A linear computation-based fully homomorphic encryption ciphertext transmission method and system

Abstract

The application discloses a kind of full homomorphic encryption ciphertext transmission method and system based on linear calculation, belong to ciphertext data transmission technical field, its method includes the encoding to each character in the data to be sent, obtains the numerical data set of decimal representation;In offline stage, based on random n-dimensional table generation by basic metadata consisting of plaintext truth table, n>=2, and send the ciphertext truth table obtained by full homomorphic encryption to the plaintext truth table to data receiving terminal;In interactive stage, each numerical data in data set is linearly split using the plaintext truth table, obtain the plaintext coordinates corresponding to the linear decomposition factor after splitting, while sending all plaintext coordinates to data receiving terminal.The application adopts the paradigm data transmission mode of "ciphertext password book+index coding combination", sends ciphertext table through idle time, sends coding coordinates when interacting, can reduce the amount of ciphertext transmission in interactive stage, and compresses transmission amount to plaintext level.

Description

Technical Field

[0001] This invention relates to the field of encrypted data transmission technology, and more specifically to a fully homomorphic encrypted encrypted data transmission method and system based on linear computation. Background Technology

[0002] With the digital upgrades of industries such as the Industrial Internet, smart grids, and fintech, the demand for cross-domain secure collaborative computation of data among different business entities is constantly increasing. Fully Homomorphic Encryption (FHE), as a crucial cryptographic technology for achieving the "computable but invisible" security paradigm, can perform arbitrary calculations such as addition and multiplication in ciphertext, providing a reliable mathematical foundation for privacy-preserving computation. However, existing FHE systems generally face problems of large ciphertext size and high network transmission costs in practical engineering applications. Mainstream ring-learning homomorphic encryption schemes (such as BFV, BGV, and CKKS) require polynomial encoding of plaintext; a typical 128-bit plaintext often expands to 1KB~16KB of ciphertext after encryption. In scenarios requiring frequent interaction and submission of large amounts of input ciphertext (such as privacy queries, ciphertext-based matching verification, and privacy control command comparison), the ciphertext transmission volume becomes a bottleneck for system performance.

[0003] To reduce network load, existing technologies typically employ the following methods: (1) Ciphertext compression: reducing ciphertext size through structural compression, encoding pruning, etc.; (2) Interaction round optimization: reducing the number of encryption rounds and interactions in the protocol; (3) Homomorphic computation optimization: shortening the ciphertext link by reducing the multiplication depth. The above methods mainly address the issue from the perspective of algorithm parameter optimization or protocol structure optimization, but they cannot solve a fundamental problem: each input still requires the complete transmission of the ciphertext body, so the network bandwidth load still increases linearly with the number of encrypted objects. When the business system generates a large number of queries or control commands in a short period of time, the network link will be quickly filled with homomorphic ciphertext, leading to a decline in overall performance or even unavailability. Especially when the data volume is large, the transmission and storage of homomorphic ciphertext will consume an unusually large amount of time and space.

[0004] Although existing technologies have studied ciphertext size and homomorphic computation efficiency, the following shortcomings and deficiencies still exist:

[0005] 1. The ciphertext still needs to be transmitted in its entirety, and the linear growth bottleneck cannot be overcome. Regardless of compression, shortening the module chain, or reducing the polynomial dimension, the complete ciphertext polynomial coefficients still need to be sent to the other party. In schemes such as CKKS / BFV, a ciphertext consists of two or three large integer polynomials, with the transmission load often reaching thousands to tens of thousands of bytes. This means: the more input, the higher the network traffic; the system cannot support high-frequency real-time interaction; and the control system is difficult to deploy in weak network or edge environments.

[0006] 2. Existing offline pre-computation schemes cannot reduce the amount of ciphertext transmitted. While research has proposed schemes such as offline computation, pre-computation of random masks, and bit window decomposition, their characteristics are: the offline stage computes "auxiliary data," such as random vectors, key overhead, and masks; the online stage still requires the submission of the complete input ciphertext, and cannot simply send "lightweight encoded information." Therefore, they cannot truly reduce the amount of ciphertext transmitted, but only the amount of computation.

