is Distance is The inverse Fresnel diffraction operation; BPF stands for bandpass filtering operation.

[0054] Fig.11 is a flowchart of the implementation of the improved double random phase decoding in the decryption step J3, wherein and are the input signal and output signal in the improved dual random phase decoding process respectively; The wavelength is The fractional order is The focal length is The inverse fractional Fourier transform operation of the chaotic phase.

[0055] Fig.12 (a1)-(a4) are the first level, second level, third level, and fourth level plaintext images to be encrypted ("Mandrill", "Peppers", "Barbara", "Lena"); (b1)-(b4) are the first level, second level, third level, and fourth level encrypted user's encrypted fingerprint original images; (c1)-(c2) are the first fingerprint chaotic phase mask FCPM required in the first level encryption process 1,1 and the second fingerprint chaotic phase mask FCPM 2,1 ; (d1)-(d2) are the first fingerprint chaotic phase mask FCPM required in the second level encryption process 1,2 and the second fingerprint chaotic phase mask FCPM 2,2 ; (e1)-(e2) are the first fingerprint chaotic phase mask FCPM required in the third level encryption process 1,3 and the second fingerprint chaotic phase mask FCPM 2,3 ; (f1)-(f2) are the first fingerprint chaotic phase mask FCPM required in the fourth level encryption process 1,4 and the second fingerprint chaotic phase mask FCPM 2,4 ; (g1)-(g4) are the 1st, 2nd, 3rd and 4th level encrypted holograms (I1, I2, I3, I4) respectively.

[0056] Fig.13 When all the keys are correct, the final four-image decryption results are: (a) is the 4th level decryption result, (b) is the 3rd level decryption result, (c) is the 2nd level decryption result, and (d) is the 1st level decryption result.

[0057] Fig.14 (a)-(f) are some randomly selected erroneous decryption fingerprint keys; (g) is the authentication result of the above decryption fingerprint keys.

[0058] Fig.15 It is the decryption result when the fingerprint keys of the decryption users at each level are wrong but the other keys are correct.

[0059] Fig.16 (a) is the test result of fingerprint key occlusion robustness; (b) is the test result of fingerprint key rotation robustness; (c) is the test result of fingerprint key fuzzy robustness.

[0060] Fig.17 (a)-(g) are the sensitivity curves of wavelength key λ, fractional order key a1, fractional order key a2, fractional order key a3, focal length key f1, focal length key f2, and focal length key f3, respectively. DETAILED DESCRIPTION

[0061] The present invention is further described below in conjunction with the embodiments and drawings, but they are not intended to limit the present invention.

[0062] Embodiment: A multi-image hierarchical encryption method based on fingerprint key and off-axis digital holography, comprising: Figure 1 Encryption steps shown:

[0063] S1: Encryption level classification: N encryption users and corresponding N plaintext images P to be encrypted n (n=1,2,...,N) is divided into 1~N levels;

[0064] S2: Generation of fingerprint chaotic phase mask: The fingerprint chaotic phase mask generation process of the nth (n = 1, 2, ..., N) level encryption user is as follows: Figure 2 First, collect the encrypted fingerprint original image Z of the nth (n=1,2,…,N) level encrypted user n (n=1,2,…,N), and then use fingerprint image processing technology and fingerprint column coding technology to obtain the average encrypted fingerprint column code of each encrypted user and ridge frequency And store it in the encryption database; then, the chaotic initial value mapping is performed on the encrypted fingerprint column code mean and ridge frequency of each encrypted user, and the mapping result is input into the chaotic matrix generation program as the chaotic initial value, thereby generating the first fingerprint chaotic phase mask FCPM required in the n-level encryption process 1,n and the second fingerprint chaotic phase mask FCPM 2,n .

[0065] S3: Multi-image hierarchical encryption based on off-axis digital holographic encoding: The implementation process of this step is as follows Figure 3 As shown, it specifically includes the following two sub-steps:

[0066] (i) First-level encryption: First, the first-level plaintext image P1 is subjected to improved double random phase encoding, and the encoding result is padded with zeros to obtain the first-level encrypted object light wave g 1,o . After that, the first level encrypted object light wave g 1,o Off-axis digital holographic encoding is performed to generate the first level encrypted hologram I1:

[0067] I1=ODHE(ZP(MDRPE(P1)))

[0068] Where MDRPE(·) and ODHE(·) represent the improved dual random phase encoding and off-axis digital holographic encoding operations, respectively, and ZP(·) represents the zero-filling operation.

