Discrete space global optimization method based on neighborhood mapping and multi-path parallel search

Abstract

This invention discloses a discrete space global optimization method based on neighborhood mapping and multi-path parallel search. The method includes: obtaining the discrete state variables to be optimized as the initial search starting point; applying neighborhood mapping rules to generate an initial candidate set and performing structural pre-screening; constructing a multi-path parallel computing architecture, using effective candidate states as local initial starting points for each independent search path, and distributing them to multiple independent computing threads; performing deep iterative search on each search path, with each round of iterative search filtering based on an evaluation index system including a first evaluation index for macroscopic evaluation and a second evaluation index for microscopic difference differentiation; periodically synchronizing the local optimal solutions output by all parallel search paths, and filtering to obtain the global optimal solution. This invention solves the search stagnation problem when constructing high-performance cryptographic components and can efficiently and stably generate high-security cryptographic components that balance high nonlinearity and low differential uniformity.

Description

Technical Field

[0001] This invention relates to the field of information security technology, and in particular to a discrete space global optimization method and system based on neighborhood mapping and multi-path parallel search. Background Technology

[0002] In the field of information security, nonlinear combinatorial optimization problems in discrete state spaces have always been a core research topic of great interest. These problems share common characteristics: a vast solution space, extremely complex topological structures of the objective functions, and typically significant nonconvexity. The security architecture of modern block cipher algorithms follows Shannon's principles of "confusion" and "diffusion." The S-box, as a core nonlinear cryptographic component in the algorithm, undertakes the crucial task of achieving the "confusion" property. The various cryptographic indices of the S-box directly determine the lower bound of the entire encryption system's resistance to various analytical attacks. Therefore, how to construct cryptographic components whose performance indices approach theoretical limits while maintaining a strict algebraic structure has become a hot topic and a challenge in global cryptographic research.

[0003] Despite the emergence of various S-box construction schemes, effective solutions are still lacking when facing the local optimum escape problem under complex constraints. For example, Chinese invention patent CN111464288A, entitled "A Method and System for Generating S-Boxes," discloses a technical solution for generating and filtering S-boxes by defining pointer functions and iterative loops. This scheme essentially relies on serial iterative updates along a single path; when the search path enters a local extremum region, the algorithm often fails to discover potentially better solutions in the neighborhood. Another example is Chinese invention patent CN119696758A, entitled "An 8-bit S-box Construction Method Based on an Improved Genetic Algorithm," which proposes an 8-bit S-box construction method based on an improved genetic algorithm. This method combines a complex chaotic system to initialize the population and optimizes the cryptographic performance of the S-boxes through a multi-objective fitness function with nonlinearity, differential uniformity, and a strict avalanche criterion. However, this method still faces the problem of dependence on the quality of the initial population and the tendency of the genetic algorithm to get trapped in local optima.

[0004] Therefore, it is necessary to propose a discrete space global optimization method and system based on neighborhood mapping and multi-path parallel search, which can solve the problems of getting trapped in local optima, low search efficiency and coarse evaluation index granularity in traditional search strategies when dealing with high-dimensional strongly constrained discrete spaces, and achieve effective crossing of local optimal solutions and acquisition of global optimal results. Summary of the Invention

[0005] In view of this, the present invention provides a discrete space global optimization method based on neighborhood mapping and multi-path parallel search, which solves the technical problem that traditional single-path iterative or random search strategies suffer from premature convergence or search stagnation when facing discrete solution spaces with complex topological structures, non-convex structures and dense distribution of extreme points, due to the lack of global vision, computational redundancy and coarse evaluation index granularity.

[0006] In a first aspect, the present invention provides a discrete space global optimization method based on neighborhood mapping and multi-path parallel search, comprising:

[0007] Obtain the discrete state variables to be optimized as the initial search starting point;

[0008] The initial candidate set, which includes multiple candidate states, is generated by applying neighborhood mapping rules to the initial search starting point, and structural pre-screening is performed on the elements in the set to obtain valid candidate states.

[0009] A multi-path parallel computing architecture is constructed, in which the effective candidate states are used as the local initial starting points of each independent search path and distributed to multiple independent computing threads respectively.

[0010] Parallel deep iterative search is performed on each search path. In each round of iterative search, the state is filtered according to the preset evaluation index system to obtain the local optimal solution of each path. The evaluation index system includes a first evaluation index for macro-evaluation and a second evaluation index for distinguishing micro-differences.