[0007] 3. There is currently no engineered solution for the security of ciphertext codebook reuse and ciphertext synthesis. Although existing research involves the algebraic structure decomposition of homomorphic encryption, it lacks mechanisms that can be used in engineering systems to ensure: that statistical characteristics are not leaked during ciphertext codebook reuse; that the generated ciphertext combination always maintains IND-CPA security; that the spatial randomness and refresh strategy of the basic ciphertext are maintained; and that noise budget control is implemented during synthesis. Therefore, current technologies do not yet possess the capability for secure, universal, and reusable "ciphertext index encoding + ciphertext synthesis".

[0008] Therefore, how to provide a fully homomorphic encrypted ciphertext transmission method to reduce the amount of ciphertext transmitted during the interaction phase is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0009] In view of the above problems, the present invention is proposed to provide a fully homomorphic encrypted ciphertext transmission method based on linear computation that overcomes or at least partially solves the above problems.

[0010] To achieve the above objectives, the present invention adopts the following technical solution: In a first aspect, embodiments of the present invention provide a fully homomorphic encrypted ciphertext transmission method based on linear computation, comprising the following steps: Each character in the data to be sent is encoded to obtain a set of numerical data in decimal representation; During the offline phase, a plaintext truth table consisting of basic metadata is generated based on a random n-dimensional table, where n>=2, and the ciphertext truth table obtained by fully homomorphically encrypting the plaintext truth table is sent to the data receiving terminal. During the interaction phase, the plaintext truth table is used to linearly decompose each numerical data in the numerical data set to obtain the plaintext coordinates corresponding to the linear decomposition factors after decomposition, and all plaintext coordinates are sent to the data receiving terminal.

[0011] Furthermore, each non-numeric data character in the data to be sent is Unicode encoded to obtain the decimal representation of the corresponding Unicode code point in the Unicode character set; When the data to be sent includes decimals, the decimals are transmitted via a combination of... Multiply the results and convert them to integers, while recording the number of decimal places j.

[0012] Furthermore, the plaintext truth table is fully homomorphically encrypted using a modulo component-based fully homomorphic encryption algorithm.

[0013] Furthermore, in the offline phase, a plaintext truth table composed of basic metadata is generated based on a random n-dimensional table, specifically including the following steps: Several basic metadata are selected as the base values ​​of the plaintext truth table, wherein the basic metadata includes several non-zero integers containing the value 1; and the base values ​​satisfy: ,in and Let N be any base value in the plaintext truth table, and let N be any numerical value in decimal representation. Randomly select any number of basic metadata from the aforementioned basic metadata, and randomly repeat each selected basic metadata to fill an n-dimensional table, thereby obtaining a plaintext truth table composed of basic values, wherein the data order in the plaintext truth table is randomly arranged.

[0014] Furthermore, during the interaction phase, the plaintext truth table is used to linearly decompose each numerical data in the numerical data set to obtain the plaintext coordinates corresponding to the linear decomposition factors after decomposition. Specifically, this includes: Each decimal numerical data N is used as the modulus, and simultaneously, plaintext data with an absolute value less than the absolute value of numerical data N is randomly selected from the plaintext truth table T. As a modulus, and d≠±1, a modulo operation is performed to obtain the quotient b. The plaintext data d and the quotient b are used as linear decomposition factors, and the coordinates of the linear decomposition factors in the plaintext truth table T are used as the plaintext coordinate sequence of the numerical data N. If a remainder c exists, then the remainder c is used as the modulus, and plaintext data with an absolute value less than the absolute value of the remainder N is randomly selected from the plaintext truth table T. As the new modulus, perform modulo estimation, and combine the new modulus and the coordinates of the new quotient after modulo estimation in the plaintext truth table T with the coordinates of the initial plaintext data d in the plaintext truth table T to obtain the plaintext coordinate sequence of the value N. Repeat the above steps until the remainder is 0.