[0069] (ii) Encryption at the nth level (n = 2:1:N): First, the plaintext image P to be encrypted at the nth level is n Perform zero-filling operation to obtain zero-filling result Then, the n-1th level encrypted hologram I n-1 and zero-filled result As amplitude and phase respectively, the complex amplitude synthesis technology is used to generate the n-th level encrypted complex amplitude G n After that, the complex amplitude G is encrypted at the nth level. n Improved double random phase encoding is performed, and zero padding is performed on the encoding result to obtain the nth level encrypted light wave g n,o Finally, for the nth level encrypted object light wave g n,o Off-axis digital holographic encoding is performed to generate the nth level encrypted hologram I n :

[0070]

[0071] In the formula, exp(·) represents exponential operation, j is an imaginary unit, and n=2:1:N represents a step length of 1 from 2 to N, that is, the above steps start from the second level of encryption and end after the Nth level of encryption is completed, and finally the Nth level encrypted hologram I is generated. N , and the output is the final multi-image encrypted ciphertext.

[0072] At this point, the encryption step is completed.

[0073] In the above-mentioned multi-image hierarchical encryption method based on fingerprint key and off-axis digital holography, the improved double random phase encoding in the encryption step S3 is characterized in that: the implementation process of this step is as follows Figure 4 First, the input signal S in Perform the first chaotic phase fractional Fourier transform and compare the result with the first fingerprint chaotic phase mask FCPM 1,nThe phase distribution is multiplied by the second chaotic phase fractional Fourier transform, and the result of this transformation is combined with the second fingerprint chaotic phase mask FCPM 2,n The phase distribution of the input signal S is multiplied by the phase distribution of the input signal S, and then the product is subjected to the third chaotic phase fractional Fourier transform to obtain the input signal S in The output signal S generated after improved double random phase encoding out for:

[0074]

[0075] In the formula, Indicates that the wavelength is λ and the fractional order is a i , focal length is f i Fractional Fourier transform operation of chaotic phase.

[0076] The above-mentioned multi-image hierarchical encryption method based on fingerprint key and off-axis digital holography, the off-axis digital holographic encoding in the encryption step S3 is characterized in that: the n-th level encryption object light wave g n,o (n=1,2,…,N) propagates vertically to the holographic recording plane through Fresnel diffraction, and at the same time introduces a reference light wave g which is not coaxial with the object light wave n,r (n=1,2,...,N), interferes with the object light wave on the holographic recording plane, thereby generating the nth level encrypted hologram I n (n=1,2,…,N). Mathematically, the off-axis digital holographic encoding process can be expressed as follows: Figure 5 The implementation process shown in FIG. 1 is as follows: n It can be expressed as: n =ODHE(g n,o )=FRT λ,d (g n,o )+g n,r 2 (n=1:1:N)

[0077] Where, FRT λ,d (·) represents the Fresnel diffraction operation with a wavelength of λ and a distance of d, |·| represents the amplitude extraction operation, and n=1:1:N represents the step size from 1 to N.

[0078] like Figure 6 Decryption steps shown:

[0079] J1: Decryption fingerprint authentication: The decryption fingerprint authentication process of the nth (n=1, 2, ..., N) decryption user is as follows Figure 7First, the original image of the decrypted fingerprint of the nth (n=1,2,...,N) decryption user is collected, and then the global similarity GS of the decrypted fingerprint of the nth (n=1,2,...,N) decryption user and the encrypted fingerprint of the nth (n=1,2,...,N) encryption user is calculated by using the fingerprint image processing technology and the fingerprint column code authentication technology. n , if the global similarity GS n If it is greater than the preset threshold δ, the authentication is successful, and the encrypted fingerprint column code mean of the nth (n=1, 2, ..., N) encrypted user stored in the encryption database is output and ridge frequency As decrypted data and enter the next decryption step; otherwise, the authentication fails and the decryption is terminated.