[0011] The local optimal solutions output by all parallel search paths are periodically synchronized, and the global optimal solution is obtained by filtering the local optimal solutions. If the preset termination condition is met, the global optimal solution is output. If the preset termination condition is not met, the global optimal solution is used as a new initial search starting point, the neighborhood is reconstructed, and the next round of iteration is started.

[0012] Furthermore, the neighborhood mapping rules include arbitrary perturbation models and local perturbation models;

[0013] The arbitrary perturbation model includes: performing random or global modifications on the current discrete state variable without local constraints; the local perturbation model includes: performing local element transformations on the current discrete state variable within a preset step size.

[0014] Furthermore, the pre-screening of the structure is achieved through a low-cost verification mechanism, including: using fixed-point threshold verification and algebraic feature lower bound verification to screen each candidate state, and removing candidate states that fail any verification.

[0015] The fixed point threshold verification includes: counting the number of fixed points for each candidate state; when the number of fixed points is greater than the preset number of points, the verification is deemed to have failed.

[0016] The algebraic feature lower bound verification includes: judging the algebraic degree of the candidate state or its lower bound estimate; if the algebraic degree or its lower bound estimate is less than a preset threshold, the verification is deemed to fail.

[0017] Furthermore, the method involves performing a deep iterative search in parallel on each search path. Each round of iterative search is conducted according to a preset evaluation index system, including:

[0018] Candidate sub-states are generated one by one according to the neighborhood mapping rule based on the current state, and the structure pre-screening is performed on each candidate sub-state, discarding the candidate sub-states that fail the screening.

[0019] The first evaluation index of the candidate sub-states that have passed the screening is calculated using an attribute algorithm;

[0020] If the first evaluation index of the candidate sub-state is different from that of the current state, the traversal will be restarted starting from the state corresponding to the better first evaluation index.

[0021] If the candidate substate is exactly the same as the first evaluation index of the current state, then the second evaluation index is calculated for fine-grained arbitration.

[0022] If the second evaluation index value of the candidate sub-state is better, then the traversal is restarted starting from the candidate sub-state.

[0023] Furthermore, the first evaluation indicator includes:

[0024] The nonlinearity is obtained by calculating the extended Walsh spectrum using FWHT, and the differential uniformity is obtained by constructing a full differential distribution table and taking its maximum value.

[0025] Furthermore, the attribute algorithm includes:

[0026] When candidate substates are generated by arbitrary perturbation models, full attribute statistics are performed on the candidate substates to obtain the first evaluation index of the candidate substates.

[0027] When candidate sub-states are generated by a local perturbation model, an incremental update method based on perturbation difference is used to perform differential correction on the statistical cache of the parent state to obtain the evaluation index of the candidate sub-state.

[0028] Furthermore, the second evaluation metric includes: a cost function based on the extended Walsh spectrum and a cost function based on the difference distribution table.

[0029] Furthermore, the preset termination condition includes at least one of the following conditions:

[0030] The first evaluation index of the global optimal solution reaches the preset security strength threshold.

[0031] The global optimal solution remains unchanged within a preset number of consecutive synchronization cycles, or the improvement is continuously lower than a preset change threshold.

[0032] The total number of iterations or the cumulative search time of each parallel path reaches the preset running limit.

[0033] Secondly, the present invention provides a discrete space global optimization system based on neighborhood mapping and multi-path parallel search, comprising:

[0034] The state initialization module is used to obtain the discrete state variables to be optimized as the initial search starting point;

[0035] The neighborhood mapping and filtering module is used to apply neighborhood mapping rules to the initial search starting point to generate an initial candidate set including multiple candidate sub-states, and to perform structural pre-filtering on the elements in the set;

[0036] The parallel distribution module is used to build a multi-path parallel computing architecture. It takes the effective candidate sub-states that have been pre-screened by the structure as the local initial starting point of each independent search path and distributes them to multiple independent computing threads.

[0037] The parallel deep search module is used to perform parallel deep iterative search on each search path. Each round of iterative search is performed according to a preset evaluation index system. The evaluation index system includes a first evaluation index for macro-level evaluation and a second evaluation index for distinguishing micro-level differences.

[0038] The global optimization module is used to periodically synchronize the local optimal solutions output by all parallel search paths, filter the local optimal solutions to obtain the global optimal solution; if the preset termination condition is met, the global optimal solution is output; if the preset termination condition is not met, the global optimal solution is used as a new initial search starting point, the neighborhood is reconstructed and the next round of iteration is started.