[0015] Furthermore, if the quotient after each modulo operation is not in the plaintext truth table, then the maximum value in the plaintext truth table that is not greater than the quotient is selected as the new quotient b. new , And perform a subtraction operation to obtain the new numerical data. :

[0016] The initial plaintext data d and the new quotient b are used to... new The remainder c and the coordinates of the value 1 are recorded as decomposition factors, and the numerical data are... Repeat the linear split as the new value to be decomposed until the remainder is 0. Record the coordinates of all the decomposition factors in turn as the plaintext coordinates of the data N to be encrypted.

[0017] Secondly, embodiments of the present invention provide a fully homomorphic encrypted ciphertext transmission system based on linear computation, comprising: The data encoding module is used to encode each character in the data to be sent, resulting in a set of numerical data in decimal representation. The data sending terminal is used to generate a public key pk in the offline stage, and at the same time generate a plaintext truth table based on a random n-dimensional table, n>=2. In the interaction stage, the plaintext truth table is used to linearly decompose each numerical data in the numerical data set to obtain the plaintext coordinates corresponding to the linear decomposition factors after the decomposition. At the same time, all plaintext coordinates and the ciphertext truth table obtained by fully homomorphically encrypting the plaintext truth table with the public key are sent to the data receiving terminal. The data receiving terminal is used to receive the generated public key pk, ciphertext truth table, and plaintext coordinates corresponding to the property decomposition factor, and to recover them into data to be sent.

[0018] Preferably, the data sending terminal generates a plaintext truth table based on a random n-dimensional table, where n>=2, specifically including: Several basic metadata are selected as the base values ​​of the plaintext truth table, wherein the basic metadata includes several non-zero integers containing the value 1; and the base values ​​satisfy: ,in and Let N be any base value in the plaintext truth table, and let N be any numerical value in decimal representation. Randomly select any number of basic metadata from the aforementioned basic metadata, and randomly repeat each selected basic metadata to obtain a plaintext truth table composed of base values. The data order in the plaintext truth table is randomly arranged.

[0019] The encrypted truth table is pre-sent to the data receiving terminal during the offline phase.

[0020] Preferably, the data sending terminal performs a linear decomposition on the data to be transmitted to obtain the plaintext coordinates corresponding to each linear decomposition factor, specifically including: Each decimal numerical data N is used as the modulus, and simultaneously, plaintext data with an absolute value less than the absolute value of numerical data N is randomly selected from the plaintext truth table T. As a modulus, and d≠±1, a modulo operation is performed to obtain the quotient b. The plaintext data d and the quotient b are used as linear decomposition factors, and the coordinates of the linear decomposition factors in the plaintext truth table T are used as the plaintext coordinate sequence of the numerical data N. If a remainder c exists, then the remainder c is used as the modulus, and plaintext data with an absolute value less than the absolute value of the remainder N is randomly selected from the plaintext truth table T. As the new modulus, perform modulo estimation, and combine the new modulus and the coordinates of the new quotient after modulo estimation in the plaintext truth table T with the coordinates of the initial plaintext data d in the plaintext truth table T to obtain the plaintext coordinate sequence of the value N. Repeat the above steps until the remainder is 0.

[0021] Preferably, if the quotient after each modulo operation is not in the plaintext truth table, then the maximum value in the plaintext truth table that is not greater than the quotient is selected as the new quotient b. new , And perform a subtraction operation to obtain the new numerical data. :

[0022] The initial plaintext data d and the new quotient b are used to... new The remainder c and the coordinates of the value 1 are recorded as decomposition factors, and the numerical data are... Repeat the linear split as the new value to be decomposed until the remainder is 0. Record the coordinates of all the decomposition factors in turn as the plaintext coordinates of the data N to be encrypted.

