A fast processing system and method of encrypted data based on number theory transform
Patent Information
- Application Number
- CN202611002419.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-07-06
- Publication Date
- 2026-09-22
AI Technical Summary
[0004]针对现有技术的不足，本发明提供了一种基于数论变换的加密数据快速处理系统及方法，通过基于有效系数长度和目标模数对预配置数论变换参数组进行双维匹配与直接调用，解决了不同数据长度、不同模数条件下加密数据处理需重复配置变换参数及处理流程、适应性较差的问题
该基于数论变换的加密数据快速处理系统及方法，通过根据第一加密数据和第二加密数据的有效系数长度及目标模数，在预先建立的数论变换参数组库中进行双维匹配，以直接获取与当前加密数据处理规格对应的目标变换参数组。由此，在处理不同长度、不同目标模数的加密数据时，无需针对每次处理任务重新确定数论变换长度、辅助模数及对应的数论变换参数，能够减少参数配置及处理流程调整所产生的开销，提高加密数据处理过程对不同数据规格的适应能力。
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Abstract
Description
Technical Field
[0001] This invention relates to the field of data encryption technology, specifically to a fast encrypted data processing system and method based on number theory transformation. Background Technology
[0002] With the development of cloud computing, edge computing, the Internet of Things, and large-scale data transmission technologies, the demand for data security protection during storage, transmission, and computation is constantly increasing. Current encrypted data processing typically requires modular arithmetic, polynomial arithmetic, matrix arithmetic, or convolutional operations; especially in encryption schemes based on lattice cryptography, homomorphic encryption, or polynomial cryptographic structures, high-dimensional polynomial multiplication and modular reduction calculations are often necessary. Number theory transformations, as discrete transformation methods performed in finite fields, can convert polynomial convolution operations into pointwise multiplication operations. Therefore, existing technologies can employ number theory transformations to transform encrypted data, thereby improving the processing efficiency of polynomial-related encryption operations.
[0003] However, existing encrypted data processing methods based on number theory transformations often require reconfiguration of transformation parameters and processing procedures when dealing with encrypted data of different lengths, data sizes, or modulus parameters, resulting in poor adaptability. Summary of the Invention
[0004] To address the shortcomings of existing technologies, this invention provides a fast encrypted data processing system and method based on number theory transformation. By performing two-dimensional matching and direct invocation of pre-configured number theory transformation parameter sets based on the effective coefficient length and target modulus, it solves the problems of repeated configuration of transformation parameters and processing procedures and poor adaptability in encrypted data processing under different data lengths and moduli.
[0005] To achieve the above objectives, the present invention provides the following technical solution: a fast method for processing encrypted data based on number theory transformations, applied to encrypted computation scenarios based on polynomial cryptography mechanisms, which performs modular polynomial multiplication on first and second encrypted data. The method includes: S1. Obtain the first encrypted data and the second encrypted data, and determine the effective coefficient length and target modulus based on the encryption polynomial coefficients in the first encrypted data and the second encrypted data; S2. Based on the effective coefficient length and the target modulus, perform two-dimensional matching in a pre-established number theory transformation parameter group library to obtain the target transformation parameter group; wherein, the number theory transformation parameter group library includes multiple pre-configured transformation parameter groups corresponding to different effective coefficient length ranges and different target modulus ranges respectively, and the target transformation parameter group includes the number theory transformation length and the number theory transformation parameters corresponding to the auxiliary modulus; S3. Call the target transformation parameter group to perform data length adaptation processing on the first encrypted data and the second encrypted data, and perform forward number theory transformation and point-by-point modular multiplication in the corresponding auxiliary modular domain to obtain product transformation data; S4. Call the target transformation parameter group to perform inverse number theory transformation, cross-modal reconstruction and target modulus reduction on the product transformation data to obtain the modular polynomial multiplication processing results of the first encrypted data and the second encrypted data.
[0006] The present invention is further configured such that determining the effective coefficient length includes: determining the coefficient positions corresponding to the highest-order non-zero encryption polynomial coefficients in the first encrypted data and the second encrypted data respectively; and determining the effective coefficient length based on the larger of the two coefficient positions.
[0007] The present invention is further configured such that the number theory transformation parameter group library includes multiple parameter index items, each parameter index item including an effective coefficient length interval, a target modulus interval, and a pre-configured transformation parameter group; the two-dimensional matching includes: determining the target effective coefficient length interval where the effective coefficient length is located and the target modulus interval where the target modulus is located, and reading the pre-configured transformation parameter group corresponding to the target effective coefficient length interval and the target modulus interval as the target transformation parameter group.
