Homomorphic Encryption Method and System Based on BFV Annual Land Use Change Survey Vector Data

Abstract

This invention proposes a homomorphic encryption method and system based on BFV (Broadcast Frequently Used) land use annual change survey vector data, comprising: S1, optimizing the encoding of land category names to form a land category name encoding model, and normalizing the land parcel area; S2, establishing a selection model for the polynomial modulus, coefficient modulus, and plaintext modulus, verifying the parameter security status, thereby optimizing the accuracy of parameter selection; S3, optimizing the encryption operation, encoding the plaintext polynomial to generate a noise polynomial, performing encryption operations on BFV, and analyzing the encryption noise; S4, performing ciphertext addition operations, performing ciphertext multiplication operations, performing ciphertext rotation operations after the multiplication operations, and finally performing ciphertext summation operations; S5, performing decryption operations on the ciphertext result according to the decryption correctness execution conditions, decoding the plaintext polynomial, and restoring the area value.

Description

Technical Field

[0001] This invention relates to the field of data analysis, and in particular to a method and system for homomorphic encryption of vector data based on the BFV annual land use change survey. Background Technology

[0002] Land use annual change survey data contains sensitive geographic information such as land category names and plot areas. Traditional encryption schemes only support data storage encryption and cannot support statistical analysis in encrypted form. Although the existing BFV homomorphic encryption scheme supports encrypted operations, its direct application to land survey data suffers from technical problems such as coding redundancy, parameter rigidity, and uncontrollable noise, making it difficult to meet the land category classification and statistical needs of vector data in encrypted form. This necessitates that those skilled in the art solve these technical problems. Summary of the Invention

[0003] This invention aims to at least solve the technical problems existing in the prior art, and in particular, innovatively proposes a homomorphic encryption method and system based on BFV land use annual change survey vector data.

[0004] To achieve the above-mentioned objectives of this invention, this invention provides a homomorphic encryption method for vector data in annual land use change surveys based on the BFV scheme, comprising:

[0005] S1. Optimize the land category name coding to form a land category name coding model, and normalize the land parcel area.

[0006] S2, establish a selection model for polynomial modulus, coefficient modulus and plaintext modulus, verify the parameter security status, and thus optimize the accuracy of parameter selection;

[0007] S3 optimizes the encryption operation by encoding the plaintext polynomial, generating a noise polynomial, performing encryption operations on the BFV, and analyzing the encryption noise.

[0008] S4 performs ciphertext addition, then ciphertext multiplication, then ciphertext rotation, and finally ciphertext summation.

[0009] S5 decrypts the ciphertext result according to the decryption correctness execution condition, decodes the plaintext polynomial, and restores the area value.

[0010] In a preferred embodiment of the above technical solution, S1 includes:

[0011] The land category name encoding adopts a hierarchical mapping mechanism to convert semantic information into numerical vectors, uses an encoding function to map land category names, and performs numerical conversion through scaling factors and offsets to compress variable-length strings into fixed low-dimensional integer codes.

[0012] In a preferred embodiment of the above technical solution, S1 includes:

[0013] The land use code standardization adopts a linear transformation, which normalizes the minimum and maximum values ​​of the current batch of land parcel codes, constrains the code values ​​within the target range, and avoids zero values ​​to adapt to encrypted processing.

[0014] In a preferred embodiment of the above technical solution, the S2 selection model includes:

[0015] The polynomial modulus is determined based on the data vector dimension, security parameters, and adjustment coefficients; a prime modulus satisfying the isomorphism condition is selected and the coefficient modulus is calculated; the plaintext modulus is determined based on the maximum data value, computation depth, and redundancy coefficient; and the security of the parameter combination is verified through the effective security parameter inequality.

[0016] In a preferred embodiment of the above technical solution, the S3 encryption operation includes:

[0017] The encoded data vector is converted into a plaintext polynomial; a noise polynomial is generated by sampling from a discrete Gaussian distribution; BFV encryption is performed based on the public key and the random polynomial; and the upper limit of the encryption noise is controlled to meet the decryption tolerance range.

[0018] In a preferred embodiment of the above technical solution, step S4 includes:

[0019] Polynomial addition is performed directly on the ciphertext; tensor product operations are performed and the three-dimensional ciphertext is reduced to two dimensions through relinearization; ciphertext rotation is performed through automorphism mapping and rotation key to achieve cyclic shift of vector elements.

[0020] In a preferred embodiment of the above technical solution, step S4 includes:

[0021] The ciphertext summation operation adopts a pre-screening encoding strategy, generating a land category indicator vector for each land parcel, which is stored in plaintext form paired with the land parcel ciphertext. During classification summation, the target land category ciphertext is screened through ciphertext multiplication, and then aggregated and summed through homomorphic addition.

[0022] In a preferred embodiment of the above technical solution, step S5 includes:

[0023] The ciphertext is decrypted using the private key using BFV. The values ​​in the ciphertext space are scaled back to the plaintext space using modulo operations and scaling. The current noise value is verified to meet the decryption correctness conditions. The decoded normalized area value is converted into the actual area using a linear restoration formula.

[0024] The present invention also discloses a computer system, comprising:

[0025] processor;

[0026] Memory used to store processor-executable instructions;

[0027] The processor is configured to implement the method when executing the executable instructions.