[0039] Furthermore, the parallel deep search module includes: a candidate generation and pre-screening unit, a property calculation unit, and a dual-index arbitration unit;

[0040] The candidate generation and pre-screening unit is used to generate the next-level candidate sub-state by applying the neighborhood mapping rule, and to eliminate inferior candidates by using a low-cost verification mechanism, thereby reducing invalid computation.

[0041] The property calculation unit is used to calculate the first evaluation index of the candidate sub-state through a full calculation mode or an incremental update mode applicable to local perturbations.

[0042] The dual-index arbitration unit is used to execute a hierarchical screening strategy; when the first evaluation index is the same, the second evaluation index is activated as a difference amplifier to identify and retain potential high-quality solutions with microstructural advantages and perform state updates.

[0043] Compared with existing technologies, the discrete space global optimization method and system based on neighborhood mapping and multi-path parallel search proposed in this invention have the following advantages:

[0044] First, a generalized global search architecture based on "parallel distribution-deep iteration" is proposed, significantly improving the algorithm's global optimization capability. This invention overcomes the limitation of traditional single-path search being prone to getting trapped in local optima by constructing a multi-source concurrent search architecture using a parallel distribution module. The system defines each element in the candidate set as an independent starting point that does not interfere with each other, and instantiates and concurrently executes its own deep iterative search task in multiple computing threads. This mechanism enables the algorithm to independently explore and evolve multiple different topological regions of the solution space within the same time slice, greatly increasing the probability of discovering a globally better solution.

[0045] Secondly, the invention achieves extremely high search efficiency through a dual mechanism of "structure pre-screening" and "flexible computational architecture." In the candidate generation stage, a structure pre-screening mechanism is introduced, eliminating invalid or low-potential candidates at the generation end, effectively avoiding the waste of subsequent high-cost computational resources. Simultaneously, the system's property calculation unit adopts a flexible architecture combining full-scale computation and incremental update modes, ensuring applicability to any S-box structure while increasing the speed of a single iteration by an order of magnitude under specific perturbations, significantly improving the overall throughput of the algorithm.

[0046] Third, a second evaluation index based on fine-grained distribution characteristics is introduced, which effectively solves the search stagnation problem and breaks through the upper limit of optimization results. Addressing the step effect caused by excessively coarse granularity of macroscopic indicators such as nonlinearity in existing technologies, the second evaluation index enhances the discrimination capability.

[0047] Fourth, the system of this invention has extremely high versatility and scalability, making it suitable for constructing various high-security cryptographic components. The search architecture does not depend on a specific underlying algebraic structure. By configuring different neighborhood mapping rules, this system is applicable to both general S-box optimization and efficient handling of complex component designs with strict algebraic constraints. Furthermore, the generated S-boxes can effectively resist differential and linear analysis attacks, making it particularly suitable for constructing quantum-resistant cryptographic algorithm components with extremely high security requirements. Attached Figure Description

[0048] Figure 1 This is a flowchart illustrating the discrete space global optimization method based on neighborhood mapping and multi-path parallel search provided by the present invention.

[0049] Figure 2 This is a schematic diagram of the algorithm execution flow provided by the present invention;

[0050] Figure 3 A schematic diagram of the discrete space global optimization system based on neighborhood mapping and multi-path parallel search provided by the present invention;

[0051] Figure 4 A schematic diagram of the working logic of the system provided by the present invention. Detailed Implementation

[0052] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0053] Example 1

[0054] Please see Figure 1 This embodiment provides a discrete space global optimization method based on neighborhood mapping and multi-path parallel search, including:

[0055] Step S101: Obtain the discrete state variables to be optimized as the initial search starting point;

[0056] Step S102: Apply neighborhood mapping rules to the initial search starting point to generate an initial candidate set including multiple candidate states, and perform structural pre-screening on the elements in the set to obtain effective candidate states;

[0057] Step S103: Construct a multi-path parallel computing architecture, using the effective candidate states as the local initial starting points of each independent search path, and distribute them to multiple independent computing threads respectively;

[0058] Step S104: Perform parallel deep iterative search on each search path. Each round of iterative search performs state filtering according to a preset evaluation index system. The evaluation index system includes a first evaluation index for macro-level evaluation and a second evaluation index for distinguishing micro-level differences.

[0059] Step S105: Periodically synchronize the local optimal solutions output by all parallel search paths, and filter the local optimal solutions to obtain the global optimal solution; if the termination condition is not met, use the global optimal solution as the new initial search starting point, reconstruct the neighborhood and start the next round of iteration.

