A method for reversible data hiding in a coupled cryptographically embedded cryptographic domain

Abstract

This invention relates to the field of cryptographic application technology and discloses a method for reversible data hiding in a coupled cryptographically embedded cryptographic domain. The method includes: generating a public key and a private key using a key generation algorithm; randomly selecting a binary vector, sampling an error vector, and generating a structured error vector based on the hidden information; calculating a first ciphertext component as the product of the random matrix and the binary vector plus the error vector; and calculating a second ciphertext component as the product of the transpose of the matrix generated by the error learning problem and the binary vector, plus the product of the encoded value of the original plaintext and a predetermined coefficient, plus the product of the transpose of the matrix used for embedding and the structured error vector; using a trapdoor basis in the private key to solve the nearest vector problem to recover the binary vector, and decrypting using the binary vector and the secret matrix in the private key, while simultaneously outputting the hidden information and the original plaintext. This invention can simultaneously achieve the dual goals of confidentiality and reversibility.

Description

Technical Field

[0001] This invention relates to the field of cryptographic application technology, particularly to error learning and reversible data hiding technology, and especially to a method for reversible data hiding of a cryptographic field coupled with cryptographic embedding. Background Technology

[0002] Reversible data hiding in encrypted images is a technique that can embed additional information while protecting data confidentiality, and can accurately recover the original image content after extraction. It has received widespread attention in recent years in fields such as cloud computing, privacy protection, and medical image transmission. This type of technology typically requires that a legitimate recipient can losslessly reconstruct the original image after decryption, while simultaneously extracting the embedded hidden information. Ideally, the encryption and data embedding processes should work closely together to improve information embedding efficiency and enhance theoretical security.

[0003] However, most existing reversible data hiding methods treat image encryption and data embedding as two separate stages. For example, they first perform standard encryption on the image, and then embed information in the ciphertext domain by modifying pixel values ​​or coefficients; or they embed information first and then encrypt it. Although this decoupled approach is simple to implement, it has obvious drawbacks: the encryption process often does not consider the subsequent embedding requirements, resulting in limited embedding capacity, changes in ciphertext statistical properties, or the need for additional auxiliary information; at the same time, due to the lack of a unified mathematical framework, its security analysis and theoretical guarantees of embedding capacity are relatively weak, making it difficult to prove the optimality of the scheme under a rigorous security model.

[0004] Therefore, this invention aims to solve the technical problems of low embedding efficiency and insufficient theoretical security proof caused by the decoupling of encryption and data embedding in the prior art, and provides a reversible data hiding scheme for the encrypted domain with a wider protection range, adjustable parameters and provable security. Summary of the Invention

[0005] The purpose of this invention is to provide a reversible data hiding method for coupled encrypted embedding of encrypted fields, so as to overcome the shortcomings of existing technologies.

[0006] Based on a first key aspect of the present invention, a method for reversibly hiding encrypted domains coupled with encrypted embeddings is provided, comprising the following stages executed by a computer:

[0007] Key generation phase: A public key and a private key are generated using a key generation algorithm. The public key includes a random matrix, a matrix generated by an error learning problem, and a matrix for embedding.

[0008] Coupled encryption embedding stage: Randomly select a binary vector, sample an error vector, and generate a structured error vector based on the hidden information;

[0009] LWE ciphertext calculation stage: The first ciphertext component is calculated as the product of the random matrix and the binary vector plus the error vector, and the second ciphertext component is calculated as the product of the transpose of the matrix generated by the error learning problem and the binary vector, plus the product of the encoded value of the original plaintext and a predetermined coefficient, plus the product of the transpose of the matrix used for embedding and the structured error vector.

[0010] Extraction and decryption phase: The nearest vector problem is solved using the trapdoor basis in the private key to recover the binary vector, and the binary vector and the secret matrix in the private key are used for decryption. At the same time, the hidden information and the original plaintext are output.