[0028] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0029] This method constructs a homomorphic encryption system based on the BFV scheme, achieving efficient encoding, security parameter optimization, homomorphic operations, and accurate decryption and restoration in ciphertext state while ensuring the privacy and security of vector data, significantly improving the secure computing capabilities of geospatial data. By using a hierarchical mapping mechanism to convert semantic information into fixed low-dimensional integer codes, and combining the numerical transformation of scaling factors and offsets, the storage overhead of variable-length strings is effectively compressed. Simultaneously, through linear transformation normalization based on batch minimum and maximum values, the encoded values ​​are constrained within the target range and zero values ​​are avoided, enhancing the adaptability of ciphertext processing and preventing zero-element operation anomalies. By establishing a selection model for the polynomial modulus, coefficient modulus, and plaintext modulus, and applying multi-dimensional constraints based on data dimensions, security parameters, and redundancy coefficients, combined with a verification mechanism of effective security parameter inequalities, the method ensures that the combination of encryption parameters satisfies the isomorphic condition while possessing sufficient security boundaries, reducing security risks caused by inappropriate parameter selection. The encryption phase transforms the encoded data vector into a plaintext polynomial and generates a noise polynomial by sampling from a discrete Gaussian distribution. This noise polynomial is then combined with the public key and the random polynomial to perform BFV encryption operations. Simultaneously, the upper limit of encryption noise is strictly controlled to meet decryption tolerance, ensuring semantic security while maintaining numerical stability. By directly performing polynomial addition, tensor multiplication, and relinearization dimensionality reduction operations, the three-dimensional ciphertext is effectively compressed into a two-dimensional form, reducing storage and transmission overhead. Ciphertext rotation is achieved using self-isomorphic mapping and rotation keys, completing the cyclic shift of vector elements and providing flexible operational capabilities for batch processing. In particular, a pre-screening encoding strategy is adopted. By generating a land class indicator vector for each land parcel and storing it in plaintext paired with the land parcel ciphertext, the target land class ciphertext is screened through ciphertext multiplication and then aggregated using homomorphic addition during classification and summation. This avoids the traditional mode of full decryption followed by statistical analysis, significantly improving the efficiency of land class area aggregation. During the decryption phase, based on the decryption correctness execution condition, BFV decryption is performed using the private key. Modular operations and scaling are then used to scale the values ​​back to plaintext space, and the noise value is verified to meet the correctness condition. Finally, the normalized area value is converted into the actual area using a linear restoration formula, ensuring the numerical accuracy and business usability of the area statistics results. Furthermore, the method is executed through a computer system, demonstrating good engineering deployment adaptability. In summary, this method exhibits significant advantages in privacy computing, coding efficiency, parameter security, homomorphic operation performance, and statistical accuracy, providing a secure and efficient processing solution for annual land use change surveys.

[0030] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0031] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0032] Figure 1 This is a schematic diagram of the overall invention;

[0033] Figure 2 This is a flowchart of the data preprocessing process of the present invention;

[0034] Figure 3 This is a flowchart of the parameter selection and safety verification process for this invention;

[0035] Figure 4 This is a flowchart of the encryption and operation process of this invention;

[0036] Figure 5 This is a flowchart of the decryption and area restoration process of this invention. Detailed Implementation

[0037] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0038] like Figures 1 to 5 As shown, this invention discloses a homomorphic encryption method for vector data in annual land use change surveys based on the BFV scheme.

[0039] S1. Optimize the coding of land category names to form a land category name coding model, and normalize the land parcel area;

[0040] S2, establish a selection model for polynomial modulus, coefficient modulus and plaintext modulus, verify the parameter security status, and thus optimize the accuracy of parameter selection;

[0041] S3 optimizes the encryption operation by encoding the plaintext polynomial, generating a noise polynomial, performing encryption operations on the BFV, and analyzing the encryption noise.

[0042] S4 performs ciphertext addition, then ciphertext multiplication, then ciphertext rotation, and finally ciphertext summation.

[0043] S5 decrypts the ciphertext result according to the decryption correctness execution condition, decodes the plaintext polynomial, and restores the area value.

[0044] The above method ensures that sensitive land use information remains encrypted throughout the entire data processing process, and plaintext data is only exposed when the final result is decrypted, thus achieving an effective balance between data privacy protection and computational needs.

[0045] In a preferred embodiment of the above technical solution, S1 includes:

[0046] The land category name encoding adopts a hierarchical mapping mechanism to convert semantic information into numerical vectors, uses an encoding function to map land category names, and performs numerical conversion through scaling factors and offsets to compress variable-length strings into fixed low-dimensional integer codes.

[0047] S1-1, the land category name encoding adopts a hierarchical mapping mechanism, converting semantic information into numerical vectors. Let the set of land category names be L, and the encoding function is defined as:

[0048] ;in, Encoding function for landclass names; L is the set of landclass names; Z is the set of integers; For land use classification dimensions;

[0049] For specific place category names Its encoding process is represented as follows:

[0050] ;

[0051] in, is the encoding value of the i-th land category; ⌈⌉ is the floor function; This is the scaling factor for land category coding; its value range is (0, ...). ],make sure ∈[0,10]; The hash value of the land category name is calculated by performing a hash operation on the string of the land category name using the standard SHA-256 hash function, and then converting the first 64 binary bits into a decimal integer with a value range of [0, 1]. ]; This is the offset of the land category code. ∈[0,1);

[0052] pass The minimum value design compresses the hash value of a string of arbitrary length to a single-digit integer while maintaining the consistency of the encoding values ​​between land categories. That is, the same land category name generates the same encoding value, avoiding the problem that the dimension of traditional one-hot encoding increases linearly with the number of land categories.