[0060] The method in this embodiment first obtains the discrete state variables to be optimized as the initial search starting point. An effective candidate state set is constructed through neighborhood mapping rules and a structure pre-screening mechanism, and then distributed to independent computing threads in a multi-path parallel computing architecture. During the deep iterative search of each path, a dual evaluation system, including a macroscopic evaluation first indicator and a microscopic difference differentiation second indicator, is used to screen states and obtain local optimal solutions. By periodically synchronizing the results of each path, the global optimal solution is selected, and the initial search starting point and reconstructed neighborhood are dynamically updated based on the performance of this solution, achieving iterative iteration until the termination condition is met. This method, through multi-path collaborative detection, hierarchical screening, and global feedback reset, effectively solves the problems of easily getting trapped in local optima, search stagnation, and slow convergence speed in large-scale discrete spaces, improving the construction efficiency and optimization accuracy of the S-box.

[0061] The following is combined Figure 2 The process of implementing global optimization of the S-box in this embodiment will be explained.

[0062] In step S101, the discrete state variables to be optimized are first initialized, where the discrete state variables are cryptographic S-boxes. The state initialization process specifically includes:

[0063] 1) Defining the solution space: In this embodiment, the discrete state variables to be optimized are defined as a finite field. An 8-bit bijective S-box (i.e., a permutation containing 256 elements from 0 to 255).

[0064] 2) Generate initial seed: Construct the initial S-box using a pseudo-random generation algorithm or a simple algebraic construction method. We will use this as the starting point for our initial search.

[0065] While initializing the variables, a preset evaluation index system is also set. The evaluation index system in this embodiment includes a first evaluation index for macro-level assessment and a second evaluation index for distinguishing micro-level differences.

[0066] The first evaluation metric is set as nonlinearity. Sum of differences uniformity As the primary screening criterion, it is used to evaluate the basic cryptographic strength of the S-box and is obtained through an attribute calculation algorithm;

[0067] Among them, nonlinearity The differential uniformity is obtained by calculating the extended Walsh spectrum using the Fast Walsh-Hadamard Transform (FWHT). It is obtained by constructing a total difference distribution table (DDT) and taking its maximum value.

[0068] Furthermore, the attribute calculation algorithm for the first evaluation indicator supports two calculation modes:

[0069] (1) Full calculation mode: When the candidate substate is generated by an arbitrary perturbation model, the extended Walsh spectrum is calculated by fast Walsh-Hadamard transform (FWHT), and the difference distribution table (DDT) is constructed by full difference statistics, so as to calculate NL and U respectively;

[0070] (2) Incremental Update Mode: When the candidate substate is generated by the local perturbation model and satisfies the preset perturbation structure, an incremental update method based on perturbation difference is adopted to perform differential correction on the relevant count terms of the extended Walsh spectrum and the difference distribution table (DDT) to accelerate the acquisition of the extended Walsh spectrum and the difference distribution table and their derived NL and U. For example, when the candidate substate is generated by a single exchange perturbation, the above differential correction can be achieved by using an incremental update method that matches the single exchange perturbation.

[0071] The second evaluation index is set as a cost function based on the spectral distribution characteristics, which is used to make fine-grained judgments on candidate solutions when the first evaluation index cannot distinguish the merits of candidate solutions.

[0072] To facilitate arbitration, the second evaluation metric includes the following two types of cost functions:

[0073] (1) Cost function based on extended Walsh spectrum :set up To expand the numerical values ​​in the Walsh spectrum equal to The number of elements, let the maximum value in the spectrum be . The cost function is defined as:

[0074]

[0075] in, This represents the floor function; This represents a histogram statistical function used to count the frequency of each specific value in the global Walsh spectrum. Represents the extended Walsh spectrum set of the S-box; This indicates the search depth control parameter; Indicates the loop index for summation; coefficient The introduction of this parameter is to reduce the influence of smaller spectral values, so that the frequency of the maximum spectral value is relative to the frequency of the maximum spectral value. It contributes the most to the total value.

[0076] The smaller the value, the fewer the number of maxima in the spectrum, and the greater the optimization potential.

[0077] (2) Cost function based on Differential Distribution Table (DDT): .set up For the value in DDT equal to The number of elements, let the maximum value in DDT be . The cost function is then defined as:

[0078]

[0079] in, Represents the set of all elements in the difference distribution table (DDT) of the S-box; This represents the weighting coefficient.