[0008] The present invention is further configured such that the target transformation parameter set includes a block length, an auxiliary modulus set, an inverse number theory transformation parameter, a cross-modulus reconstruction parameter, and a block merging parameter. The auxiliary modulus set includes at least two pairwise coprime auxiliary moduli. Each of the auxiliary moduli has a primitive root of unity in the finite field corresponding to the number theory transformation length, and the product of the auxiliary moduli satisfies the encryption polynomial coefficient reconstruction requirement.
[0009] The present invention is further configured such that the data length adaptation process includes: dividing the encryption polynomial coefficients in the first encrypted data and the second encrypted data into continuous blocks according to the block length; filling each data block with zero values on the higher-order coefficient side so that the coefficient length of each data block reaches the number theory transformation length; and recording the starting coefficient sequence number of each data block as a block position identifier.
[0010] The present invention is further configured such that the forward number theory transformation and point-by-point modular multiplication include: for each auxiliary modulus in the auxiliary modulus set, transforming each padded data block to the corresponding auxiliary modulus domain, and calling the corresponding forward number theory transformation parameters to perform a forward number theory transformation; combining each data block of the first encrypted data with each data block of the second encrypted data, performing point-by-point modular multiplication on the corresponding forward number theory transformation result to obtain product transformation data; and determining the product position identifier of the product transformation data according to the block position identifier of the data blocks participating in the combination.
[0011] The present invention is further configured such that the inverse number theory transformation, cross-modal reconstruction, and target modulus reduction include: for each of the auxiliary moduli, calling the corresponding inverse number theory transformation parameters to perform an inverse number theory transformation on the product transformation data; for inverse transformation results with the same product position identifier and the same coefficient index, performing cross-modal reconstruction using the cross-modal reconstruction parameters; performing target modulus reduction on the reconstruction results, and performing position superposition according to the product position identifier to obtain the modular polynomial multiplication processing result.
[0012] A fast encrypted data processing system based on number theory transformations, applied to encrypted computation scenarios based on polynomial cryptography mechanisms, performs modular polynomial multiplication processing on first and second encrypted data. The system includes: The data acquisition module is used to acquire the first encrypted data and the second encrypted data, and determine the effective coefficient length and the target modulus based on the encryption polynomial coefficients in the first encrypted data and the second encrypted data; The parameter matching module is used to perform two-dimensional matching in a pre-established number theory transformation parameter group library according to the effective coefficient length and the target modulus to obtain the target transformation parameter group; wherein, the number theory transformation parameter group library includes multiple pre-configured transformation parameter groups corresponding to different effective coefficient length ranges and different target modulus ranges respectively, and the target transformation parameter group includes the number theory transformation length and the number theory transformation parameters corresponding to the auxiliary modulus; The forward transformation processing module is used to call the target transformation parameter group, perform data length adaptation processing on the first encrypted data and the second encrypted data, and perform forward number theory transformation and pointwise modular multiplication in the corresponding auxiliary modular domain to obtain product transformation data. The result reconstruction module is used to call the target transformation parameter group to perform inverse number theory transformation, cross-modal reconstruction and target modulus reduction on the product transformation data to obtain the modular polynomial multiplication processing results of the first encrypted data and the second encrypted data.
[0013] This invention provides a fast system and method for processing encrypted data based on number theory transformations. It has the following beneficial effects: This system and method for rapid processing of encrypted data based on number theory transformation directly obtains the target transformation parameter set corresponding to the current encrypted data processing specification by performing a two-dimensional matching in a pre-established number theory transformation parameter set library based on the effective coefficient length and target modulus of the first and second encrypted data. Therefore, when processing encrypted data of different lengths and target moduli, it is unnecessary to redetermine the number theory transformation length, auxiliary modulus, and corresponding number theory transformation parameters for each processing task. This reduces the overhead of parameter configuration and processing flow adjustments, and improves the adaptability of the encrypted data processing process to different data specifications.
[0014] Furthermore, this invention, based on the target transformation parameter set, completes data length adaptation, forward number theory transformation, pointwise modular multiplication, inverse number theory transformation, cross-modal reconstruction, and target modulus reduction. This enables the modular polynomial multiplication process to be completed within an auxiliary modulus domain adapted to the current target modulus, and restores the processing result to the target modulus. The combination of block processing, auxiliary modulus domain operations, and cross-modal reconstruction helps ensure the correctness of modular polynomial multiplication results under different data lengths, while simultaneously improving computational continuity and processing efficiency during large-scale encrypted data processing. Attached Figure Description
[0015] Figure 1 This is a flowchart of the fast encrypted data processing method based on number theory transformation of the present invention; Figure 2 This is a flowchart of the number theory transformation parameter group matching and calling process of the present invention. Detailed Implementation
[0016] 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.