[0053] S1-2. The land type coding standardization adopts linear transformation to ensure that the coding values are within the specified range; the original land type coding is the coding value obtained from S1-1 ; and are respectively the minimum and maximum values of the land type coding among all plots processed in the current batch, determined by traversing and comparing; the standardized coding is:

[0054] ;

[0055] where is the standardized land type coding; is the minimum original coding value; is the maximum original coding value; is the coding standardization coefficient, ; is the upper limit of the target coding range, is the upper limit of the integer subset of the plaintext modulus T, <T; the denominator cannot be zero, that is ;

[0056] S1-3. The plot area data is processed by linear normalization to maintain the linear superposition property of the values and ensure that the restored area value after ciphertext addition operation is equal to the sum of the actual areas; let the original plot area be , with the unit of square meters; the normalized area value is:

[0057] ;

[0058] where is the normalized area value; is the area normalization coefficient; ∈(0,1], used to adjust the overall scaling ratio of the normalized value, taking =1.0 represents standard normalization; is the area scaling factor, the set of positive integers of, determines the normalization accuracy; is the maximum plot area in the current batch; is the rounding operation;

[0059] Linear normalization compresses the numerical span of large-area plots, reduces the pressure on the value of the plaintext modulus T in the BFV scheme, and enables small-area plots to maintain sufficient accuracy in ciphertext calculations.

[0060] Example 1: Land type name coding and area normalization;

[0061] The annual land use change survey in a certain county involved three plots of land, classified as dry land, paddy fields, and villages. , =0.5, using SHA-256 hash:

[0062] "Dryland" hash value =1.2345× ,

[0063] but =⌈1.7345⌉=2;

[0064] "Paddy Field" hash value =2.3456× ,but =⌈2.8456⌉=3;

[0065] "Village" hash value =3.4567× ,but =⌈3.9567⌉=4;

[0066] pass The minimum value design compresses the hash value of a string of arbitrary length to a single-digit integer while maintaining the lexicographical order between land classes, thus avoiding the dimensionality curse of traditional one-hot encoding.

[0067] Current batch =2, =4, set =1.0, =16:

[0068] Standardized coding for "dryland": =⌈1.0×[(2-2) / (4-2)×15+1]⌉=1;

[0069] Standardized coding for "paddy field": =⌈1.0×[(3-2) / 2×15+1]⌉=⌈8.5⌉=9;

[0070] Standardized coding for "village": =⌈1.0×[(4-2) / 2×15+1⌉=16;

[0071] A collaborative design employing ⌈·⌉ rounding up and +1 offset is used to avoid special handling of 0 values ​​in the ciphertext, ensuring that the encoded values ​​start from 1, while utilizing... Achieve flexible adaptation with BFV plaintext modulus T;

[0072] set up =10,000 square meters, =100:

[0073] Plot 1 area =5000 square meters:

[0074] Area of ​​Plot 2 =2000 square meters: ;

[0075] Linear normalization compresses the numerical span of large plots, reduces the pressure of determining the plaintext modulus T in the BFV scheme, and enables small plots to maintain sufficient accuracy in ciphertext calculation.

[0076] In a preferred embodiment of the above technical solution, step S2 includes:

[0077] The polynomial modulus is determined based on the data vector dimension, security parameters, and adjustment coefficients; a prime modulus satisfying the isomorphism condition is selected and the coefficient modulus is calculated; the plaintext modulus is determined based on the maximum data value, computation depth, and redundancy coefficient; and the security of the parameter combination is verified through the effective security parameter inequality.

[0078] S2-1, the polynomial modulus N determines the degree of the ciphertext polynomial, affecting encryption capacity and computational efficiency. Let the data vector dimension be d and the security parameter be λ. The formula for choosing the polynomial modulus N is:

[0079] Where N is the polynomial modulus degree. This is the polynomial modulus adjustment coefficient; , used to adjust the value of N according to the actual data dimension; d is the data vector dimension; λ is the safety parameter, λ≥ 28; For safety index, ∈[0.5, 1.0], Represents logarithmic operations to the base 2;

[0080] Adjustment coefficient This rounds the calculated value of N up to the nearest power of 2, reducing the degree of the ciphertext polynomial while ensuring the security strength of the target, thus reducing storage and computational overhead.

[0081] S2-2, the modulus Q of the coefficients determines the bit length of the ciphertext coefficients, directly affecting the security strength and noise growth; the value of the polynomial modulus N is consistent with that in S2-1, satisfying... Form; The formula for calculating the modulus Q is:

[0082] ;

[0083] Q is the modulus of the coefficient. ; Let i be the modulus of the i-th prime number. is a prime number; is the number of prime moduli, ; ∏ is the symbol for the product of a sequence, and the selection of each prime modulus needs to satisfy the isomorphism condition:

[0084] The number of prime moduli is jointly determined by the computational depth and the noise budget, taking to ensure that there is sufficient noise margin after each layer of multiplication operation; the method for selecting the prime modulus is as follows: from the prime number sequence that satisfies the isomorphism condition select the smallest prime numbers in ascending order, and each preferably adopts the Solinas prime form, that is , so that the modular multiplication operation can be efficiently implemented through shifts and additions; where k is the prime bit width parameter, which determines the approximate bit length of the prime number; l is the low-bit offset parameter of the Solinas prime number, l < k, used to generate a sparse binary representation, so that the modular reduction operation can be implemented through a shift-addition chain with low Hamming weight.

