Linear path automatic analysis method and system oriented to ARX type cryptographic algorithm

Abstract

The invention relates to the technical field of cryptographic analysis, and discloses an automatic linear path analysis method and system for an ARX type cryptographic algorithm, and the method comprises the following steps: constructing a round function, configuring a linear analysis target, and selecting a search strategy; performing linear mask initialization on the round function, and establishing an association relationship between inter-round mask variables; generating local linear mask propagation expressions based on the linear approximation characteristic of each basic operation unit, combining the local linear mask propagation expressions into a global linear approximation model, and calculating a correlation expression of a linear path; executing a search strategy on the global linear approximation model; converting the global linear approximation model and the search strategy into constraint description and solving the constraint description; according to the method, the modeling complexity of linear analysis is reduced through visual modeling and selection of the path search strategy, and automation of the linear path search process is achieved.

Description

Technical Field

[0001] This invention relates to the field of cryptanalysis technology, specifically to an automated linear path analysis method and system for ARX-type cryptographic algorithms. Background Technology

[0002] Symmetric cryptographic algorithms, as the cornerstone of information security, have always had their security strength assessment as a cutting-edge topic in cryptographic research. Linear analysis, as one of the core methods for evaluating the security of block ciphers, explores the statistical properties of the algorithm under specific linear combinations of inputs, providing a crucial basis for quantifying the algorithm's ability to resist known-plaintext attacks.

[0003] In recent years, ARX-type cryptographic algorithms (such as Speck, ChaCha20, and BLAKE2 / 3) composed of three basic operations—modular addition, cyclic shift, and XOR—have been widely used in lightweight cryptography, hash functions, and stream ciphers due to their significant advantages, including simple structure, efficient hardware and software implementation, and strong resistance to side-channel attacks. However, the core nonlinearity of the ARX structure originates solely from the modular addition operation, and its bit-level carry propagation mechanism makes the analysis of the linear relationship between input and output exceptionally complex. Traditional linear analysis methods face a series of challenges when dealing with this type of structure, including high levels of modeling abstraction, complex constraints, and the difficulty of manual derivation.

[0004] Currently, linear analysis of ARX ciphers primarily relies on analysts' professional experience, combined with some scripts or semi-automated tools, for modeling and path searching. This method is not only inefficient but also has the following inherent limitations:

[0005] The modeling threshold is high: it requires analysts to have a deep understanding of the linear approximation characteristics of the modular addition method (such as correlation coefficient calculation and linear shell effect) and to be able to manually construct complex bit-level constraint equations.

[0006] Limited automation: Existing tools mostly focus on assisting in calculation or verification, lacking the ability to automatically generate the entire process from algorithm description to complete constraint model.

[0007] The analysis is limited in scope: the search process focuses primarily on finding a single highly correlated linear path, with insufficient support for multi-path joint effects (linear shells), path aggregation characteristics under specific masking patterns, and path exploration with constraints (such as predefined active bits). This makes it difficult for existing methods to systematically evaluate the true security boundary of the algorithm under multiple linear approximation.

[0008] In summary, current technological systems are insufficient to meet the urgent needs of ARX cryptography for rapid, systematic, and automated security evaluation during the algorithm design phase. Therefore, researching how to significantly reduce the modeling complexity of linear analysis while ensuring analytical accuracy, and achieving efficient, multi-dimensional automated path searching, has become a key technological bottleneck in improving the design and evaluation capabilities of ARX-type cryptographic algorithms. Summary of the Invention

[0009] To address the technical problems of existing technologies, such as high modeling thresholds, limited automation, and single analytical dimensions, this invention proposes an automated linear path analysis method and system for ARX-type cryptographic algorithms. The technical solution is as follows:

[0010] Step 1: Construct the round function structure of the ARX-type cryptographic algorithm and configure the linear analysis target. Select the linear path search strategy according to the linear analysis requirements.