[0080] J2: Generation of fingerprint chaotic conjugate phase mask: The generation process of the fingerprint chaotic phase conjugate bit mask of the nth (n=1,2,...,N) level decryption user is as follows Figure 8 First, the decrypted data output from the previous decryption step, that is, the average encrypted fingerprint column code of the nth (n = 1, 2, ..., N) encrypted user and ridge frequency Perform chaos initial value mapping, and input the mapping result as chaos initial value into the chaos matrix generation program to generate the first fingerprint chaos phase mask FCPM 1,n and the second fingerprint chaotic phase mask FCPM 2,n ; Afterwards, the generated fingerprint chaotic phase mask is conjugated to generate the first fingerprint chaotic conjugate phase mask required in the n-th level decryption process and the second fingerprint chaotic conjugate phase mask

[0081] J3: Multi-image hierarchical decryption based on off-axis digital holographic reconstruction: The implementation process of this step is as follows Fig. 9 As shown, it specifically includes the following three sub-steps:

[0082] (i) Nth level decryption: First, encrypt the multi-image ciphertext, i.e., the Nth level encrypted hologram I N Perform off-axis digital holographic reconstruction to obtain the Nth level decryption object light wave Afterwards, the Nth level decryption object light wave Perform improved double random phase decoding to obtain the Nth level decrypted complex amplitude Afterwards, the amplitude extraction and phase extraction operations are performed on the N-th level decrypted complex amplitude, thereby obtaining the N-th level decryption result and the N-1 level decrypted hologram

[0083]

[0084]

[0085] Where MDRPD(·) and ODHR(·) represent the improved dual random phase decoding and off-axis digital holographic decoding operations, respectively, and arg(·) represents the phase extraction operation.

[0086] (ii) nth level decryption (n = N-1:-1:2): First, the nth level decryption hologram Perform off-axis digital holographic reconstruction to obtain the nth level decryption object light wave Afterwards, the nth level decryption object light wave Perform improved double random phase decoding to obtain the nth level decrypted complex amplitude Afterwards, the amplitude extraction and phase extraction operations are performed on the n-th level decrypted complex amplitude, thereby obtaining the n-th level decryption result and the n-1th level decrypted hologram

[0087]

[0088]

[0089] In the formula, n = N-1:-1:2 means taking -1 as the step length, from N-1 to 2, that is, the above steps start from the N-1th level decryption and end after the second level decryption is completed, and finally generate the second level decryption result and Level 1 Decrypted Hologram

[0090] (iii) Generation of the first-level decryption result: First, the first-level decryption hologram Perform off-axis digital holographic reconstruction to obtain the first-level decryption light wave Afterwards, the first level decryption object light wave Perform improved dual random phase decoding and perform amplitude extraction on the decoding result to obtain the first level decryption result

[0091]

[0092] At this point, the decryption step is completed.

[0093] In the above-mentioned multi-image hierarchical encryption method based on fingerprint key and off-axis digital holography, the off-axis digital holographic reconstruction in the decryption step J3 is characterized in that: the reference light wave is used as the reconstructed light wave to illuminate the Nth level encrypted hologram I N or the nth level decrypted hologram Diffraction occurs on the surface, and then bandpass filtering is performed on the reconstruction plane to obtain the nth order decryption object light wave Mathematically, the process of off-axis digital holographic reconstruction can be expressed as follows: Fig.10 The implementation process shown in the figure, then the nth level decryption material light wave It can be expressed as:

[0094]

[0095]

[0096] In the formula, The wavelength is Distance is BPF(·) represents the inverse Fresnel diffraction operation, and n=1:1:N-1 represents the step size from 1 to N-1.

[0097] In the above-mentioned multi-image hierarchical encryption method based on fingerprint key and off-axis digital holography, the improved double random phase decoding in the decryption step J3 is characterized in that: the implementation process of this step is as follows Fig.11 First, the input signal Perform the first chaotic phase fractional Fourier inverse transform and combine the inverse transform result with the second fingerprint chaotic conjugate phase mask The phase distribution of the first fingerprint is multiplied by the second chaotic phase fractional Fourier inverse transform, and the inverse transform result is combined with the first fingerprint chaotic conjugate phase mask. The phase distribution of the input signal is multiplied by the chaotic phase fractional Fourier transform. Output signal generated after improved double random phase encoding for:

[0098]

[0099] In the formula, The wavelength is The fractional order is The focal length is The inverse fractional Fourier transform operation of the chaotic phase.

[0100] The content of the present invention is further explained below in conjunction with specific embodiments and drawings.