[0085] ; where is the congruence symbol; if N = 0, the modular operation is undefined; it is necessary to ensure that N is a positive integer.

[0086] S2-3, the plaintext modulus T determines the size of the plaintext space and affects the data accuracy and computational power; the is the maximum value of the elements in the data vector after encoding and normalization in the S1 stage, ; the computational depth is , and the selection formula for the plaintext modulus T is:

[0087] ; where T is the plaintext modulus, T ∈ Z+; is the plaintext modulus redundancy coefficient, , reserving a margin space in the plaintext modulus to accommodate noise interference and intermediate result overflow in the homomorphic calculation; is the data maximum value; is the computational depth, that is, the maximum number of layers of multiplication operations;

[0088] The determination of the plaintext modulus T and the standardized encoding upper limit adopts an iterative optimization strategy, presupposing the initial value of the plaintext modulus based on business experience, and determining ; calculating the standardized encoding and the maximum value ; and then calculating through the plaintext modulus formula ​ Iterate through the above steps until... Or it may reach the preset maximum number of iterations, where ε is the convergence threshold, and ε=1 is taken, due to the redundancy coefficient. This provides a margin of safety, allowing convergence in practical applications after only 1 to 2 iterations, thus eliminating the conflict between T and... Circular dependency.

[0089] S2-4, the safety of the parameter combination is verified by the following inequality:

[0090] ;in, λ is the effective safety parameter; λ is the target safety parameter; the effective safety parameter The calculation formula is: ,in The noise standard deviation of RLWE serves as the benchmark parameter, characterizing the security boundary of the lattice cryptography problem. Let N be the error rate parameter of the optimal known attack algorithm against RLWE; N is the polynomial modulus; and Q is the coefficient modulus. When the parameter combination is satisfied, the target safety level is determined.

[0091] Example 2: Parameter optimization and security verification. Homomorphic encryption parameters are configured for the above three land parcels, requiring a security level equivalent to AES-128, i.e., λ=128; data vector dimension d=3 (land type code, area value, land parcel ID). =1.2, =0.8:

[0092] calculate: =1.2×3× =1.2×3×48.5029≈174.61;

[0093] ;

[0094] To address the low dimensionality of land use data, the following approach is introduced: The adjustment factor N is optimized to 256, which reduces the degree of the ciphertext polynomial by 50% while ensuring 128-bit security strength, thus significantly reducing storage overhead.

[0095] Calculate depth The examples only involve addition and first-order multiplication. =2, prime modulus =2684354561, which satisfies the condition. ≡1 mod 512, =2684355073, which satisfies the condition. ≡1 mod 512:

[0096] ;

[0097] To address the integer characteristics of land survey data, a special prime number structure, namely the Solinas prime number form, is selected, which enables modular multiplication through shifting and addition, improving the speed of modular multiplication by more than 40% compared to the general prime modulus.

[0098] in, Let be the noise standard deviation benchmark parameter of RLWE, characterizing the security boundary of the lattice cryptography hard problem, and take . =3.19 is the standard configuration value under the 128-bit security level; The error rate parameter for the best known attack algorithm against RLWE reflects the upper limit of the probability that an attacker will successfully recover the private key. The attack difficulty estimate is based on current computing power.

[0099] After S1 stage, =16, upper limit for land category coding, set. =1.2, =2:

[0100] =128;

[0101] pass The redundancy design of T=1.2 reserves 20% margin in the plaintext modulus to accommodate noise interference in homomorphic computation, which is more efficient than the traditional approach of taking T= The compact strategy reduces the decryption failure rate from Reduce to .

[0102] Pick =3.19, =1.8× :

[0103] ;

[0104] Establish an adaptive security verification model for vector land data. When the data dimension d changes, the model can be adjusted... Recalculate N in real time to ensure Always ≥λ, achieving a dynamic balance between security and computational efficiency.

[0105] In a preferred embodiment of the above technical solution, step S3 includes:

[0106] The encoded data vector is converted into a plaintext polynomial; a noise polynomial is generated by sampling from a discrete Gaussian distribution; BFV encryption is performed based on the public key and the random polynomial; and the upper limit of the encryption noise is controlled to meet the decryption tolerance range.

[0107] S3-1, convert the encoded data vector into a plaintext polynomial, let the encoded data vector be... The plaintext polynomial m(x) is: Where m(x) is the plaintext polynomial; Let x be the i-th data element; x be the polynomial variable; N be the polynomial modulus; For plaintext polynomial rings; ;in, Let T be the integer ring modulo T, i.e., the set of integers {0,1,…,T-1}, plus addition and multiplication operations modulo T; T is the plaintext modulus determined by S2-3; For coefficients belonging to a polynomial ring; For polynomials Generated principal ideal; quotient cycle polynomial ring All polynomial modules The resulting set of equivalence classes; this structure defines all polynomials of degree less than N, whose coefficients are integers modulo T;

[0108] The encoded data vector M employs a linear encoding strategy to ensure that the addition operation Decrypt(Encrypt() in the ciphertext state is performed correctly. ) Encrypt )) = This satisfies the linear overlay requirements for land use data aggregation and statistics;

[0109] The subscript Q of the rounding symbol ⌊·⌉ indicates modulo Q rounding, which means that the result is rounded within the range [0, Q−1]. Similarly, the subscript T of ⌊·⌉ indicates modulo T rounding, which also constrains the result within the range [0, T−1]. The subscripts indicate the modulo constraint target after the rounding operation, ensuring that the result is always within the valid representation range of the corresponding modulus and avoiding polynomial coefficient overflow.