[0011] This invention divides the method into four stages: key generation, coupled encryption embedding, LWE ciphertext calculation, extraction, and decryption. It also clarifies that the public key includes a random matrix, an LWE matrix, and an embedding matrix, and that the ciphertext calculation simultaneously includes plaintext encoded values ​​and a structured error vector. This limits the coupling mechanism in which encryption and embedding share the same random vector and public key matrix within the LWE framework. This directly solves the problems of inconsistent theoretical foundations and weak security proofs caused by the decoupling of encryption and data embedding processes in existing technologies, and provides a unified mathematical foundation for subsequent reversible extraction.

[0012] Optionally, the key generation stage includes: generating a random matrix. A matrix generated from an error learning problem and a matrix for embedding. ;

[0013] in, Represents the modulus; express an integer ring; , , All are positive integers; Represents a random matrix The number of columns in a random matrix Transposed representation of a matrix number of rows; Represents a random matrix number of rows; Representation matrix The number of columns; Represents a random matrix transpose; This represents the secret matrix, which is part of the private key; Represents the error matrix;

[0014] The matrix generated by the error learning problem This is a matrix generated from the LWE problem, and its calculation process includes:

[0015] Sampling error matrix Each element is independently derived from a discrete Gaussian distribution. Sampling, among which, Indicates standard deviation; The representation is defined in the integer lattice. Discrete Gaussian distribution on;

[0016] make ; , , These represent the error matrices respectively. The , , List;

[0017] Calculate the matrix generated by the error learning problem. As a public key matrix:

[0018] ;

[0019] generate There are 1 independent LWE samples, each sample being:

[0020] ;

[0021] in, It is the first One sample, yes The List, yes The List;

[0022] Uniformly and randomly selected matrix as the matrix for embedding. ,and It is the full term of service;

[0023] Output public and private keys ;in, It is a public key. It's the private key. Representation and random matrix Associated trapdoor base.

[0024] The above scheme ensures the randomness of the public key and the solvability of trapdoors through the provably secure construction of the standard LWE problem. This guarantees that anyone can encrypt and embed information without revealing the private key, and only the private key holder can correctly recover the random vector. This provides a solution to the problem of how to embed extractable information while securely encrypting it.

[0025] Optionally, the binary vector is The error vector is It follows a Gaussian distribution;

[0026] Generating a structured error vector based on hidden information specifically includes: setting a scaling factor. Define mapping function ,in Calculate the structured error vector ;

[0027] in, Indicates length is binary vector space, , It is a positive integer; The representation is defined in the integer lattice. Discrete Gaussian distribution on, Indicates standard deviation; Represents the mapping function, domain ,range ; Represents the hidden information vector. This represents the hidden information bits, i.e., the hidden information vector. The One component; Represents mapping function Acting on The first of the resulting vectors One component; express 3D integer vector space; Represents the modulus.

[0028] The above scheme utilizes the scaling factor to form a multiple relationship with the predetermined coefficient in the subsequent decryption decision, so that the hidden information is presented in the form of large error in the ciphertext, while the plaintext is superimposed in the form of small error. Thus, the two can be separated by threshold decision during decryption, solving the core technical problem of separable embedding of hidden information and plaintext in the same ciphertext space.

[0029] Optionally, the predetermined coefficient mentioned in the LWE ciphertext calculation stage is The encoded value of the original plaintext is Encoding function Original plaintext Encoded as vector;

[0030] The first ciphertext component is: ;

[0031] The second ciphertext component is ,in, , It is a positive integer. Modulus; express ; Representation matrix transpose; Representation matrix transpose; Modulus of 3D integer vector space; Modulus of 3D integer vector space.

[0032] The above scheme clarifies that the plaintext encoded values ​​are superimposed using predetermined coefficients, while the hidden information is... The superposition process ensures that the influence of the hidden information is evenly distributed throughout the ciphertext space, enhancing security and embedding capacity. At the same time, it ensures that the plaintext and hidden information can be accurately recovered separately when correctly decrypted, solving the problem of embedding without destroying the encryption format or sacrificing reversibility.