[0017] Example 1: As Figure 1 As shown, this embodiment of the invention provides a fast method for processing encrypted data based on number theory transformations, applied to encrypted computation scenarios based on polynomial cryptography mechanisms. The method involves performing modular polynomial multiplication on first and second encrypted data. The method includes: S1. Obtain the first encrypted data and the second encrypted data, and determine the effective coefficient length and the target modulus based on the encrypted polynomial coefficients in the first encrypted data and the second encrypted data.
[0018] Determining the effective coefficient length includes: determining the coefficient positions corresponding to the highest-order non-zero encryption polynomial coefficients in the first and second encrypted data, respectively; and determining the effective coefficient length based on the larger of the two coefficient positions.
[0019] S2. Based on the effective coefficient length and the target modulus, perform two-dimensional matching in a pre-established number theory transformation parameter group library to obtain the target transformation parameter group; wherein, the number theory transformation parameter group library includes multiple pre-configured transformation parameter groups corresponding to different effective coefficient length ranges and different target modulus ranges respectively, and the target transformation parameter group includes the number theory transformation length and the number theory transformation parameters corresponding to the auxiliary modulus.
[0020] The number theory transformation parameter set library includes multiple parameter index entries. Each parameter index entry includes an effective coefficient length interval, a target modulus interval, and a pre-configured transformation parameter set. Two-dimensional matching includes: determining the target effective coefficient length interval where the effective coefficient length is located and the target modulus interval where the target modulus is located, and reading the pre-configured transformation parameter set corresponding to the target effective coefficient length interval and the target modulus interval as the target transformation parameter set.
[0021] In this embodiment, the number theory transformation parameter set library is pre-established before performing encrypted data processing; for different effective coefficient length ranges and target modulus ranges, corresponding number theory transformation lengths, auxiliary moduli, and number theory transformation parameters are pre-configured to form a pre-configured transformation parameter set. When no corresponding pre-configured transformation parameter set is matched, the current modular polynomial multiplication processing is stopped.
[0022] The target transformation parameter set also includes block length, auxiliary module set, inverse number theory transformation parameters, cross-module reconstruction parameters, and block merging parameters. The auxiliary module set includes at least two pairwise coprime auxiliary modules, and each auxiliary module has a primitive root of unity in its corresponding finite field, which is used to accommodate the convolution result after polynomial multiplication of the corresponding data block. The product of each auxiliary module in the auxiliary module set is greater than the range of coefficient values of the corresponding convolution result to ensure the determinism of the cross-module reconstruction result. Furthermore, the product of each auxiliary module satisfies the requirements for encrypted polynomial coefficient reconstruction.
[0023] S3. Call the target transformation parameter group to perform data length adaptation processing on the first and second encrypted data, and perform forward number theory transformation and pointwise modular multiplication in the corresponding auxiliary modular domain to obtain product transformation data.
[0024] The data length adaptation process includes: dividing the encrypted polynomial coefficients in the first and second encrypted data into continuous blocks according to the block length; padding each data block with zero values on the higher-order coefficient side so that the coefficient length of each data block reaches the number theory transformation length; and recording the starting coefficient sequence number of each data block as a block position identifier.
[0025] Forward number theory transformation and point-by-point modular multiplication include: for each auxiliary modulus in the auxiliary modulus set, transforming each padded data block to the corresponding auxiliary modulus domain, and calling the corresponding forward number theory transformation parameters to perform the forward number theory transformation; combining each data block of the first encrypted data with each data block of the second encrypted data, performing point-by-point modular multiplication on the corresponding forward number theory transformation results to obtain the product transformation data; and determining the product position identifier of the product transformation data based on the block position identifier of the data blocks involved in the combination.
[0026] S4. Call the target transformation parameter group to perform inverse number theory transformation, cross-modal reconstruction and target modulus reduction on the product transformation data to obtain the modular polynomial multiplication processing results of the first encrypted data and the second encrypted data.
[0027] The inverse number theory transformation, cross-modal reconstruction, and target modulus reduction include: for each auxiliary modulus, calling the corresponding inverse number theory transformation parameters to perform inverse number theory transformation on the product transformation data; for inverse transformation results with the same product position identifier and the same coefficient index, performing cross-modal reconstruction using cross-modal reconstruction parameters; performing target modulus reduction on the reconstruction results, and performing position superposition according to the product position identifier to obtain the modular polynomial multiplication processing result.