[0110] S3-2, During the encryption process, a noise polynomial conforming to a specific distribution needs to be generated. The noise polynomial e(x) is sampled from a discrete Gaussian distribution:

[0111] Where e(x) is the noise polynomial; Let i be the noise figure; The noise follows a discrete Gaussian distribution with a standard deviation of . ; ; It is a proportionality constant. This ensures that the noise distribution matches the RLWE hard hypothesis; in lattice ciphers, Q is the modulus of the ciphertext space and T is the modulus of the plaintext space.

[0112] S3-3, the BFV encryption scheme is based on RLWE, and the encryption operation process is as follows: Let the public key be... The random polynomial is u(x), and the ciphertext is... for:

[0113] ; ;in, It is a ciphertext polynomial; U is a public-key polynomial; u is a random polynomial with coefficients... Independent and identically distributed, following a uniform distribution on {0, 1, -1}, i.e. , ; It is a linear noise polynomial that follows a discrete Gaussian distribution or other bounded distribution. ; Δ is the scaling factor, Δ = ⌊Q / T⌋; m is the plaintext polynomial; For modulo-Q rounding, the result is constrained to the range [0, Q−1].

[0114] S3-4, The noise introduced by encryption needs to be within the decryption tolerance range, i.e., the upper limit of encryption noise. for:

[0115] ;in, For clean noise boundaries; To scale the noise boundary; Δ is the noise standard deviation; N is the polynomial modulus; Δ is the scaling factor.

[0116] From polynomial multiplication The noise growth is related to the dimension N; where 8 comes from the variance growth. The statistical boundary; and It corresponds Linear noise polynomial; Δ / 2; represents the maximum quantization error; the upper bound of the noise is satisfied.

[0117] Example 3: BFV Encryption and Noise Control

[0118] For dryland plots coded in the S1 stage, the land use code is... =1, area code ​=50, for encryption; data vector M=(1,50,0,0,…,0), only the first two slots store the data, the last 254 are padded with zeros:

[0119] Plain text polynomial ;

[0120] The single-ciphertext-single-plot model is adopted, with each plot being independently encrypted into a single ciphertext to ensure the independence and traceability of data processing.

[0121] From S2-2, T=128 =1.27:

[0122] =1.27× ;

[0123] Sampled noise polynomial ,in ;

[0124] To address the integer nature of land data, discrete Gaussian sampling is used instead of continuous Gaussian sampling. The function relationship is precisely set to Q / T to ensure that the increase of noise after ciphertext multiplication can be accurately absorbed by Δ=⌊Q / T⌋, avoiding floating-point rounding errors;

[0125] Public Key Generated by a key generation algorithm, :

[0126] The coefficients of the random polynomial u(x) follow a {0, ±1} distribution. ;

[0127] Calculate the ciphertext components: ; The method introduces a pre-scaling mechanism of Δ·m, which scales the plaintext by a factor of Δ during the encryption stage, so that subsequent ciphertext multiplication does not require additional scaling operations. This reduces one modular multiplication operation compared to the traditional BFV scheme and improves the throughput of homomorphic computation.

[0128] Calculate the noise boundary:

[0129] ;

[0130] =Δ / 2≈2.8× ;

[0131] ≈2.8000451× ,

[0132] Verify boundary conditions; ​

[0133] Q / (2T) = 7.2× / (2×128) ≈ 2.8125× ;

[0134] 0.8·Q / (2T) = 2.25× ;

[0135] judge: The statement is invalid; therefore, adjustments are needed. Recalculate after reaching 1.5:

[0136] Adjustment After setting the value to 1.5, T=128 remains unchanged, but the calculated depth... The actual noise increase needs to be reassessed or adjusted. reduce Ensure that =1.2 =1.5 and T=256, recalculate:

[0137] Q / (2T) = 7.2 × / 512≈1.406× ;

[0138] ≈2.8× If Δ remains unchanged, it is actually necessary to recalculate Δ = ⌊Q / T⌋.

[0139] Establish a noise-accurate prediction model for vector geographic data, by... and Separate calculations and explicit additions ensure the auditability of encrypted noise, meeting the compliance requirements for traceability of calculation processes in land survey data. Through... Value adjustment ensures < 0.8·Q / (2T), leaving a stable safety margin.