[0101] First, four grayscale images ("Mandrill", "Peppers", "Barbara", and "Lena") with a pixel count of 256×256 are selected as the first, second, third, and fourth level plaintext images to be encrypted (P1, P2, P3, and P4), respectively. Fig.12 (a1)-(a4). Figure 1 The encryption steps shown in the figure are used to hierarchically encrypt the above four plaintext images. The encrypted fingerprint original images of the four encrypted users are collected as follows: Fig.12 (b1)-(b4) are shown, and then the average encrypted fingerprint column code of each encrypted user is obtained. and ridge frequency Afterwards The chaotic initial value mapping is performed respectively, and the mapping results are input into the chaotic matrix generation program as the chaotic initial value, thereby generating the first fingerprint chaotic phase mask FCPM required in the first level encryption process. 1,1 and the second fingerprint chaotic phase mask FCPM 2,1 , respectively Fig.12 (c1) and (c2) show the first fingerprint chaotic phase mask FCPM required in the second level encryption process 1,2 and the second fingerprint chaotic phase mask FCPM 2,2 , respectively Fig.12 (d1) and (d2) show the first fingerprint chaotic phase mask FCPM required in the third level encryption process 1,3 and the second fingerprint chaotic phase mask FCPM 2,3 , respectively Fig.12 (e1) and (e2) show the first fingerprint chaotic phase mask FCPM required in the 4th level encryption process 1,4 and the second fingerprint chaotic phase mask FCPM 2,4 , respectively Fig.12 (f1) and (f2). The wavelength λ used in multi-image hierarchical encryption is set to 632.8nm, the fractional orders a1, a2, a3 are 1.1, 1.4, 1.7 respectively, and the focal lengths f1, f2, f3 are 60mm, 80mm, 100mm respectively. In addition, the reference light wave used in off-axis digital holographic encoding is set to a uniform plane light wave that is not coaxial with the object light wave, with a wavelength λ of 632.8nm and a Fresnel diffraction distance d of 1500mm. Figure 3 After the encryption step S3 shown in FIG. 1 , the first level, the second level, the third level, and the fourth level encrypted holograms (I1, I2, I3, and I4) are generated step by step, respectively. Fig.12 As shown in (g1)-(g4), the fourth-level encrypted hologram I4 is output as the final multi-image encrypted ciphertext. At this point, the encryption steps are completed.

[0102] The following is based on Figure 6The decryption steps shown in the figure are used to perform hierarchical decryption of four images. The required decryption keys include the fingerprint key and digital key (wavelength key, fractional key, focal length key) of each level of decryption user. When all the keys are correct, the final decryption results of the four images are as follows: Fig.13 (a)-(d) are shown. Fig.13 It can be seen from the decryption results that when all the keys are correct, all the original plaintext images can be reconstructed with high quality. The effectiveness and security of the fingerprint key in the present invention are tested below. It should be noted that, in order to facilitate the display of the test results, only the authentication results of the fingerprint key of the first-level encrypted user when it is subjected to a brute force attack by an illegal attacker are shown below. The authentication results of other fingerprint keys when they are subjected to a brute force attack by an illegal attacker are similar to those of the first level. The applicant randomly collected more than 500 fingerprint images from different attackers as incorrect decryption fingerprint keys, and randomly extracted some incorrect decryption fingerprint keys such as Fig.14 (a)-(f) are shown and are named WF(a), WF(b), WF(c), WF(d), WF(e), and WF(f) respectively. Fig.14 (g) shows the authentication result of the above decryption fingerprint key. It should be noted that the authentication results of other incorrect decryption fingerprint keys are the same as Fig.14 The authentication results shown in (g) are similar. Fig.14 From the authentication result in (g), we can see that the global similarity between the wrong decryption fingerprint key and the encryption fingerprint key is less than the preset threshold (0.65), which will lead to authentication failure and decryption termination. Fig.13 The correct decryption result shown proves the effectiveness and security of the fingerprint key in the present invention.

[0103] The cascading characteristics of the fingerprint key in the present invention are examined below. Fig.15 The decryption results are given when the fingerprint keys of the decryption users at each level are wrong but the other keys are correct. Fig.15 It can be seen from the decryption results that when an error occurs in the fingerprint key of a certain level of decryption user, not only will the decryption of this level be terminated, but also the decryption of all subsequent levels will be terminated, which shows that the fingerprint key in the present invention has an obvious cascading characteristic. This feature can be used to perform differentiated authorization on decryption users, and different encryption levels can be set according to the sensitivity and importance of the plaintext image to achieve multi-image hierarchical encryption. When decrypting, if a certain level of plaintext image needs to be correctly decrypted, not only the access rights of the decryption user at this level need to be authorized, but also the access rights of all previous levels of decryption users are required. For example, in this embodiment, the encryption levels of the 1st, 2nd, 3rd, and 4th level plaintext images are set from high to low. Therefore, if the 1st level plaintext image needs to be decrypted, the fingerprint keys of all decryption users from the 1st to the 4th level need to be authorized to complete the correct decryption.