[0028] Specifically, based on the block position identifiers of the first and second data blocks involved in the operation, the target coefficient positions corresponding to each reconstruction result are determined; reconstruction results with the same target coefficient positions are accumulated, and the accumulated results are reduced by the target modulus to obtain the modular polynomial multiplication processing results.
[0029] A fast encrypted data processing system based on number theory transformations is applied to encrypted computation scenarios based on polynomial cryptography mechanisms. It performs modular polynomial multiplication on first and second encrypted data. The system includes: The data acquisition module is used to acquire the first encrypted data and the second encrypted data, and to determine the effective coefficient length and the target modulus based on the encrypted polynomial coefficients in the first encrypted data and the second encrypted data.
[0030] The parameter matching module is used to perform two-dimensional matching in a pre-established number theory transformation parameter group library based on the effective coefficient length and the target modulus to obtain the target transformation parameter group. The number theory transformation parameter group library includes multiple pre-configured transformation parameter groups corresponding to different effective coefficient length ranges and different target modulus ranges, and the target transformation parameter group includes the number theory transformation length and the number theory transformation parameters corresponding to the auxiliary modulus.
[0031] The forward transformation processing module is used to call the target transformation parameter group, perform data length adaptation processing on the first and second encrypted data, and perform forward number theory transformation and pointwise modular multiplication in the corresponding auxiliary modular domain to obtain product transformation data.
[0032] The result reconstruction module is used to call the target transformation parameter group to perform inverse number theory transformation, cross-modal reconstruction and target modulus reduction on the product transformation data, and obtain the modular polynomial multiplication processing results of the first encrypted data and the second encrypted data.
[0033] Example 2: Figure 2 As shown, this embodiment uses the modular polynomial multiplication of the first encrypted data and the second encrypted data as an example for explanation. After obtaining the first encrypted data and the second encrypted data, the coefficient positions corresponding to the highest-order non-zero encrypted polynomial coefficients of the two are determined respectively, and the effective coefficient length is determined according to the larger of the two coefficient positions; at the same time, the target modulus corresponding to the current polynomial cryptography mechanism is obtained.
[0034] Specifically, the effective coefficient length is determined to be 920, and the target modulus is determined to be 12289. Based on the effective coefficient length of 920, it is determined to be within the preset effective coefficient length range of 513 to 1024, and based on the target modulus of 12289, it is determined to be within the preset target modulus range of 8192 to 16384. Therefore, the pre-configured transformation parameter set corresponding to the effective coefficient length range and the target modulus range is read from the number theory transformation parameter set library.
[0035] The pre-configured transformation parameter set includes number-theoretical transformation length, block length, auxiliary module set, and forward number-theoretical transformation parameters, inverse number-theoretical transformation parameters, and cross-module reconstruction parameters corresponding to each auxiliary module. After calling this pre-configured transformation parameter set, the first and second encrypted data are block-wise and length-filled. Forward number-theoretical transformation, pointwise modular multiplication, inverse number-theoretical transformation, and cross-module reconstruction are performed within each auxiliary module domain. Finally, target module reduction and block result merging are performed to obtain the modular polynomial multiplication processing result.
[0036] In this embodiment, when the effective coefficient length and target modulus change, it is only necessary to redetermine the corresponding effective coefficient length range and target modulus range, and then match and call the corresponding pre-configured transformation parameter group from the number theory transformation parameter group library, without having to reconfigure the number theory transformation processing parameters.
[0037] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art 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 appended claims and their equivalents.
Claims
1. A fast method for processing encrypted data based on number theory transformations, characterized in that, Applied to cryptographic computation scenarios based on polynomial cryptography, the method involves performing modular polynomial multiplication on first and second encrypted data. The method includes: S1. Obtain the first encrypted data and the second encrypted data, and determine the effective coefficient length and target modulus based on the encryption polynomial coefficients in the first encrypted data and the second encrypted data; S2. Based on the effective coefficient length and the target modulus, perform two-dimensional matching in a pre-established number theory transformation parameter group library to obtain the target transformation parameter group; wherein, the number theory transformation parameter group library includes multiple pre-configured transformation parameter groups corresponding to different effective coefficient length ranges and different target modulus ranges respectively, and the target transformation parameter group includes the number theory transformation length and the number theory transformation parameters corresponding to the auxiliary modulus; S3. Call the target transformation parameter group to perform data length adaptation processing on the first encrypted data and the second encrypted data, and perform forward number theory transformation and point-by-point modular multiplication in the corresponding auxiliary modular domain to obtain product transformation data; S4. Call the target transformation parameter group to perform inverse number theory transformation, cross-modal reconstruction and target modulus reduction on the product transformation data to obtain the modular polynomial multiplication processing results of the first encrypted data and the second encrypted data.