[0023] As can be seen from the above technical solutions, compared with the prior art, the present invention discloses a fully homomorphic encrypted ciphertext transmission method and system based on linear computation, which has the following beneficial effects: This invention discloses a paradigm data transmission method of "ciphertext codebook + index encoding combination". By sending the ciphertext table during idle time and sending the encoded coordinates during interaction, the amount of ciphertext transmitted during the interaction stage can be reduced, and the amount of transmission can be compressed to the plaintext level. Attached Figure Description

[0024] 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 embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0025] Figure 1 This is a schematic diagram of the overall process of the fully homomorphic encrypted ciphertext transmission method based on linear computation provided in the embodiments of the present invention; Figure 2 This is a flowchart of another complete form of fully homomorphic encrypted ciphertext transmission method provided in an embodiment of the present invention; Figure 3 This is a pseudocode example of linear decomposition provided in an embodiment of the present invention. Detailed Implementation

[0026] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] like Figure 1 As shown, this invention discloses a fully homomorphic encrypted ciphertext transmission method based on linear computation, comprising the following steps: Each character in the data to be sent is encoded to obtain a set of numerical data in decimal representation; During the offline phase, a plaintext truth table consisting of basic metadata is generated based on a random n-dimensional table, where n>=2, and the ciphertext truth table obtained by fully homomorphically encrypting the plaintext truth table is sent to the data receiving terminal. During the interaction phase, the plaintext truth table is used to linearly decompose each numerical data in the numerical data set to obtain the plaintext coordinates corresponding to the linear decomposition factors after decomposition, and all plaintext coordinates are sent to the data receiving terminal.

[0028] Figure 2 The overall process of the present invention is illustrated. In this complete transmission process, taking sender A (data sending terminal) and receiver B (data receiving terminal) as examples, the fully homomorphic encrypted ciphertext transmission method based on linear computation disclosed in the present invention is described in detail.

[0029] Offline phase: S1. The sender A (data sending terminal) generates a key pair (pk, sk) based on the modular component fully homomorphic encryption algorithm and publishes the public key pk. S2, Receiver B (data receiving terminal) receives pk; in addition, it can be extended to multiple data receiving terminals C, D, etc.

[0030] S3. Sender A (data sending terminal) generates a random two-dimensional (multi-dimensional) table and generates basic metadata. The basic metadata is repeated multiple times and shuffled before being filled into the table to obtain a plaintext truth table. The plaintext truth table is then sent to receiver B (data receiving terminal) after being fully homomorphically encrypted. Here, fully homomorphically encrypting the plaintext truth table means homomorphically encrypting each basic data in the plaintext truth table.

[0031] S4. Receiver B (data receiving terminal) receives the encrypted truth table and stores it; Interaction phase: S5. The sender A (data sending terminal) linearly splits the data to be transmitted to obtain the corresponding coordinates and sends the plaintext coordinates to the calculator. This step refers to directly performing linear splitting on numerical data using the basic metadata in the plaintext truth table to obtain the plaintext coordinates corresponding to the linear decomposition factors. For non-numerical data, it is converted into unique numerical data through a known encoding method.

[0032] S6. Receiver B (data receiving terminal) obtains the plaintext coordinates and transmits them as parameters to the processing module. The processing module extracts the data based on the parameters and the truth table, performs calculations, and obtains the ciphertext information.

[0033] The processing module in receiver B only needs to retrieve the ciphertext data at the corresponding position in the ciphertext truth table, according to N = E(a1). E(d1) + ...+ E(a n ) E(d n To restore, where N represents the data to be transmitted, a i 、E(d i ) represents the ciphertext value corresponding to the coordinate in the ciphertext truth table.

[0034] Overall, this invention focuses on compressing the size of fully homomorphic ciphertext to the plaintext level, significantly reducing communication overhead. Specifically, it enables the transmission of a small amount of plaintext coordinates, allowing participating parties to fully utilize computing resources and combine a small amount of plaintext into a large amount of ciphertext through linear combinations of ciphertext in the truth table. This satisfies security requirements while shortening interaction time.