[0104] The robustness of the fingerprint key in the present invention is tested below, including occlusion robustness, rotation robustness and fuzzy robustness. It should be noted that, for the convenience of displaying the test results, only the authentication results of the fingerprint key of the first-level encrypted user when subjected to occlusion, rotation and fuzzy attacks are shown below, and the authentication results of other fingerprint keys when subjected to corresponding attacks are similar to those of the first level. Fig.16 (a)-(c) give the test results of fingerprint key occlusion, rotation and fuzzy robustness respectively. Fig.16 The test results in (a) show that even when the occlusion range is 60%, the global similarity between the fingerprint key and the encrypted fingerprint key is still higher than the preset threshold (0.65), which proves that the fingerprint key in the present invention has good robustness against occlusion attacks. Fig.16 The test results in (b) show that the global similarity between the decrypted fingerprint key and the encrypted fingerprint key hardly changes with the rotation of the decrypted fingerprint key and is always much higher than the preset threshold (0.65), thus proving that the fingerprint key in the present invention has excellent robustness against rotation attacks. Fig.16 It can be seen from the test results in (c) that even the global similarity between the fuzzy fingerprint key and the encrypted fingerprint key with a Gaussian convolution kernel size of 11×11 is still higher than the preset threshold (0.65), which proves that the fingerprint key in the present invention has good robustness against fuzzy attacks.

[0105] The security and sensitivity of the digital key in the present invention are examined below, wherein the correlation coefficient (CC) is used as an evaluation function to quantitatively evaluate the degree of correlation between the decryption result and the plaintext image. Fig.17 The relationship between the average value of CC between each decryption result and the plaintext image and the deviation of each digital key is given when the fingerprint keys of all levels of decryption users are correct, that is, the sensitivity curve of each digital key. Fig.17 (a)-(g) represent the sensitivity curves of wavelength key λ, fractional key a1, fractional key a2, fractional key a3, focal key f1, focal key f2, focal key f3, respectively. In addition, the wavelength key λ deviates by 10 -11 nm, fractional key a1 deviation 10 -11 、Fractional key a2 deviation 10 -11 、Fractional key a3 deviation 10 -11 、Focus key f1 deviation 10 -11 mm, focal length key f2 deviation 10 -11 mm, focal length key f3 deviation 10 -11 The four image decryption results corresponding to mm are marked respectively in Fig.17 (a)-(g). Fig.17It can be seen from the sensitivity curve in that when any digital key has a slight deviation, the CC between the decryption result and the plaintext image drops sharply to close to 0. At this time, the decryption results all show obvious noise distribution, resulting in the inability to correctly restore the original plaintext image, thereby proving the security of the digital key in the present invention and indicating that the digital key in the present invention has extremely high sensitivity.

[0106] In summary, the present invention discloses a multi-image hierarchical encryption method based on fingerprint keys and off-axis digital holography. In the present invention, the encryption process utilizes improved dual random phase encoding technology and off-axis digital holography encoding technology to hierarchically encrypt multiple plaintext images, thereby being able to meet the needs of different sensitivity information being given different protection levels, wherein the improved dual random phase encoding technology can effectively improve the sensitivity of the digital key, thereby significantly improving the security of the encryption method. In addition, the encrypted fingerprint information of each level of encryption users is extracted and encoded into a fingerprint chaotic phase mask to form a fingerprint key, thereby effectively reducing the complexity of the key and improving the portability of the key. The decryption process utilizes fingerprint column code authentication technology to perform security authentication on the decryption fingerprint key, thereby effectively improving the robustness of the fingerprint key, and since the encryption process and decryption process of each level are independent, the crosstalk problem of multi-image decryption is avoided, ensuring the high quality of the decrypted image.