[0080] A steeper weighting coefficient is used here. This is to more forcefully punish the high-frequency differential terms in DDT. The smaller the value, the less frequent the maximum value is in the difference table, and the higher the probability that this state will reduce the uniformity of the difference in subsequent iterations.

[0081] By statistically analyzing the frequency of different values ​​in the extended Walsh spectrum or difference distribution table (DDT), and assigning greater penalty weights to the categories that are close to the maximum value, the impact of "maximum frequency" on the subsequent optimization potential can be characterized.

[0082] The evaluation index system preset in this embodiment adopts dual index arbitration and updates the state according to the hierarchical arbitration rules. Specifically, the first evaluation index is used for screening first; when the first evaluation index is the same, the second evaluation index is activated to conduct a refined evaluation of the candidate sub-states. This index is used to amplify the differences in microstructure between the candidate sub-states and the current state, thereby selecting the solution with higher evolutionary potential for updating.

[0083] In step S102, the single initial S-box is... Expanding to a candidate set and performing structural pre-screening, valid candidate states are distributed to independent threads to build a parallel task array, specifically including the following details:

[0084] 1) Neighborhood mapping: The initial S-box is expanded by applying configurable neighborhood mapping rules to generate an initial candidate set. The neighborhood mapping rules can be configured as arbitrary perturbation models or local perturbation models.

[0085] The arbitrary perturbation model is to perform random or global modifications on the current discrete state variable without local restrictions; the local perturbation model is to perform local element transformations on the current discrete state variable within a preset step size.

[0086] This embodiment takes the local perturbation model as an example and adopts a one-time exchange rule, that is: exchange any two positions in the S-box output permutation to generate candidate states.

[0087] 2) Structure pre-screening: Perform structure pre-screening on each candidate S-box in the set. The structure pre-screening is implemented through a low-cost verification mechanism, which includes: fixed-point threshold verification and algebraic feature lower bound verification.

[0088] Fixed-point threshold verification includes: counting the number of candidate fixed points. ,when Timely elimination, optimal selection .

[0089] Here is an explanation of the definition of a fixed point: for an s-box function If a certain input value exists , making ,So That is, it is a fixed point.

[0090] During the encryption process, if a large amount of data remains unchanged (i.e., input = output), the structural characteristics of the plaintext will be exposed, reducing the algorithm's ability to resist linear attacks or specific algebraic attacks. Therefore, this method forms a fast circuit breaker mechanism through simple traversal comparison to eliminate solutions that do not meet security standards in advance.

[0091] The algebraic feature lower bound check includes: judging the algebraic degree of the candidate state or its lower bound estimate; if the algebraic degree or its lower bound estimate is less than a preset threshold, the check is deemed to have failed.

[0092] Specifically, if we consider the S-box as a Boolean algebraic polynomial, the algebraic degree is the highest degree of the terms in the polynomial. If the algebraic degree is too low (e.g., only degree 1 or 2), then the nonlinear relationship of the S-box is very weak, and an attacker can establish a simple system of equations to derive the key. For the 8-bit S-box in this embodiment ( The maximum theoretical value of its algebraic degree is In this embodiment, a preset threshold is used. The contemporary number of times or its lower bound estimate is less than the threshold. Remove them when necessary.

[0093] 3) Task distribution: Define the selected valid candidate S-boxes as independent search starting points and distribute them to multiple parallel computing threads in the system to start multi-path search.

[0094] In step S103, parallel deep iterative search is performed on each search path, and each round of iterative search is state-filtered according to a preset evaluation index system.

[0095] Specifically, each parallel path uses its assigned starting point as its current state. The following three sub-steps are executed independently in a loop, and their specific implementation can be broken down into the following details:

[0096] Dynamic generation and structure pre-screening: based on the current state Candidate states are generated one by one according to the neighborhood mapping rule. For each candidate, perform the same structural pre-screening as in step S102. Candidates that fail the screening are discarded, while those that pass the screening are retained. .

[0097] Evaluation index calculation: for candidates that pass the screening Calculate its first evaluation index The perturbation type is determined according to the neighborhood mapping rule, and a full calculation mode or incremental update mode is selected accordingly: when the candidate does not meet the preset local perturbation structure or the cache is not enabled, the full calculation mode is adopted; when the neighborhood mapping rule is a local perturbation model, such as the candidate sub-state used in this example, it is generated by a single exchange perturbation (i.e., Furthermore, when the system maintains the spectral statistics cache of the parent state, it enables the incremental update method based on the perturbation difference to correct the statistics in order to accelerate the acquisition of the corresponding indicators.