[0033] Optionally, the extraction and decryption phases may utilize trapdoor bases in the private key to solve the nearest vector problem, including:

[0034] Using the trapdoor base in the private key The binary vector is recovered using the nearest plane algorithm, i.e., the calculation is performed. Output Make near ;

[0035] in, This represents the recovered binary vector; This represents the nearest plane algorithm function; Indicates length is binary vector space, It is a positive integer.

[0036] The above scheme leverages the ability of trapdoor bases in the LWE problem to solve systems of linear equations with errors. This allows a legitimate receiver to recover the correct random vector with a high probability, even with encryption errors, while attackers cannot. This solves the problem of accurately recovering the temporary random vector used for decryption from noisy ciphertext, a prerequisite for ensuring the correctness of subsequent extraction of hidden information and plaintext.

[0037] Optionally, the extracted and decrypted binary vector is obtained during the extraction and decryption stages. Next, calculate the intermediate vector. Then calculate the vector ;

[0038] Through vectors The hidden information is recovered from the components: for each Set a threshold ,like Then determine ,like ,but ;

[0039] in, Indicates a circular index. It is a positive integer; Representing vectors The Each component.

[0040] The above solutions directly utilize and The numerical relationship, by judgment Is it close? or To uniquely determine the hidden information bits This method enables blind extraction of hidden information, i.e., extraction without the need for the original plaintext. The decision method is simple, efficient, and mathematically provable, solving the problem of robustly extracting hidden information in the presence of plaintext interference.

[0041] Optionally, after recovering the hidden information, the structured error is reconstructed. Calculate the intermediate vector after removing the influence of hidden information. ;

[0042] The intermediate vector after removing the influence of hidden information The components are used to recover the original plaintext: for each ,Will Normalization to interval, if Closer to 0 or Then the code bit is determined to be 0. Closer Then the encoded bit is determined to be 1, thus obtaining Then through the decoding function Output the original plaintext; where, For circular index, It is a positive integer. express The One component; This indicates decoding.

[0043] The above scheme, after recovering the hidden information, reconstructs the structured error and subtracts it to obtain the plaintext encoded value, then uses the same threshold decision to recover the original plaintext. This achieves a layered reversible mechanism of "extracting hidden information first, then recovering plaintext," ensuring lossless recovery of the original plaintext. It solves the core requirement of reversible data hiding—how to accurately restore the original image / message content after extracting hidden information—and achieves a strict reversibility objective.

[0044] Optionally, the module The matrix used for embedding row norm, standard deviation of error vector and the length of the hidden information Configured to satisfy: for the calculated Each component The absolute value of the portion contributed by the encoded value of the original plaintext is less than This allows the hidden information bits to be hidden. Able to compare and The distance is uniquely determined.

[0045] The above scheme provides sufficient mathematical conditions for the correct operation of the scheme from the perspective of parameter configuration, enabling those skilled in the art to select appropriate parameters according to security requirements and embedding capacity. It solves the problem of how to ensure the theoretical correctness of the method and its reliability in actual deployment, and demonstrates the engineering feasibility of the present invention.

[0046] Based on a second key aspect of the present invention, an electronic device is provided, comprising one or more processors;

[0047] Storage device for storing one or more programs;

[0048] When one or more programs are executed by one or more processors, the one or more processors implement the aforementioned method for reversible data hiding of cryptographically embedded coupled cryptographic domains.

[0049] Based on a third key aspect of the present invention, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed, implements the aforementioned method for reversible data hiding of coupled encrypted embedded encrypted fields.

[0050] Compared to existing technologies, this invention achieves tight coupling between encryption and data embedding within the LWE (Learning Error Learning) framework. It directly encodes hidden information as structured errors and integrates them into the ciphertext generation process, overcoming the limitations of traditional methods such as limited embedding capacity, redundant auxiliary information, and difficulties in proving security, which result from the separation of encryption and embedding. By sharing the same random vector and public key matrix, the ciphertext of this invention simultaneously carries both plaintext encryption information and hidden information. Furthermore, both can be recovered hierarchically through threshold decisions during decryption, thus simultaneously achieving data confidentiality protection, covert information transmission, and lossless restoration of the original content within a single mathematical framework. Compared to decoupled schemes, this invention significantly improves embedding efficiency and ciphertext compactness, and its security can be reduced to the standard LWE assumptions, providing a theoretically provable guarantee of security.