[0035] Specifically: During the offline preprocessing stage, sender A generates a randomly generated plaintext truth table and then generates a ciphertext truth table through fully homomorphic encryption, and transmits the resulting ciphertext truth table.

[0036] S1. Sender A (data sending terminal) first generates a key pair (pk, sk) consisting of a public key and a private key, and publishes its public key pk; specifically, the following steps are included: Sender A (data sending terminal) uses fully homomorphic encryption based on modulo components, which can also be extended to algorithms such as CKKS and BFV to generate key pairs (pk, sk).

[0037] S2, receiver B (data receiving terminal), etc. receive pk; including the following steps: Receiver B (data receiving terminal) receives pk and stores it locally for subsequent calculations. Other receivers B, C, etc., can also store the public key for subsequent encrypted calculations.

[0038] S3. Sender A (data sending terminal) generates a random two-dimensional (multi-dimensional) table, generates basic elements, repeats this table multiple times and shuffles the order, then fills the table to obtain a plaintext truth table. The truth table is then encrypted and sent to receiver B (data receiving terminal). This includes the following steps: Sender A (data sending terminal) selects several basic metadata (such as...) The base values ​​are used as the base values ​​of the truth table. Then, the base values ​​are randomly selected and repeated randomly. In the final truth table, the number and position of the base values ​​are random.

[0039] The truth table must have at least two dimensions; the selection of the base values ​​must satisfy the following condition: given a rational number with finite precision (encoded numerical value N), there exist a finite number of base values. , so that:

[0040] Furthermore, the linear combination is represented by a finite number of terms.

[0041] Sender A (data sending terminal) uses the public key to encrypt the truth table, obtaining an n (n>=2) dimensional ciphertext truth table, and sends the ciphertext truth table to the computer.

[0042] S4. Receiver B (data receiving terminal) receives and stores the encrypted truth table; this includes the following steps: Receiver B (data receiving terminal) receives the encrypted truth table and stores it locally.

[0043] This phase can occur offline and does not consume online interaction time. The ciphertext truth table can be dynamically rotated based on usage frequency (e.g., every three months).

[0044] During the online interaction phase, the data to be transmitted is linearly decomposed using the basic metadata in the plaintext truth table. This yields the plaintext coordinates of the linear decomposition factors in the truth table, which are then transmitted via these coordinates. The specific steps include: S5. Sender A (data sending terminal) linearly splits the data to be transmitted to obtain the corresponding coordinates and sends the plaintext coordinates to the calculator. This step occurs during the online interaction phase and specifically includes the following steps: Sender A (data sending terminal) linearly decomposes the plaintext data to be transmitted (with controlled precision, such as retaining four decimal places). This is done by constructing a numerical decomposition process based on a plaintext truth table, representing the plaintext data as a linear combination of multiple primitives. Specifically, each participant selects any plaintext data from the plaintext truth table as the initial value to be decomposed, and performs integer division and modulo operations on this value based on preset rules to obtain the corresponding quotient. When the quotient cannot be directly represented by the plaintext truth table, the decomposition continues until all factors satisfy the representation conditions of the plaintext truth table.

[0045] Since each split is a linear combination of addition and multiplication, if there are two coordinates, their corresponding positions are multiplied together; if there are four coordinates, the coordinates are multiplied in pairs in order and then added together. Therefore, the symbols can be omitted during transmission.

[0046] refer to Figure 3 The pseudocode shown illustrates that the linear splitting process can be represented by the following steps: Let the plaintext truth table be a discrete set T, and the values ​​to be split be rational numbers N after quantization.

[0047] Randomly select the divisor from the truth table T. Perform division with remainder on N:

[0048] judge: like End, and there is:

[0049] like ,but:

[0050] Iterative update

[0051] Then The recursion continues with the new value.

[0052] Since any numerical element can be factored into an expression containing only addition, subtraction, and multiplication, the original data to be sent can be correctly restored through a finite number of steps using the homomorphism of the ciphertext.