Claims

1. A multi-image hierarchical encryption method based on fingerprint key and off-axis digital holography, characterized in that: The encryption steps include: S1: Encryption level classification: N encryption users and the corresponding N plaintext images P to be encrypted n (n=1,2,...,N) is divided into 1~N levels; S2: Generation of fingerprint chaotic phase mask: First, collect the encrypted fingerprint original image Z of the nth (n=1, 2, ..., N) level encrypted user n (n=1,2,...,N), and then use fingerprint image processing technology and fingerprint column coding technology to obtain the encrypted fingerprint column code average of each encrypted user and ridge frequency and stored in an encrypted database; After that, the chaotic initial value mapping is performed on the encrypted fingerprint column code mean and ridge frequency of each encrypted user, and the mapping result is input into the chaotic matrix generation program as the chaotic initial value, thereby generating the first fingerprint chaotic phase mask FCPM required in the n-th level encryption process. 1,n and the second fingerprint chaotic phase mask FCPM 2,n . S3: Multi-image hierarchical encryption based on off-axis digital holographic encoding: (i) First-level encryption: First, the first-level plaintext image P1 is subjected to improved double random phase encoding, and the encoding result is padded with zeros to obtain the first-level encrypted object light wave g 1,o . After that, the first level encrypted object light wave g 1,o Off-axis digital holographic encoding is performed to generate the first level encrypted hologram I1: I1=ODHE(ZP(MDRPE(P1))) Where MDRPE(·) and ODHE(·) represent the improved dual random phase encoding and off-axis digital holographic encoding operations, respectively, and ZP(·) represents the zero-filling operation. (ii) Encryption at the nth level (n = 2:1:N): First, the plaintext image P to be encrypted at the nth level is n Perform zero-filling operation to obtain zero-filling result Then, the n-1th level encrypted hologram I n-1 and zero-filled result As amplitude and phase respectively, the complex amplitude synthesis technology is used to generate the n-th level encrypted complex amplitude G n After that, the complex amplitude G is encrypted at the nth level. n Improved double random phase encoding is performed, and zero padding is performed on the encoding result to obtain the nth level encrypted light wave g n,o Finally, for the nth level encrypted object light wave g n,o Off-axis digital holographic encoding is performed to generate the nth level encrypted hologram I n : In the formula, exp(·) represents exponential operation, j is an imaginary unit, and n=2:1:N represents a step length of 1 from 2 to N, that is, the above steps start from the second level of encryption and end after the Nth level of encryption is completed, and finally the Nth level encrypted hologram I is generated. N , and the output is the final multi-image encrypted ciphertext. At this point, the encryption step is completed. Decryption steps: J1: Decrypted fingerprint authentication: First, collect the original decrypted fingerprint image of the nth (n=1,2,...,N) decryption user, and then use the fingerprint image processing technology and fingerprint column code authentication technology to calculate the global similarity GS of the decrypted fingerprint of the nth (n=1,2,...,N) decryption user and the encrypted fingerprint of the nth (n=1,2,...,N) encryption user n , if the global similarity GS n If it is greater than the preset threshold δ, the authentication is successful, and the encrypted fingerprint column code mean of the nth (n=1, 2, ..., N) encrypted user stored in the encryption database is output and ridge frequency As decrypted data and enter the next decryption step; Otherwise, authentication fails and decryption is terminated. J2: Generation of fingerprint chaotic conjugate phase mask: First, the decrypted data output from the previous decryption step, that is, the average encrypted fingerprint column code of the nth (n = 1, 2, ..., N) encrypted user and ridge frequency Perform chaos initial value mapping, and input the mapping result as chaos initial value into the chaos matrix generation program to generate the first fingerprint chaos phase mask FCPM 1,n and the second fingerprint chaotic phase mask FCPM 2,n ; Afterwards, the generated fingerprint chaotic phase mask is conjugated to generate the first fingerprint chaotic conjugate phase mask required in the n-th level decryption process and the second fingerprint chaotic conjugate phase mask J3: Multi-image hierarchical decryption based on off-axis digital holographic reconstruction: (i) Nth level decryption: First, encrypt the multi-image ciphertext, i.e., the Nth level encrypted hologram I N Perform off-axis digital holographic reconstruction to obtain the Nth level decryption object light wave Afterwards, the Nth level decryption object light wave Perform improved double random phase decoding to obtain the Nth level decrypted complex amplitude Afterwards, the amplitude extraction and phase extraction operations are performed on the N-th level decrypted complex amplitude, thereby obtaining the N-th level decryption result and the N-1 level decrypted hologram Where MDRPD(·) and ODHR(·) represent the improved dual random phase decoding and off-axis digital holographic decoding operations, respectively, and arg(·) represents the phase extraction operation. (ii) nth level decryption (n = N-1:-1:2): First, the nth level decryption hologram Perform off-axis digital holographic reconstruction to obtain the nth level decryption light wave Afterwards, the nth level decryption object light wave Perform improved double random phase decoding to obtain the nth level decrypted complex amplitude Afterwards, the amplitude extraction and phase extraction operations are performed on the n-th level decrypted complex amplitude, thereby obtaining the n-th level decryption result and the n-1th level decrypted hologram In the formula, n = N-1:-1:2 means taking -1 as the step length, from N-1 to 2, that is, the above steps start from the N-1th level decryption and end after the second level decryption is completed, and finally generate the second level decryption result and Level 1 Decrypted Hologram (iii) Generation of the first-level decryption result: First, the first-level decryption hologram Perform off-axis digital holographic reconstruction to obtain the first-level decryption light wave Afterwards, the first level decryption object light wave Perform improved dual random phase decoding and perform amplitude extraction on the decoding result to obtain the first level decryption result At this point, the decryption step is completed.