[0051] This invention further achieves reliable separation of hidden information and plaintext through parameterized design and threshold-based extraction logic. A legitimate recipient can recover the random vector using the trapdoor basis in the private key, and then sequentially decode the hidden information and plaintext encoding values, ensuring reversibility even with minor errors. Attackers, without trapdoors, cannot distinguish between ciphertext and random noise, thus resisting chosen-plaintext attacks and ciphertext-distinguishing attacks. Experiments and analysis show that this method maintains a high embedding rate while resisting common noise perturbations and statistical analysis methods, making it particularly suitable for applications requiring both confidentiality and reversibility, such as cloud computing, medical image transmission, and privacy-preserving watermarking.

[0052] Furthermore, the technical solution of this invention possesses excellent scalability and parameter adjustment capabilities: by adjusting the modulus, Gaussian distribution standard deviation, and matrix dimension, a flexible trade-off can be made between security, embedding capacity, and computational efficiency. Compared with existing lattice-based reversible data hiding methods for encrypted domains, this invention avoids additional error-correcting codes or auxiliary data transmission, reduces communication overhead, and the recovery process is entirely based on deterministic threshold comparisons, requiring no iterative search or heuristic estimation. Therefore, this invention provides an efficient, secure, and theoretically sound solution for reversible data hiding in encrypted domains. Attached Figure Description

[0053] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, obtaining other drawings based on these drawings without creative effort still falls within the scope of the present invention.

[0054] Figure 1 The following is a flowchart illustrating the execution of a reversible data hiding method for coupled cryptographic embedding in one embodiment of the present invention. Detailed Implementation

[0055] The preferred embodiments of the present invention will be described in detail below to provide a clearer understanding of the purpose, features, and advantages of the invention. It should be understood that the following embodiments are not intended to limit the scope of the invention, but are merely illustrative of the essential spirit of the technical solution of the invention.

[0056] In the following description, certain specific details are set forth for the purpose of illustrating various disclosed embodiments in order to provide a thorough understanding of the various disclosed embodiments. However, those skilled in the art will recognize that embodiments may be practiced without one or more of these specific details. In other instances, well-known techniques associated with the invention may not have been shown or described in detail to avoid unnecessarily obscuring the description of the embodiments.

[0057] Throughout this specification, references to "an embodiment" or "an embodiment" indicate that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment. Therefore, the appearance of "in an embodiment" or "an embodiment" in various places throughout the specification does not necessarily refer to the same embodiment. Furthermore, a particular feature, structure, or characteristic may be combined in any manner in one or more embodiments.

[0058] The following are the main technical terms that may be involved in the embodiments of this invention and their meanings:

[0059] Error Learning (LWE) Problem: A Difficult Problem in Lattice Cryptography. Assumptions: Given a random matrix... sum vector (in For secret vectors, (for small error vectors), when it is unknown and In the case of being unable to distinguish With uniform random vectors. This invention utilizes the one-way nature of the LWE problem and the trapdoor property to couple encryption and data embedding.

[0060] Coupled encryption embedding: refers to the encryption process and the information embedding process being completed simultaneously in the same LWE ciphertext generation step, sharing the same random vector and public key matrix, so that the ciphertext carries both the original plaintext and the hidden information at the same time, rather than a two-stage decoupling method of encrypting first and then embedding or embedding first and then encrypting.

[0061] Structured error vector: An error vector with a specific mathematical structure generated from hidden information through a mapping function and a scaling factor.

[0062] Scaling factor: Used to map hidden information into large-amplitude structured errors. Its value is such that during decryption, the influence of the hidden information on the ciphertext components exceeds the contribution of the original plaintext encoding, thus allowing the hidden information bits to be uniquely determined through threshold decision.