2. The method for fast processing of encrypted data based on number theory transformation according to claim 1, characterized in that: The determination of the effective coefficient length includes: determining the coefficient positions corresponding to the highest-order non-zero encryption polynomial coefficients in the first encrypted data and the second encrypted data, respectively; and determining the effective coefficient length based on the larger of the two coefficient positions.
3. The method for fast processing of encrypted data based on number theory transformation according to claim 1, characterized in that: The number theory transformation parameter group library includes multiple parameter index items, each of which includes an effective coefficient length interval, a target modulus interval, and a pre-configured transformation parameter group; the two-dimensional matching includes: determining the target effective coefficient length interval where the effective coefficient length is located and the target modulus interval where the target modulus is located, and reading the pre-configured transformation parameter group corresponding to the target effective coefficient length interval and the target modulus interval as the target transformation parameter group.
4. The method for fast processing of encrypted data based on number theory transformation according to claim 1, characterized in that: The target transformation parameter set further includes block length, auxiliary modulus set, inverse number theory transformation parameters, cross-modulus reconstruction parameters, and block merging parameters. The auxiliary modulus set includes at least two pairwise coprime auxiliary moduli. Each auxiliary modulus has a primitive root of unity in the finite field corresponding to the number theory transformation length, and the product of each auxiliary modulus satisfies the encryption polynomial coefficient reconstruction requirements.
5. The method for fast processing of encrypted data based on number theory transformation according to claim 4, characterized in that: The data length adaptation process includes: dividing the encrypted polynomial coefficients in the first encrypted data and the second encrypted data into continuous blocks according to the block length; filling each data block with zero values on the higher-order coefficient side so that the coefficient length of each data block reaches the number theory transformation length; and recording the starting coefficient sequence number of each data block as a block position identifier.
6. The method for fast processing of encrypted data based on number theory transformation according to claim 5, characterized in that: The forward number theory transformation and point-by-point modular multiplication include: for each auxiliary modulus in the auxiliary modulus set, transforming each filled data block to the corresponding auxiliary modulus domain, and calling the corresponding forward number theory transformation parameters to perform a forward number theory transformation; combining each data block of the first encrypted data with each data block of the second encrypted data, performing point-by-point modular multiplication on the corresponding forward number theory transformation results to obtain product transformation data; and determining the product position identifier of the product transformation data according to the block position identifier of the data blocks participating in the combination.
7. The method for fast processing of encrypted data based on number theory transformation according to claim 6, characterized in that: The inverse number theory transformation, cross-modal reconstruction, and target modulus reduction include: for each of the auxiliary moduli, calling the corresponding inverse number theory transformation parameters to perform an inverse number theory transformation on the product transformation data; for inverse transformation results with the same product position identifier and the same coefficient index, performing cross-modal reconstruction using the cross-modal reconstruction parameters; performing target modulus reduction on the reconstruction results, and performing position superposition according to the product position identifier to obtain the modular polynomial multiplication processing result.
8. A fast encrypted data processing system based on number theory transformations, characterized in that, A system for performing modular multinomial multiplication on first and second encrypted data, applicable to cryptographic computation scenarios based on multinomial cryptography, comprises: The data acquisition module is used to acquire the first encrypted data and the second encrypted data, and determine the effective coefficient length and the target modulus based on the encryption polynomial coefficients in the first encrypted data and the second encrypted data. The parameter matching module is used to perform two-dimensional matching in a pre-established number theory transformation parameter group library according to the effective coefficient length and the target modulus to obtain the target transformation parameter group; wherein, the number theory transformation parameter group library includes multiple pre-configured transformation parameter groups corresponding to different effective coefficient length ranges and different target modulus ranges respectively, and the target transformation parameter group includes the number theory transformation length and the number theory transformation parameters corresponding to the auxiliary modulus; The forward transformation processing module is used to call the target transformation parameter group, perform data length adaptation processing on the first encrypted data and the second encrypted data, and perform forward number theory transformation and point-by-point modular multiplication in the corresponding auxiliary modular domain to obtain product transformation data. The result reconstruction module is used to call the target transformation parameter group to perform inverse number theory transformation, cross-modal reconstruction and target modulus reduction on the product transformation data to obtain the modular polynomial multiplication processing results of the first encrypted data and the second encrypted data.