[0053] For the truth table, several elements are repeated a certain number of times (the frequency and order of each element are unrelated), and the homomorphic ciphertext of the same data is also different. Therefore, the "ciphertext truth table" itself does not reveal any information. Furthermore, the factorization of each numerical data is random, so the position changes are also random (in other words, the factorization of the same element is different; even if the factorization is the same, the position of the element in the "ciphertext truth table" is also different, thus ensuring security). That is, 100 = 50. 2 or 100 = 25 4 or 100 = 30 3+10 1,....,There are many ways to split it, so it is impossible to deduce the original value from the position, frequency, length, etc., which greatly increases the difficulty of combination.

[0054] The specific process of the present invention will be further explained below through two more specific implementation examples.

[0055] Implementation Example 1: Suppose the encoded numerical data from the sender is N=90000, and the selected two-dimensional truth table for the encoding range contains... .

[0056] (1) The decomposition process is as follows: Suppose that the randomly selected truth table value is d=9, and a division is performed once, resulting in a quotient b=10000 and a remainder c=0. Checking the plaintext table, we find that the values ​​of d and b are both in the table. Let's assume that the coordinates of d are (1,0) and the coordinates of b are (8,2). Then the coordinates after N decomposition are ZB=[(1,0),(8,2)]. The sender sends ZB to the receiver.

[0057] (2) The recovery process is as follows: After receiving the coordinates ZB, the receiver retrieves the data from the encrypted truth table according to the coordinates and performs linear calculations to obtain the original data: N_ 恢复 = E_ (1,2) E_ (8,2) = E(9) E(10000) = E(90000) E_ (x,y) E represents the ciphertext value of the (x, y) coordinates, and E(·) represents the data after homomorphic encryption.

[0058] The following are two specific implementation examples. Implementation Example 2: Suppose the encoded numerical data from the sender is N=80803, and the selected two-dimensional truth table for the encoding range contains... .

[0059] (1) The decomposition process is as follows: Suppose we select a randomly chosen value from the truth table, d=8. Performing a division operation yields a quotient b=10100 and a remainder c=3. Looking up the plaintext table, we find d and b are present, but b is not. Now, we select the largest value in the table smaller than the quotient b, b_new=10000. Let's assume the coordinates of d are (3,0), b_new is (8,2), c is (11,1), and 1 is (3,11). Then, the coordinates of N after decomposition are ZB = [(3,0),(5,6),(11,1),(3,11)]. Performing a subtraction operation, we get N_new = N - d. b_new - c = 80803 - 8 10000 - 3 = 800.

[0060] Continuing the decomposition with N_new=800, assuming the randomly selected truth table value is d=20, performing one division yields a quotient b=40 and a remainder c=0. Checking the plaintext table, we find the values ​​of d and b are present. Let's assume the coordinates of d are (7,2) and the coordinates of b are (6,2). All factors are in the plaintext truth table, and the decomposition ends. The final result is ZB= [(3,0),(5,6),(11,1),(3,11),(7,2),(6,2)]. The sender then sends ZB to the receiver.

[0061] (2) The recovery process is as follows: After receiving the coordinates ZB, the receiver retrieves the data from the encrypted truth table according to the coordinates and performs linear calculations to obtain the original data: N_recovery = E_(3,0) E_(5,6) + E_(11,1) E_(3,11)+ E_(7,2) E_(6,2) = E(8) E(10000) + E(3) E(1) + E(20) + E(40) = E(80803) E_(x,y) represents the ciphertext value of the (x,y) coordinates, and E(·) represents the data after homomorphic encryption.

[0062] Similarly, the floating-point number processing procedure is the same; you only need to increase N in advance to make it an integer.

[0063] For non-numerical data (such as text or symbols), it can be converted into the corresponding integer or rational number representation using existing encoding methods (such as character encoding, byte encoding, or hash mapping) before encryption. The encoded data can then be directly applied to the method described above.