[0063] Preset coefficient: A constant used to amplify the original plaintext encoded value. This coefficient forms a multiple relationship with the scaling factor, so that the plaintext encoded value and the hidden information are in different order of magnitude ranges in the modulus space, which facilitates layered recovery.

[0064] Trapdoor basis: A short basis associated with a random matrix, used as part of a private key. This trapdoor basis can be used to efficiently solve the nearest vector problem on a lattice, thus recovering binary random vectors from erroneous LWE samples—something an attacker unaware of the trapdoor basis cannot do.

[0065] The nearest plane algorithm is an approximate algorithm for solving the nearest vector problem using lattice basis (trapdoor basis).

[0066] Reversible data hiding: an information hiding technique that requires a legitimate recipient to be able to recover the original carrier content without loss after extracting the embedded hidden information.

[0067] Full-rank matrix: matrix number of rows Less than or equal to the number of columns And the row vectors are linearly independent, that is .

[0068] Mapping function: Transforms binary hidden information vectors Mapped to A function of vectors. This mapping makes the hidden information bit 0 correspond to... Bit 1 corresponds to This makes it easier to make a judgment based on symbols or distance during decryption.

[0069] Please see Figure 1 The present invention provides an embodiment of a method for reversible data hiding of a coupled encrypted embedded encrypted domain, comprising steps S100 to S400 executed by a computer system.

[0070] Step S100, Key Generation Stage: Generate a public key and a private key using a key generation algorithm. The public key includes a random matrix, a matrix generated by an error learning problem, and a matrix for embedding.

[0071] Step S200, Coupled Encryption Embedding Stage: Randomly select a binary vector, sample an error vector, and generate a structured error vector based on the hidden information;

[0072] Step S300, LWE ciphertext calculation stage: calculate the first ciphertext component as the product of the random matrix and the binary vector plus the error vector, and calculate the second ciphertext component as the product of the transpose of the matrix generated by the error learning problem and the binary vector, plus the product of the encoded value of the original plaintext and a predetermined coefficient, plus the product of the transpose of the matrix used for embedding and the structured error vector;

[0073] Step S400, Extraction and Decryption Stage: The nearest vector problem is solved using the trapdoor basis in the private key to recover the binary vector, and the binary vector and the secret matrix in the private key are used for decryption, while the hidden information and the original plaintext are output.

[0074] The following describes a possible embodiment of the present invention in further detail.

[0075] In step S100, a public key and a private key are generated using a key generation algorithm. The public key includes a random matrix, a matrix generated by an error learning problem, and a matrix for embedding. Specifically, a random matrix is ​​first generated. A matrix generated from an error learning problem and a matrix for embedding. ;

[0076] in, Represents the modulus; express an integer ring; , , All are positive integers; Represents a random matrix The number of columns in a random matrix The transpose represents the matrix. number of rows; Represents a random matrix number of rows; Representation matrix The number of columns; Represents a random matrix transpose; This represents the secret matrix, which is part of the private key; Represents the error matrix;

[0077] Sampling error matrix Each element is independently derived from a discrete Gaussian distribution. Mid-sampling, of which Indicates standard deviation; The representation is defined in the integer lattice. The discrete Gaussian distribution on the surface.

[0078] Let , the statistical characteristics of the error be and ; , , respectively represent the th , , column of the error matrix; represents the mathematical expectation (mean value) of the error matrix ; represents the variance of each element in the error matrix ; represents the standard deviation, that is, the standard deviation of the discrete Gaussian distribution, which controls the amplitude of the error vector; represents the spectral norm (the largest singular value) of the matrix ; is the security parameter (usually can be set to 80, 128, 256, etc.); represents the probability of an event occurring; , etc. represent positive integers in the present invention.

[0079] And calculate the public key matrix:

[0080] ;

[0081] Generate independent LWE samples, and each sample is

[0082] ;

[0083] Among them, is the th sample, is 's th column, is 's th column.