[0098] Dual-indicator arbitration:

[0099] First indicator for initial screening: If the sub-state The nonlinearity or difference uniformity is better than the current state. (Right now or If so, it is directly determined to be better, and a state update is performed. And restart the traversal from the new state.

[0100] Difference Amplification and Arbitration: If the first index of the sub-state is exactly the same as the current state (i.e. and Then, the second evaluation index is calculated for fine-grained arbitration, letting... .

[0101] Decision logic: If the second index value of the sub-state is better, that is, if any of the following conditions are met: (b) Then determine the substate. It has higher evolutionary potential, performing state updates and restarting the traversal. This mechanism ensures that the algorithm can continuously explore the potential of the solution space and escape local optima.

[0102] Therefore, step S103 outputs the local optimal results of each thread and uses them as input for step S104.

[0103] In step S104, global optimization and feedback iteration are performed, and the specific implementation can be divided into the following details:

[0104] 1) Results aggregation: Collect the locally optimal S-boxes of all parallel path outputs.

[0105] 2) Comprehensive selection: The collected S-boxes are sorted according to the evaluation index system, and the one with the best comprehensive performance is selected as the global optimal solution for this round.

[0106] 3) Termination Judgment and Feedback:

[0107] Case A (Objective Satisfies): If the global optimal solution has satisfied the preset extreme performance index (e.g., when the first evaluation index of the global optimal solution satisfies the preset safety threshold), then output the solution and end the algorithm.

[0108] Case B (Continued Optimization): If the requirements are not met and the system has not reached the preset maximum number of global iterations, the global optimal solution is used as the new initial seed, and the feedback jumps to step S102. The system will reconstruct and distribute the neighborhood around this solution, initiating the next round of parallel search on a larger scale. For example, if the evaluation metrics of the global optimal solution (including the cost function values ​​of the first and second metrics) do not improve in a preset number of consecutive global iterations (e.g., 100 iterations), it indicates that the current neighborhood mapping and search logic can no longer find a better solution in the current region. In this case, the optimal solution is used as the new initial seed to initiate the next round of parallel search on a larger scale.

[0109] Case C (Forced Termination): If the maximum number of iterations has been reached or the total search time has reached the preset time and the conditions are not met, the search is forcibly terminated, and the currently found historical best solution is output to prevent the algorithm from getting stuck in an infinite loop.

[0110] If the objective is not met and the threshold is not reached, the result is used as a new initial seed and fed back to step S102 to reconstruct the neighborhood and start the next round of iteration.

[0111] The method in this embodiment performs a deep iterative search involving "candidate generation, property calculation, and dual index arbitration" through multi-threaded concurrent execution. It introduces a second evaluation index based on fine-grained distribution characteristics, which solves the problem of search stagnation caused by the coarse granularity of traditional indexes when constructing high-performance cryptographic components (S-boxes). Combined with a candidate set pre-screening mechanism and a general / incremental calculation strategy, it can efficiently and stably generate high-security cryptographic components that balance high nonlinearity and low differential uniformity.

[0112] Example 2

[0113] like Figure 3 As shown, this embodiment of the invention also provides a discrete space global optimization system 300 based on neighborhood mapping and multi-path parallel search, comprising:

[0114] The state initialization module 301 is used to obtain the discrete state variables to be optimized as the initial search starting point;

[0115] The neighborhood mapping and filtering module 302 is used to apply neighborhood mapping rules to the initial search starting point to generate an initial candidate set including multiple candidate sub-states, and to perform structural pre-filtering on the elements in the set;

[0116] The parallel distribution module 303 is used to construct a multi-path parallel computing architecture, which uses the effective candidate sub-states pre-screened by the structure as the local initial starting point of each independent search path and distributes them to multiple independent computing threads respectively.

[0117] The parallel deep search module 304 is used to perform parallel deep iterative search on each search path. Each round of iterative search is performed according to a preset evaluation index system. The evaluation index system includes a first evaluation index for macro-level evaluation and a second evaluation index for distinguishing micro-level differences.

[0118] The global optimization module 305 is used to periodically synchronize the local optimal solutions output by all parallel search paths, filter the local optimal solutions to obtain the global optimal solution; if the preset termination condition is met, the global optimal solution is output; if the preset termination condition is not met, the global optimal solution is used as a new initial search starting point, the neighborhood is reconstructed and the next round of iteration is started.

[0119] like Figure 4 As shown, Figure 4 This diagram illustrates the working logic of the system. Specifically:

[0120] The state initialization module is responsible for the system's startup configuration. This module constructs the discrete state variables to be optimized and defines an evaluation system that includes a first evaluation index and a second evaluation index.