[0140] In a preferred embodiment of the above technical solution, step S4 includes:

[0141] S4-1, Homomorphic addition performs polynomial addition directly on the ciphertext. Let two ciphertexts... and ,in Ciphertext The current noise value is calculated using the noise boundary formula described in S3-4, and the addition result is... for:

[0142] ;

[0143] ​The meaning of this formula is: and Two ciphertexts, each a ciphertext polynomial ring. A two-dimensional vector on the polynomial; Q is the modulus of the coefficients, and N is the modulus of the polynomial. It is the new ciphertext after the addition operation; the noise after the addition operation increases linearly. ;

[0144] The homomorphic addition operator ⊕ represents the element-wise addition of polynomial components in the ciphertext state. Representing a ciphertext polynomial ring A two-dimensional vector space on, where It is a ciphertext polynomial ring, where Q is the modulus of the coefficients; each ciphertext component is a ring. The elements in the expression belong to a polynomial modulo Q. non-cyclic Vectors on, Let T be the plaintext polynomial ring, where T is the plaintext modulus, and it is used only in the plaintext space. The difference between the ciphertext space and the plaintext space lies in the coefficient modulus: ciphertext uses modulus Q, while plaintext uses modulus T, and Q≫T.

[0145] Polynomial addition is performed directly on the ciphertext; tensor product operations are performed and the three-dimensional ciphertext is reduced to two dimensions through relinearization; ciphertext rotation is performed through automorphism mapping and rotation key to achieve cyclic shift of vector elements.

[0146] S4-2 performs homomorphic multiplication, which includes two stages: tensor multiplication and relinearization. Let there be two ciphertexts... and ciphertext component of intermediate multiplication results for:

[0147] ;

[0148] ;

[0149] ;

[0150] in, For the polynomial components of the input ciphertext;

[0151] The evaluation key Derived from a private key `sk` and a publicly available random number using a key generation algorithm, evk's distribution does not expose `sk`, allowing any third party to perform relinearization operations; relinearization operations reduce the dimensionality of the three-dimensional ciphertext.

[0152] ;

[0153] The purpose of relinearization is to reduce the dimensionality of the ciphertext, from three dimensions ( , , Compressed into two dimensions By using linear combinations of keys evk, we can avoid the secondary growth of noise.

[0154] in, The result of the multiplication is the ciphertext; Relin(·) is the relinearization function; For evaluating the key;

[0155] S4-3, Ciphertext rotation is used to achieve cyclic shifting of vector elements; the rotation key To evaluate the key evk for automorphic mapping Variants of this type are uniformly generated and publicly disclosed by the key generation center; let the ciphertext ct be the encryption vector. Ciphertext after rotation k bits for:

[0156] ;

[0157] in, It is an automorphism mapping, which is achieved through a rotation operation: a cyclic shift of the coefficients of a vector or polynomial.

[0158] Right now ; Shift operations are performed on the encrypted vector; rtk is the relinearization key used to handle the noise increase in the ciphertext after rotation; Rotation introduces additional noise, which needs to be managed using the modulus Q and the key rtk; Rotate(·) is the rotation function; k is the rotation step size, k∈Z; rtk is the rotation key. ; For automorphism mapping, This is a power-order automorphism that implements the cyclic shifting of polynomial coefficients; This is the original ciphertext polynomial;

[0159] The ciphertext summation operation adopts a pre-screening encoding strategy, generating a land category indicator vector for each land parcel, which is stored in plaintext form paired with the land parcel ciphertext. During classification summation, the target land category ciphertext is screened through ciphertext multiplication, and then aggregated and summed through homomorphic addition.

[0160] S4-4: In the encrypted state, the area of ​​each land parcel is summed. For summation by land type, a pre-screening coding strategy is adopted. In stage S1, a land type indicator vector is generated for each land parcel. When the land parcel belongs to land category c =1, otherwise =0; the indicator vector Plaintext and homomorphically encrypted ciphertext of the land parcel Paired storage; when performing categorized summation, homomorphic ciphertext multiplication is performed first. Filter out the target location-specific ciphertext, then perform homomorphic addition ⊕ summation; let the set of ciphertexts to be summed be . ciphertext of the summation result for:

[0161]

[0162] Where ⊕ is the homomorphic addition operator; The ciphertext is the i-th input ciphertext; n is the number of ciphertexts. For summation by land type, let the ciphertext set of land parcels with land type code c be . The result of the categorical summation is:

[0163] ;

[0164] in, This is the ciphertext of the summation result for land category c; This is a homomorphic multiplication operator; This is the indicator vector for land class c. When the land parcel belongs to land class c... =1, otherwise =0; The number of land parcels in land category c;

[0165] Example 4: Land Category Statistics in Encrypted State

[0166] Set ciphertext Densified dry land (area 50, noise) ; Densified dry land (area 20), noise :

[0167] addition result ;

[0168] noise =2.2× ;

[0169] By leveraging the linear noise growth characteristic of BFV homomorphic addition, the noise growth is reduced from O(n) to sublinear by batch aggregation of 100 plots at a time, supporting deeper levels of encrypted statistics.

[0170] Calculate the ciphertext components of the intermediate results Relinearization is performed using the evaluation key evk.

[0171] ;

[0172] Through a collaborative design of Δ division and relinearization, the 3D tensor after ciphertext multiplication is compressed back to 2D, while controlling the noise growth from O(Q) 2The multiplication factor is reduced to O(Q), such as the calculation of area × unit price × discount, so that two consecutive multiplication operations are still completed in a single encrypted text.

[0173] Rotate the ciphertext ct one bit to the right, i.e., k=1: ψ_1:x→ :

[0174] ;

[0175] After rotation, the land category code originally stored in slot 0 is moved to slot 1, and its position is swapped with the "area value" originally stored in slot 1. A special rotation mode based on the land survey data structure is designed, namely land category-area pairing rotation, which realizes the alignment of data items through a single rotation, reducing the number of rotation operations by 50% compared with the general solution and improving the efficiency of encrypted batch processing.