[0084] Uniformly and randomly select the matrix , and is row full rank, that is . Finally, output the public and private keys . Among them, is the public key, is the private key, represents the trapdoor basis associated with the random matrix , represents the rank condition of the matrix , A positive integer represents a matrix. number of rows.

[0085] Step S200 mainly involves completing the coupling encryption embedding stage, which includes randomly selecting a binary vector, sampling an error vector, and generating a structured error vector based on the hidden information. Specifically, the hidden information is encoded into a structured error and coupled to the error term of the LWE.

[0086] Enter public key plain text Hidden information The final output is a ciphertext. .in, This is the first ciphertext component. This is the first ciphertext component. Specifically, the mapping function is defined as follows:

[0087] ;

[0088] satisfy If ,but ,on the contrary ,but This function maps binary strings to... Vectors are convenient for manipulation on a lattice. Randomly select a binary vector. Binary vectors can produce more compact ciphertext.

[0089] Sampling error vector , To account for encryption errors, a Gaussian distribution is used. A scaling factor is set. Calculate the structured error vector:

[0090] ;

[0091] Each component is or , Its norm is relatively large, and it is used in the scheme through a matrix. Add it to the overall space.

[0092] in, Indicates length is binary vector space, Indicates length is binary vector space, , It is a positive integer; The representation is defined in the integer lattice. Discrete Gaussian distribution on, Indicates standard deviation; Represents the mapping function, domain ,range ; Represents the hidden information vector. This represents the hidden information bits, i.e., the hidden information vector. The One component; Represents mapping function Acting on The first of the resulting vectors One component; express 3D integer vector space; Represents the modulus.

[0093] In step S300, during the LWE ciphertext calculation stage, the first ciphertext component is calculated as the product of the random matrix and the binary vector plus the error vector. The second ciphertext component is calculated as the product of the transpose of the matrix generated by the error learning problem and the binary vector, plus the product of the encoded value of the original plaintext and a predetermined coefficient, plus the product of the transpose of the matrix used for embedding and the structured error vector.

[0094] Calculate the LWE ciphertext as the first ciphertext component:

[0095] ;

[0096] ;

[0097] in, It is the linear part. It's an error. express The other embodiments are the same. Indicates the first ciphertext component The One component; Represents a random matrix The Line 1 Column elements, Indicates row index, Indicates column index; Representing a binary vector The One component; Error vector The One component; for Dimensions.

[0098] And calculate the second ciphertext component:

[0099] ;

[0100] It is plain text Encoded as The encoding function for vectors.

[0101] in, , , It is a positive integer. Modulus; express ; Representation matrix transpose; Representation matrix transpose; Modulus of 3D integer vector space; Modulus of 3D integer vector space.

[0102] In step S400, during the extraction and decryption phase, the trapdoor basis in the private key is used to solve the nearest vector problem to recover the binary vector, and the binary vector and the secret matrix in the private key are used for decryption, while the hidden information and the original plaintext are output.

[0103] In one embodiment, the extraction and decryption algorithm used in this invention simultaneously extracts hidden information and decrypts the original plaintext, utilizing the trapdoor base in the private key. To solve the CVP problem and thus recover the random vector. Then use and the secret matrix To decrypt, enter the private key. and containing ciphertext Output hidden information and the original plaintext Specifically, this involves using a trapdoor to restore... Given:

[0104] ;

[0105] Using the nearest plane algorithm on the input as well as Output a vector , making Very close More formally, this embodiment first calculates:

[0106] ;

[0107] in, This represents the nearest plane algorithm function. The algorithm utilizes trapdoor basis Antique Perform reduction, then find the grid points. Make Minimum, because Very small, and It is a binary vector, and this embodiment can be expected to... It is highly likely to be true.

[0108] Next, calculate the intermediate vector:

[0109] ;

[0110] ;

[0111] Record residual error ,satisfy .like but:

[0112] ;

[0113] ;

[0114] Here we assume ,Require or .because It is a binary vector and It's random, as long as and Very close, minor differences can be handled through error correction mechanisms. For simplicity, we assume here... .