[0121] The neighborhood mapping and filtering module receives the initial state, applies neighborhood mapping rules to generate an initial candidate set, and uses structural pre-screening to remove inferior candidates.

[0122] The parallel distribution module, acting as the task control center, is responsible for transforming single-point search into multi-path parallel search, encapsulating valid candidate sub-states into independent tasks, and distributing them to various parallel computing threads.

[0123] The parallel deep search module serves as the core execution unit. This module constructs multiple independent search paths within the system. Each search path integrates three sub-units: candidate generation and pre-screening, property calculation, and dual-index arbitration. Through closed-loop iteration, it deeply mines local optima in its respective search domain.

[0124] The global optimization module is responsible for result aggregation and closed-loop feedback. This module collects the local optimal solutions of each path and selects the globally optimal result; if the result does not meet the criteria, it is fed back to the parallel distribution module as the starting point for a new round of search, until the criteria are met or the iteration threshold is reached.

[0125] In a preferred embodiment, the parallel depth search module integrates the following three execution sub-units:

[0126] Subunit A (Candidate Generation and Pre-screening Unit): Configured to generate the next-level candidate sub-states by applying neighborhood mapping rules and to eliminate inferior candidates using a low-cost verification mechanism, thereby reducing invalid computation;

[0127] Sub-unit B (Property Calculation Unit): Configures the first evaluation index for calculating candidate sub-states; this unit supports configuring a general full calculation mode and an incremental update mode suitable for local perturbations.

[0128] Subunit C (Dual-Indicator Arbitration Unit): Configured to execute a hierarchical screening strategy; when the first evaluation index is the same, the second evaluation index is activated as a difference amplifier to identify and retain potential high-quality solutions with microstructural advantages and perform state updates.

[0129] The system in this embodiment solves the local optimum trap problem commonly found in high-dimensional discrete solution spaces (such as the 8-bit S-box permutation space). It adopts a strategy of "generalized parallel distribution + deep iterative search" to ensure that the traversal of the solution space has both breadth and depth. At the same time, the system introduces a dual-index hierarchical screening mechanism to solve the search stagnation problem caused by the excessively coarse granularity of traditional evaluation indicators.

[0130] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for global optimization of discrete spaces based on neighborhood mapping and multi-path parallel search, characterized in that, include: Obtain the discrete state variables to be optimized as the initial search starting point; The initial candidate set, which includes multiple candidate states, is generated by applying neighborhood mapping rules to the initial search starting point. The elements in the set are then pre-screened to obtain valid candidate states. The pre-screening is implemented through a low-cost verification mechanism, which includes: using fixed-point threshold verification and algebraic feature lower bound verification to screen each candidate state and removing candidate states that fail any verification. The fixed point threshold verification includes: counting the number of fixed points for each candidate state; when the number of fixed points is greater than the preset number of points, the verification is deemed to have failed. The algebraic feature lower bound verification includes: judging the algebraic degree of the candidate state or its lower bound estimate; if the algebraic degree or its lower bound estimate is less than a preset threshold, the verification is deemed to fail. A multi-path parallel computing architecture is constructed, in which the effective candidate states are used as the local initial starting points of each independent search path and distributed to multiple independent computing threads respectively. Parallel deep iterative search is performed on each search path. Each iteration searches according to a preset evaluation index system to obtain a local optimum for each path. The evaluation index system includes a first evaluation index for macro-level assessment and a second evaluation index for distinguishing micro-level differences. The parallel deep iterative search on each search path, with each iteration searching according to the preset evaluation index system, includes: Candidate sub-states are generated one by one according to the neighborhood mapping rule based on the current state, and the structure pre-screening is performed on each candidate sub-state, discarding the candidate sub-states that fail the screening. The first evaluation index of the candidate sub-states that have passed the screening is calculated using an attribute algorithm; If the first evaluation index of the candidate sub-state is different from that of the current state, the traversal will be restarted starting from the state corresponding to the better first evaluation index. If the candidate substate is exactly the same as the first evaluation index of the current state, then the second evaluation index is calculated for fine-grained arbitration. If the second evaluation index value of the candidate sub-state is better, then the traversal is restarted starting from the candidate sub-state; The local optimal solutions output by all parallel search paths are periodically synchronized, and the global optimal solution is obtained by filtering the local optimal solutions. If the preset termination condition is met, the global optimal solution is output. If the preset termination condition is not met, the global optimal solution is used as a new initial search starting point, the neighborhood is reconstructed, and the next round of iteration is started.