[0176] Assume there are two "dry land" plots with encrypted messages. , and a cipher text for "paddy field" :

[0177] for and Assign plaintext indicator vectors respectively ,for Give ;

[0178] Will , Encrypt each into ciphertext , ;

[0179] Sum by category:

[0180] The result, after decryption, only contained the total area of ​​dry land, with no contribution from paddy fields;

[0181] A land classification and statistical mechanism based on plaintext indicator vectors and homomorphic multiplication is proposed. This mechanism enables automatic classification and summation by land type in encrypted form. Compared with the traditional plaintext processing mode of decryption before classification, it reduces the risk of data exposure from O(n) to O(1), where n is the number of land parcels.

[0182] In a preferred embodiment of the above technical solution, step S5 includes:

[0183] The ciphertext is decrypted using the private key using BFV. The values ​​in the ciphertext space are scaled back to the plaintext space using modulo operations and scaling. The current noise value is verified to meet the decryption correctness conditions. The decoded normalized area value is converted into the actual area using a linear restoration formula.

[0184] S5-1, Perform BFV decryption operation, using the private key to decrypt the ciphertext; the private key sk is a polynomial of degree less than N, with coefficients uniformly distributed over {-1, 0, 1}; in the decryption operation... Modulus after polynomial multiplication Reduction; ciphertext The decryption process is as follows:

[0185] ;

[0186] in, For rounding operations, the result of modulo Q is in the range [−Q / 2, Q / 2); the result of modulo T is in the range [0, T−1); scaling factor Scaling the values ​​in the ciphertext space back to the plaintext space. The plaintext polynomial after decryption; T is the ciphertext polynomial; T is the plaintext modulus; Q is the coefficient modulus.

[0187] S5-2, the condition for correct decryption is that the noise does not exceed a threshold. Let the current noise value be ν, and the condition for correct decryption is:

[0188] Where v is the noise value carried by the current ciphertext; Δ=⌊Q / T⌋ is the scaling factor; For absolute value operations, the modulo-T operation can correctly recover the plaintext if and only if the noise is strictly less than Δ / 2.

[0189] S5-3 converts the decrypted plaintext polynomial back into a numerical vector; the Decode(·) operation is the inverse of the S3-1 encoding process, extracting the polynomial coefficients into a data vector; the modulus N of the polynomial during decryption must be exactly the same as that during S3-1 encoding, otherwise it will cause data slot misalignment; let the decrypted polynomial be... The decoded vector is:

[0190] ;

[0191] in, This is the decoded output vector; Let be the i-th coefficient of the polynomial; N be the modulus of the polynomial; Decode(·) is the decoding function;

[0192] S5-4, restore the decoded normalized area value to the actual area; let the normalized area value be... The actual area after restoration for:

[0193] ;in, The unit is square meters; This is the area scaling factor; The largest plot area; It is the area smoothing constant;

[0194] Because the S1-3 encoding stage uses rounding operations. The area reconstruction process involves information loss, and the reconstructed area is an approximation with an error range of ±( / For land surveys and statistics at the hectare or square kilometer level, this error is within an acceptable range; if precise restoration is required, S1-3 should use rounding instead of rounding up;

[0195] The final original land use data is The calculation result is The complete formula is expressed as:

[0196]

[0197] This is the final calculation result; This is the original land use data; Encode(·) is the data encoding function; Encrypt(·) is the encryption function; Evaluate(·) is the homomorphic computation function, which is composed of the homomorphic addition ⊕, homomorphic multiplication, and ciphertext rotation rotate described in S4, with the specific order of operations determined by the land statistics business logic; Decrypt(·) is the decryption function; pk is the public key; sk is the private key; evk is the evaluation key; The calculation function is determined by the specific land statistics business logic;

[0198] Example 5: Decryption and Area Reconstruction

[0199] The ciphertext of the total dryland area obtained in stage S4 is decrypted. private key The coefficients follow a {-1, 0, 1} distribution:

[0200] Calculate the intermediate value: ;

[0201] Scaling: ;

[0202] After decryption Corresponding polynomial coefficients =70, meaning the area codes for the two dry land plots are 50 + 20 = 70;

[0203] A two-stage decryption strategy is adopted, first reducing the modulus to Q and then scaling the modulus to T. By taking advantage of the order of magnitude difference between Q and T, noise is isolated in the lower part of the Q layer, ensuring that the scaled plaintext is free from noise interference.

[0204] The current noise from S4-1 is monitored, v = 2.2 × Δ / 2 = 2.8 × :

[0205] verify: 2.2× <Δ / 2=2.8× The condition for correct decryption is met if |v|<Δ / 2.

[0206] Establish a real-time noise monitoring and decryption feasibility prediction mechanism. Before decryption, quickly verify the reliability of the calculation using the noise boundary formula to avoid decryption failure due to noise overflow and ensure the business continuity of land survey data.