[0115] Simultaneously calculate:

[0116] ;

[0117] ;

[0118] Record interference terms Then there is a disturbance norm bound. .in, for If satisfied ,So:

[0119] ;

[0120] in yes The matrix, due to If it is a full rank, such as a prime number. Large enough, then exist The above is reversible with a high probability. Furthermore, from... Then we have:

[0121] ;

[0122] And further observations Each component is:

[0123] ;

[0124] in, For small error terms, It is an embedded matrix The row vectors Indicates plaintext contributions. Indicates hidden information contribution items; due to ,and The absolute value does not exceed , The absolute value is Multiplying by a certain constant, and through appropriate parameter selection, can achieve... Dominant and thus through To determine by the symbol or range Finally recovered ,remember To recover the first Each hidden information vector; the specific decoding method is as follows: for each... ,Will Treat as an interval Integers in the calculation of decision metrics ,and:

[0125] ;

[0126] Equivalent to Let the recovered hidden information vector .like Closer or Then judge ,Right now ,like Closer Then judge ,Right now .

[0127] For more precision, set a threshold. ,like ,but ,like ,but It is worth noting that this judgment may be incorrect, and it is necessary to ensure that... The impact is small enough. Reconstructing the structure error. Remove the impact of hidden information:

[0128] ;

[0129] ;

[0130] when hour, but .for ,Will Normalization to An interval that satisfies:

[0131] ;

[0132] Equivalent to ,make Finally, decoding and verification are performed. Output . Representing the original plaintext The vector obtained after encoding by the encoding function is the first... Each component.

[0133] It should be understood that the program code used to implement the methods of the present invention can be written in any combination of one or more programming languages. This program code can be provided to a processor or controller of a general-purpose computer, special-purpose computer, or other programmable data processing device, such that when executed by the processor or controller, the program code causes the functions / operations specified in the flowcharts and / or block diagrams to be implemented. The program code can be executed entirely on the machine, partially on the machine, as a standalone software package partially on the machine and partially on a remote machine, or entirely on a remote machine or server.

[0134] The acquisition, storage, and application of user personal information involved in the technical solution of this invention all comply with the provisions of relevant laws and regulations and do not violate public order and good morals.

[0135] It should be understood that the various forms of processes shown above can be used, with steps reordered, added, or deleted. For example, the steps described in this invention can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution of this invention can be achieved, and this invention is not limited thereto.

[0136] The technical terms, principles, or means related to the technical solutions of the present invention mentioned in the above embodiments, which are not described in detail above, are all well-known technologies or common practices that are known to those skilled in the art.

[0137] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A method for reversible data hiding in a coupled encrypted field, characterized in that, This includes the following stages performed by a computer: Key generation phase: A public key and a private key are generated using a key generation algorithm. The public key includes a random matrix, a matrix generated by an error learning problem, and a matrix for embedding. Coupled encryption embedding stage: Randomly select a binary vector, sample an error vector, and generate a structured error vector based on the hidden information; LWE ciphertext calculation stage: The first ciphertext component is calculated as the product of the random matrix and the binary vector plus the error vector, and the second ciphertext component is calculated as the product of the transpose of the matrix generated by the error learning problem and the binary vector, plus the product of the encoded value of the original plaintext and a predetermined coefficient, plus the product of the transpose of the matrix used for embedding and the structured error vector. Extraction and decryption phase: The nearest vector problem is solved using the trapdoor basis in the private key to recover the binary vector, and the binary vector and the secret matrix in the private key are used for decryption. At the same time, the hidden information and the original plaintext are output.