[0064] In practical applications, the data to be transmitted is usually in the form of a data sequence or a data vector. The method of this application can perform linear splitting on each data element in the data sequence independently or in blocks. For any data element, it can be decomposed based on a plaintext truth table through iterative division and modular arithmetic to obtain the corresponding coefficients and primitive indices, and then homomorphic operations are performed in the ciphertext domain. That is, for example, continuous data such as ID card numbers and telephone numbers only need to be transformed into a vector composed of several numerical values ​​in the preprocessing stage. Essentially, it is still the processing of numerical data.

[0065] Based on the principles of the above transmission method, this invention also discloses a fully homomorphic encrypted ciphertext transmission system based on linear computation, comprising: The data encoding module is used to encode each character in the data to be sent, resulting in a set of numerical data in decimal representation. The data sending terminal is used to generate a public key pk in the offline stage, and at the same time generate a plaintext truth table based on a random n-dimensional table, n>=2. In the interaction stage, the plaintext truth table is used to linearly decompose each numerical data in the numerical data set to obtain the plaintext coordinates corresponding to the linear decomposition factors after the decomposition. At the same time, all plaintext coordinates and the ciphertext truth table obtained by fully homomorphically encrypting the plaintext truth table with the public key are sent to the data receiving terminal. The data receiving terminal is used to receive the generated public key pk, ciphertext truth table, and plaintext coordinates corresponding to the property decomposition factor, and to recover them into data to be sent.

[0066] The detailed processing procedures for each structure are available in the reference methods and will not be repeated here.

[0067] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to in the method section.

[0068] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A fully homomorphic encrypted ciphertext transmission method based on linear computation, characterized in that, Includes the following steps: Each character in the data to be sent is encoded to obtain a set of numerical data in decimal representation; In the offline phase, a plaintext truth table consisting of basic metadata is generated based on a random n-dimensional table, where n>=2, and the ciphertext truth table obtained by fully homomorphically encrypting the plaintext truth table using a public key is sent to the data receiving terminal. Specifically, the generation of a plaintext truth table composed of basic metadata based on a random n-dimensional table includes: Several basic metadata are selected as the base values ​​of the plaintext truth table, wherein the basic metadata includes several non-zero integers containing the value 1; and the base values ​​satisfy: ,in and Let N be any base value in the plaintext truth table, and let N be any numerical value in decimal representation. Randomly select any number of basic metadata from the aforementioned basic metadata, and randomly repeat each selected basic metadata to fill an n-dimensional table, thereby obtaining a plaintext truth table composed of basic values, wherein the data order in the plaintext truth table is randomly arranged. During the interaction phase, the plaintext truth table is used to linearly partition each numerical data in the numerical data set to obtain the plaintext coordinates corresponding to the linear decomposition factors after partitioning. Simultaneously, all plaintext coordinates are sent to the data receiving terminal. Specifically, the linear partitioning of each numerical data in the numerical data set using the plaintext truth table includes: Each decimal numerical data N is used as the modulus, and simultaneously, plaintext data with an absolute value less than the absolute value of numerical data N is randomly selected from the plaintext truth table T. As a modulus, and d≠±1, a modulo operation is performed to obtain the quotient b. The plaintext data d and the quotient b are used as linear decomposition factors, and the coordinates of the linear decomposition factors in the plaintext truth table T are used as the plaintext coordinate sequence of the numerical data N. If a remainder c exists, then the remainder c is used as the modulus, and plaintext data with an absolute value less than the absolute value of the remainder N is randomly selected from the plaintext truth table T. As the new modulus, perform modulo estimation, and combine the new modulus and the coordinates of the new quotient after modulo estimation in the plaintext truth table T with the coordinates of the initial plaintext data d in the plaintext truth table T to obtain the plaintext coordinate sequence of the value N. Repeat the above steps until the remainder is 0. If the quotient after each modulo operation is not in the plaintext truth table, then the maximum value in the plaintext truth table that is not greater than the quotient is selected as the new quotient b. new , And perform a subtraction operation to obtain the new numerical data. : The initial plaintext data d and the new quotient b are used to... new The remainder c and the coordinates of the value 1 are recorded as decomposition factors, and the numerical data are... Repeat the linear split as the new value to be decomposed until the remainder is 0. Record the coordinates of all the decomposition factors in turn as the plaintext coordinates of the data N to be encrypted.