2. The method according to claim 1, characterized in that, The neighborhood mapping rules include arbitrary perturbation models and local perturbation models; The arbitrary perturbation model includes: performing random or global modifications on the current discrete state variable without local constraints; the local perturbation model includes: performing local element transformations on the current discrete state variable within a preset step size.

3. The method according to claim 1, characterized in that, The first evaluation index includes: The nonlinearity is obtained by calculating the extended Walsh spectrum using FWHT, and the differential uniformity is obtained by constructing a full differential distribution table and taking its maximum value.

4. The method according to claim 1, characterized in that, The attribute algorithm includes: When candidate substates are generated by arbitrary perturbation models, full attribute statistics are performed on the candidate substates to obtain the first evaluation index of the candidate substates. When candidate sub-states are generated by a local perturbation model, an incremental update method based on perturbation difference is used to perform differential correction on the statistical cache of the parent state to obtain the evaluation index of the candidate sub-state.

5. The method according to claim 1, characterized in that, The second evaluation metric includes: a cost function based on the extended Walsh spectrum and a cost function based on the difference distribution table.

6. The method according to claim 1, characterized in that, The preset termination condition includes at least one of the following conditions: The first evaluation index of the global optimal solution reaches the preset security strength threshold. The global optimal solution remains unchanged within a preset number of consecutive synchronization cycles, or the improvement is continuously lower than a preset change threshold. The total number of iterations or the cumulative search time of each parallel path reaches the preset running limit.

7. A discrete-space global optimization system based on neighborhood mapping and multi-path parallel search, characterized in that, include: The state initialization module is used to obtain the discrete state variables to be optimized as the initial search starting point; The neighborhood mapping and filtering module is used to apply neighborhood mapping rules to the initial search starting point to generate an initial candidate set including multiple candidate states, and to perform structural pre-filtering on the elements in the set. The pre-screening of the structure is achieved through a low-cost verification mechanism, including: screening each candidate state using fixed-point threshold verification and algebraic feature lower bound verification, and removing candidate states that fail either verification; wherein, the fixed-point threshold verification includes: counting the number of fixed points for each candidate state, and determining that the verification fails when the number of fixed points is greater than a preset number; the algebraic feature lower bound verification includes: judging the algebraic degree or its lower bound estimate of the candidate state, and determining that the verification fails when the algebraic degree or its lower bound estimate is less than a preset threshold; The parallel distribution module is used to build a multi-path parallel computing architecture. It takes the effective candidate states that have been pre-screened by the structure as the local initial starting point of each independent search path and distributes them to multiple independent computing threads. A parallel deep search module is used to perform parallel deep iterative search on each search path. Each round of iterative search is performed according to a preset evaluation index system. The evaluation index system includes a first evaluation index for macroscopic evaluation and a second evaluation index for microscopic difference differentiation. The parallel execution of deep iterative search on each search path, with each round of iterative search performed according to the preset evaluation index system, includes: generating candidate sub-states one by one according to the neighborhood mapping rule based on the current state, and performing the structure pre-screening on each candidate sub-state, discarding candidate sub-states that fail the screening; calculating the first evaluation index of the candidate sub-states that have passed the screening using an attribute algorithm; if the first evaluation index of a candidate sub-state is different from that of the current state, the traversal is restarted starting from the state corresponding to the better first evaluation index. The global optimization module is used to periodically synchronize the local optimal solutions output by all parallel search paths, filter the local optimal solutions to obtain the global optimal solution; if the preset termination condition is met, the global optimal solution is output; if the preset termination condition is not met, the global optimal solution is used as a new initial search starting point, the neighborhood is reconstructed and the next round of iteration is started.

8. The system according to claim 7, characterized in that, The parallel deep search module includes: a candidate generation and pre-screening unit, a property calculation unit, and a dual-index arbitration unit; The candidate generation and pre-screening unit is used to generate the next-level candidate sub-state by applying the neighborhood mapping rule, and to eliminate inferior candidates by using a low-cost verification mechanism, thereby reducing invalid computation. The property calculation unit is used to calculate the first evaluation index of the candidate sub-state through a full calculation mode or an incremental update mode applicable to local perturbations. The dual-index arbitration unit is used to execute a hierarchical screening strategy; when the first evaluation index is the same, the second evaluation index is activated as a difference amplifier to identify and retain potential high-quality solutions with microstructural advantages and perform state updates.

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