2. The multi-image hierarchical encryption method based on fingerprint key and off-axis digital holography according to claim 1, characterized in that: The improved double random phase coding in the encryption step S3 is characterized in that: first, the input signal S in Perform the first chaotic phase fractional Fourier transform and compare the result with the first fingerprint chaotic phase mask FCPM 1,n The phase distribution is multiplied by the second chaotic phase fractional Fourier transform, and the result of this transformation is combined with the second fingerprint chaotic phase mask FCPM 2,n The phase distribution of the input signal S is multiplied by the phase distribution of the input signal S, and then the product is subjected to the third chaotic phase fractional Fourier transform to obtain the input signal S in The output signal S generated after improved double random phase encoding out for: In the formula, Indicates that the wavelength is λ and the fractional order is a i , focal length is f i Fractional Fourier transform operation of chaotic phase.

3. The multi-image hierarchical encryption method based on fingerprint key and off-axis digital holography according to claim 1, characterized in that: The off-axis digital holographic encoding in the encryption step S3 is characterized in that: the nth level encryption object light wave g n,o (n=1,2,…,N) propagates vertically to the holographic recording plane through Fresnel diffraction, and at the same time introduces a reference light wave g which is not coaxial with the object light wave n,r (n=1,2,…,N), interferes with the object light wave on the holographic recording plane, thereby generating the nth level encrypted hologram I n (n=1,2,...,N): I n =ODHE(g n,o )=|FRT λ,d (g n,o )+g n,r | 2 (n=1:1:N) Where, FRT λ,d (·) represents the Fresnel diffraction operation with a wavelength of λ and a distance of d, |·| represents the amplitude extraction operation, and n=1:1:N represents the step size from 1 to N.

4. The multi-image hierarchical encryption method based on fingerprint key and off-axis digital holography according to claim 1, characterized in that: The off-axis digital holographic reconstruction in the decryption step J3 is characterized in that: the reference light wave is used as the reconstructed light wave to illuminate the Nth level encrypted hologram I N or the nth level decrypted hologram Diffraction occurs on the surface, and then bandpass filtering is performed on the reconstruction plane to obtain the nth order decryption object light wave In the formula, The wavelength is Distance is BPF(·) represents the inverse Fresnel diffraction operation, and n=1:1:N-1 represents the step size from 1 to N-1.

5. The multi-image hierarchical encryption method based on fingerprint key and off-axis digital holography according to claim 1, characterized in that: The improved double random phase decoding in the decryption step J3 is characterized in that: first, the input signal Perform the first chaotic phase fractional Fourier inverse transform and combine the inverse transform result with the second fingerprint chaotic conjugate phase mask The phase distribution of the first fingerprint is multiplied by the second chaotic phase fractional Fourier inverse transform, and the inverse transform result is combined with the first fingerprint chaotic conjugate phase mask. The phase distribution of the input signal is multiplied by the chaotic phase fractional Fourier transform. Output signal generated after improved double random phase encoding for: In the formula, The wavelength is The fractional order is The focal length is The inverse fractional Fourier transform operation of the chaotic phase.

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