2. The method for reversible data hiding in a coupled encrypted field according to claim 1, characterized in that, The key generation stage includes: generating a random matrix. A matrix generated from an error learning problem and a matrix for embedding. ; in, Represents the modulus; express an integer ring; , , All are positive integers; Represents a random matrix The number of columns in a random matrix The transpose represents the matrix. number of rows; Represents a random matrix number of rows; Representation matrix The number of columns; Represents a random matrix transpose; This represents the secret matrix, which is part of the private key; Represents the error matrix; The matrix generated by the error learning problem This is a matrix generated from the LWE problem, and its calculation process includes: Sampling error matrix Each element is independently derived from a discrete Gaussian distribution. Sampling, among which, Indicates standard deviation; The representation is defined in the integer lattice. Discrete Gaussian distribution on; make ; , , These represent the error matrices respectively. The , , List; Calculate the matrix generated by the error learning problem. As a public key matrix: ； generate There are 1 independent LWE samples, each sample being: ； in, It is the first One sample, yes The List, yes The List; Uniformly and randomly selected matrix as the matrix for embedding. ,and It is the full term of service; Output public and private keys ;in, It is a public key. It's the private key. Representation and random matrix Associated trapdoor base.

3. The method for reversible data hiding in a coupled encrypted field according to claim 2, characterized in that, The binary vector is The error vector is It follows a Gaussian distribution; Generating a structured error vector based on hidden information specifically includes: setting a scaling factor. Define mapping function ,in Calculate the structured error vector ; in, Indicates length is binary vector space, , It is a positive integer; The representation is defined in the integer lattice. Discrete Gaussian distribution on, Indicates standard deviation; Represents the mapping function, domain ,range ; Represents the hidden information vector. This represents the hidden information bits, i.e., the hidden information vector. The One component; Represents mapping function Acting on The first of the resulting vectors One component; express 3D integer vector space; Represents the modulus.

4. The method for reversible data hiding in a coupled encrypted field according to claim 3, characterized in that, The predetermined coefficient mentioned in the LWE ciphertext calculation stage is: The encoded value of the original plaintext is Encoding function Original plaintext Encoded as vector; The first ciphertext component is: ; The second ciphertext component is ,in, , , It is a positive integer. Modulus; express ; Representation matrix transpose; Representation matrix transpose; Modulus of 3D integer vector space; Modulus of 3D integer vector space.

5. The method for reversible data hiding in a coupled encrypted field according to claim 4, characterized in that, The extraction and decryption phases utilize trapdoor bases in the private key to solve the nearest vector problem, including: Using the trapdoor base in the private key The binary vector is recovered using the nearest plane algorithm, i.e., the calculation is performed. Output Make near ; in, This represents the recovered binary vector; This represents the nearest plane algorithm function; Indicates length is binary vector space, It is a positive integer.

6. The method for reversible data hiding in a coupled encrypted field according to claim 5, characterized in that, The recovered binary vector is obtained during the extraction and decryption stages. Next, calculate the intermediate vector. Then calculate the vector ; Through vectors The hidden information is recovered from the components: for each Set a threshold ,like Then determine ,like ,but ; in, Indicates a circular index. It is a positive integer; Representing vectors The Each component.

7. The method for reversible data hiding in a coupled encrypted field according to claim 6, characterized in that, After recovering the hidden information, the structured error is reconstructed. Calculate the intermediate vector after removing the influence of hidden information. ; The intermediate vector after removing the influence of hidden information The components are used to recover the original plaintext: for each ,Will Normalization to interval, if Closer to 0 or Then the code bit is determined to be 0. Closer Then the encoded bit is determined to be 1, thus obtaining Then through the decoding function Output the original plaintext; where, For circular index, It is a positive integer. express The One component; This indicates decoding.

8. The method for reversible data hiding in a coupled encrypted field according to claim 7, characterized in that, The modulus The matrix used for embedding row norm, standard deviation of error vector and the length of the hidden information Configured to satisfy: for the calculated Each component The absolute value of the portion contributed by the encoded value of the original plaintext is less than This allows the hidden information bits to be hidden. Able to compare and The distance is uniquely determined.

9. An electronic device, characterized in that, Includes one or more processors; Storage device for storing one or more programs; When one or more programs are executed by one or more processors, the one or more processors implement the coupled cryptographically embedded reversible data hiding method for cryptographic fields as described in any one of claims 1-8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed, it implements the reversible data hiding method of coupled cryptographic embedding of any one of claims 1-8.

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