2. The method as described in claim 1, characterized in that, Encode each character in the data to be sent, specifically by performing Unicode encoding on each non-numeric data character in the data to be sent, to obtain the decimal representation of the corresponding Unicode code point in the Unicode character set; When the data to be sent includes decimals, the decimals are transmitted via a combination of... Multiply the results and convert them to integers, while recording the number of decimal places j.

3. The method as described in claim 1, characterized in that, The plaintext truth table is fully homomorphically encrypted using a modulo component-based fully homomorphic encryption algorithm.

4. A fully homomorphic encrypted ciphertext transmission system based on linear computation, characterized in that, include: The data encoding module is used to encode each character in the data to be sent, resulting in a set of numerical data in decimal representation. A data sending terminal is used to generate a public key pk in the offline phase, and simultaneously generate a plaintext truth table based on a random n-dimensional table, where n>=2. In the interaction phase, it uses the plaintext truth table to linearly decompose each numerical data in the numerical data set, obtaining the plaintext coordinates corresponding to the linear decomposition factors. Simultaneously, it sends all plaintext coordinates and a ciphertext truth table obtained by fully homomorphically encrypting the plaintext truth table using the public key to the data receiving terminal. Specifically, generating the plaintext truth table based on a random n-dimensional table, where n>=2, includes: Several basic metadata are selected as the base values ​​of the plaintext truth table, wherein the basic metadata includes several non-zero integers containing the value 1; and the base values ​​satisfy: ,in and Let N be any base value in the plaintext truth table, and let N be any numerical value in decimal representation. Randomly select any number of basic metadata from the aforementioned basic metadata, and randomly repeat each selected basic metadata to obtain a plaintext truth table composed of base values. The data in the plaintext truth table is arranged in a random order. The data sending terminal performs a linear decomposition on the data to be transmitted, obtaining the plaintext coordinates corresponding to each linear decomposition factor, specifically including: Each decimal numerical data N is used as the modulus, and simultaneously, plaintext data with an absolute value less than the absolute value of numerical data N is randomly selected from the plaintext truth table T. As a modulus, and d≠±1, a modulo operation is performed to obtain the quotient b. The plaintext data d and the quotient b are used as linear decomposition factors, and the coordinates of the linear decomposition factors in the plaintext truth table T are used as the plaintext coordinate sequence of the numerical data N. If a remainder c exists, then the remainder c is used as the modulus, and plaintext data with an absolute value less than the absolute value of the remainder N is randomly selected from the plaintext truth table T. As the new modulus, perform modulo estimation, and combine the new modulus and the coordinates of the new quotient after modulo estimation in the plaintext truth table T with the coordinates of the initial plaintext data d in the plaintext truth table T to obtain the plaintext coordinate sequence of the value N. Repeat the above steps until the remainder is 0. If the quotient after each modulo operation is not in the plaintext truth table, then the maximum value in the plaintext truth table that is not greater than the quotient is selected as the new quotient b. new , And perform a subtraction operation to obtain the new numerical data. : The initial plaintext data d and the new quotient b are used to... new The remainder c and the coordinates of the value 1 are recorded as decomposition factors, and the numerical data are... Repeat the linear split as the new value to be decomposed until the remainder is 0. Record the coordinates of all the decomposition factors in turn as the plaintext coordinates of the data N to be encrypted. The data receiving terminal is used to receive the generated public key pk, ciphertext truth table, and plaintext coordinates corresponding to the property decomposition factor, and to recover them into data to be sent.

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