[0011] Step 2: Initialize the round function structure with a linear mask and establish the association between the inter-round mask variables;

[0012] Step 3: Based on the linear approximation characteristics of each basic operation unit in the round function structure, generate the corresponding local linear mask propagation expression;

[0013] Step 4: Combine the local linear mask propagation expression into a global linear approximation model, and calculate the correlation expression of the linear path;

[0014] Step 5: Execute a linear path search strategy on the global linear approximation model;

[0015] Step 6: Convert the global linear approximation model and linear path search strategy into constraint descriptions that can be recognized by the constraint solver, and then solve them;

[0016] Step 7: Analyze the results of the above solution, extract the linear paths that meet the correlation conditions, and output the linear path structure and its correlation statistics.

[0017] Furthermore, the linear analysis objectives of step 1 include the input linear mask space, the round number range, and the correlation threshold.

[0018] Further, step 2 specifically involves: modeling the linear mask, defining a linear mask variable for each intermediate variable of the round function, allowing it to participate in the computation process, and constructing a deterministic or probabilistic constraint equation from the input mask to the output mask.

[0019] Further, step 4 specifically involves: concatenating the local linear mask propagation expressions of each basic operation in the round function, i.e., the output mask of the previous local operation is the input mask of the next local operation, and calculating the correlation coefficient of the entire path.

[0020] Furthermore, the linear path search strategy in step 5 includes:

[0021] 1) Parallel construction strategy using multiple linear paths;

[0022] 2) Linear aggregation analysis strategy;

[0023] 3) Linear path filtering strategy.

[0024] Furthermore, the parallel construction strategy for multiple linear paths specifically involves: searching for multiple linear paths, solving them in batches, and combining and statistically analyzing the multiple linear paths.

[0025] Furthermore, the linear aggregation analysis strategy specifically involves fixing the input and output masks, identifying all linear paths that satisfy the correlation condition, and calculating the probability of the aggregated path based on the path set.

[0026] Furthermore, the linear path filtering strategy specifically involves filtering linear paths based on constraints such as round number or weight conditions.

[0027] An automated linear path analysis system for ARX-type cryptographic algorithms, used to implement any of the methods described above, includes the following modules:

[0028] Front-end modeling module: used to visualize the round function structure of cryptographic algorithms and configure linear analysis targets;

[0029] Linear mask propagation module: used to perform linear mask initialization on the round function structure and establish the association between mask variables between rounds;

[0030] Backend parsing module: used to generate linear approximation models and calculate the correlation expression of linear paths;

[0031] Parallel construction module for multiple linear paths: used to search and output multiple linear paths;

[0032] Linear Aggregation Analysis Module: Used to find linear paths that meet certain conditions and perform aggregation analysis under fixed input and output masks;

[0033] Linear path filtering module: used to filter linear paths under preset constraints;

[0034] Constraint generation module: used to convert the global linear approximation model and linear path search strategy into constraint descriptions that can be recognized by the constraint solver;

[0035] Solver Call Module: Used to call the constraint solver to solve for linear paths that meet the conditions;

[0036] Parsing Feedback Module: Used to parse the results of linear paths and feed the path information back to the system front end.

[0037] Beneficial effects:

[0038] This invention reduces the modeling complexity of linear analysis of ARX-type cryptographic algorithms through a visual modeling platform; it automates the linear path search process by automatically calling the corresponding modules to implement the strategy and solve the problem by selecting a linear path filtering strategy; and it systematically analyzes the real security boundary of the algorithm under multiple linear approximations through parallel search of multiple linear paths. Attached Figure Description

[0039] Figure 1 This is a flowchart of an automated linear path analysis method for ARX-type cryptographic algorithms. Detailed Implementation

[0040] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0041] like Figure 1 As shown, the present invention provides an automated linear path analysis method for ARX-type cryptographic algorithms, comprising the following steps:

[0042] Step 1: Construct the round function structure of the ARX-type cryptographic algorithm and configure the linear analysis target. Select the linear path search strategy according to the linear analysis requirements.

[0043] Step 2: Initialize the round function structure with a linear mask and establish the association between the inter-round mask variables;

[0044] Step 3: Based on the linear approximation characteristics of each basic operation unit in the round function structure, generate the corresponding local linear mask propagation expression;

[0045] Step 4: Combine the local linear mask propagation expression into a global linear approximation model, and calculate the correlation expression of the linear path;

[0046] Step 5: Execute a linear path search strategy on the global linear approximation model;

[0047] Step 6: Convert the global linear approximation model and linear path search strategy into constraint descriptions that can be recognized by the constraint solver, and then solve them;

[0048] Step 7: Analyze the results of the above solution, extract the linear paths that meet the correlation conditions, and output the linear path structure and its correlation statistics.