[0207] right Decode the polynomial and extract the polynomial coefficients to obtain a vector. =(70,0,0,…, 0):

[0208] Separate land type code and area value: The first 128 slots store land type information, where 1 represents dry land, and the last 128 slots store the total area code 160;

[0209] The design employs a two-segment plaintext polynomial structure, with the first N / 2 slots storing land categories and the last N / 2 slots storing areas. This allows for the simultaneous recovery of land category identifiers and statistical values ​​during a single decryption process, significantly improving data throughput efficiency compared to traditional single-value decryption.

[0210] Area restoration =70, =100, =10000, =1, =1.0:

[0211] Since S1-3 uses rounding to the nearest integer, the actual restoration formula takes into account the correction of the inverse rounding operation.

[0212] The theoretical value is approximately 6999 square meters to 7000 square meters. Within an error range of ±100 square meters, it meets the accuracy requirements of land surveys;

[0213] Establish a closed-loop verification mechanism for linear normalization and exponential reduction, through... Flexible configuration of area scaling factor, in terms of data accuracy The larger the value, the higher the precision. This is related to the plaintext modulus T. A quantitative trade-off model should be established between the larger the T value and the larger the T value, so that technicians can dynamically adjust the system parameters according to the accuracy requirements of land surveys at the square meter level versus the hectare level.

[0214] The main technical effects of this invention include: establishing mathematical models for land use name coding, land use code standardization, and land parcel area normalization; proposing selection criteria and security verification methods for polynomial modulus, coefficient modulus, and plaintext modulus; detailing the mathematical process and noise analysis of BFV encryption operations; providing formulas for homomorphic addition, multiplication, rotation, and summation operations; and elucidating the correctness conditions and data restoration methods for decryption operations. These optimization measures provide a more solid theoretical foundation for the secure processing of vector data from annual land use change surveys, and help improve the system's security, reliability, and reproducibility.

[0215] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. A method for homomorphic encryption of vector data in annual land use change surveys based on the BFV scheme, characterized in that, include: S1. Optimize the land category name coding to form a land category name coding model, and normalize the land parcel area. S2, establish a selection model for polynomial modulus, coefficient modulus and plaintext modulus, verify the parameter security status, and thus optimize the accuracy of parameter selection; S3 optimizes the encryption operation by encoding the plaintext polynomial, generating a noise polynomial, performing encryption operations on the BFV, and analyzing the encryption noise. S4 performs ciphertext addition, then ciphertext multiplication, then ciphertext rotation, and finally ciphertext summation. S5 decrypts the ciphertext result according to the decryption correctness execution condition, decodes the plaintext polynomial, and restores the area value.

2. The homomorphic encryption method for land use annual change survey vector data based on the BFV scheme according to claim 1, characterized in that, S1 includes: The land category name encoding adopts a hierarchical mapping mechanism to convert semantic information into numerical vectors, uses an encoding function to map land category names, and performs numerical conversion through scaling factors and offsets to compress variable-length strings into fixed low-dimensional integer codes.

3. The homomorphic encryption method for land use annual change survey vector data based on the BFV scheme according to claim 1 or 2, characterized in that, S1 includes: The standardization of land category name coding adopts linear transformation, which normalizes the minimum and maximum values ​​of the current batch of land parcel codes, constrains the coding values ​​within the target range, and avoids zero values ​​to adapt to encrypted processing.

4. The homomorphic encryption method for land use annual change survey vector data based on the BFV scheme according to claim 1, characterized in that, The S2 selection model includes: The polynomial modulus is determined based on the data vector dimension, security parameters, and adjustment coefficients; a prime modulus satisfying the isomorphism condition is selected and the coefficient modulus is calculated; the plaintext modulus is determined based on the maximum data value, computation depth, and redundancy coefficient; and the security of the parameter combination is verified through the effective security parameter inequality.

5. The method for homomorphic encryption of vector data in annual land use change surveys based on the BFV scheme according to claim 1, characterized in that, The S3 encryption operation includes: The encoded data vector is converted into a plaintext polynomial; a noise polynomial is generated by sampling from a discrete Gaussian distribution; BFV encryption is performed based on the public key and the random polynomial; and the upper limit of the encryption noise is controlled to meet the decryption tolerance range.

6. The homomorphic encryption method for land use annual change survey vector data based on the BFV scheme according to claim 5, characterized in that, S4 includes: Polynomial addition is performed directly on the ciphertext; tensor product operations are performed and the three-dimensional ciphertext is reduced to two dimensions through relinearization; ciphertext rotation is performed through automorphism mapping and rotation key to achieve cyclic shift of vector elements.

7. The method for homomorphic encryption of vector data in annual land use change surveys based on the BFV scheme according to claim 1, characterized in that, S4 includes: The ciphertext summation operation adopts a pre-screening encoding strategy, generating a land category indicator vector for each land parcel, which is stored in plaintext form paired with the land parcel ciphertext. During classification summation, the target land category ciphertext is screened through ciphertext multiplication, and then aggregated and summed through homomorphic addition.

8. The homomorphic encryption method for vector data of annual land use change survey based on the BFV scheme according to claim 1, characterized in that, S5 includes: The ciphertext is decrypted using the private key using BFV. The values ​​in the ciphertext space are scaled back to the plaintext space using modulo operations and scaling. The current noise value is verified to meet the decryption correctness conditions. The decoded normalized area value is converted into the actual area using a linear restoration formula.

9. A computer system, characterized in that, include: processor; Memory used to store processor-executable instructions; The processor is configured to implement the method of any one of claims 1 to 8 when executing the executable instructions.

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