[0049] The method of the present invention described above is implemented in a modelable system, which mainly consists of a front-end module and a back-end module, and the two interact with each other through network communication.

[0050] Users construct the round function structure of the ARX-type cryptographic algorithm to be analyzed by dragging and dropping through the front-end modeling module. The round function structure consists of multiple basic operation units, including a modular addition unit, a circular shift unit, and an XOR unit.

[0051] While constructing the round function structure, users can configure linear analysis objectives, including the input linear mask space, the range of rounds, and the correlation threshold. After construction, the current content can be saved for user modification.

[0052] Users can choose a linear path search strategy based on their linear analysis needs, including:

[0053] 1) Parallel construction strategy for multiple linear paths: Search for multiple linear paths, solve them in batches, and combine and statistically analyze multiple linear paths;

[0054] 2) Linear aggregation analysis strategy: With fixed input and output masks, find all linear paths that satisfy the correlation condition, and calculate the probability of the aggregated path based on the path set;

[0055] 3) Linear path selection strategy: Select linear paths based on round or weight constraints.

[0056] The linear mask propagation module generates corresponding local linear mask propagation expressions based on the linear approximation characteristics of each basic operation unit in the round function structure, combines the local linear mask propagation expressions into a global linear approximation model, and calculates the correlation expression of the linear path.

[0057] The system executes the linear path search strategy selected above.

[0058] The constraint generation module transforms the global linear approximation model and linear path search strategy into constraint descriptions that can be recognized by the constraint solver, and calls the STP constraint solver to solve the constraint descriptions through the solver call module.

[0059] After the solution is completed, the system analyzes the solution results, extracts the linear path information and its statistical characteristics that meet the analysis conditions, and feeds the linear path information back to the front-end interface for display.

[0060] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An automated linear path analysis method for ARX-type cryptographic algorithms, characterized in that: Includes the following steps: Step 1: Construct the round function structure of the ARX-type cryptographic algorithm and configure the linear analysis target. Select the linear path search strategy according to the linear analysis requirements. Step 2: Initialize the round function structure with a linear mask and establish the association between the inter-round mask variables; Step 3: Based on the linear approximation characteristics of each basic operation unit in the round function structure, generate the corresponding local linear mask propagation expression; Step 4: Combine the local linear mask propagation expressions into a global linear approximation model, and calculate the correlation expression of the linear path; Step 5: Execute a linear path search strategy on the global linear approximation model; Step 6: Convert the global linear approximation model and linear path search strategy into constraint descriptions that can be recognized by the constraint solver, and then solve them; Step 7: Analyze the results of the above solution, extract the linear paths that meet the correlation conditions, and output the linear path structure and its correlation statistics.

2. The automated linear path analysis method for ARX-type cryptographic algorithms as described in claim 1, characterized in that: The linear analysis objectives in step 1 include the input linear mask space, the round number range, and the correlation threshold.

3. The automated linear path analysis method for ARX-type cryptographic algorithms as described in claim 1, characterized in that: Step 2 specifically involves: modeling the linear mask, defining a linear mask variable for each intermediate variable of the round function, allowing it to participate in the computation process, and constructing a deterministic or probabilistic constraint equation from the input mask to the output mask.

4. The automated linear path analysis method for ARX-type cryptographic algorithms as described in claim 1, characterized in that: Step 4 specifically involves: concatenating the local linear mask propagation expressions of each basic operation in the round function, i.e., the output mask of the previous local operation is the input mask of the next local operation, and calculating the correlation coefficient of the entire path.

5. The automated linear path analysis method for ARX-type cryptographic algorithms as described in claim 1, characterized in that: The linear path search strategy in step 5 includes: 1) Parallel construction strategy using multiple linear paths; 2) Linear aggregation analysis strategy; 3) Linear path filtering strategy.

6. The automated linear path analysis method for ARX-type cryptographic algorithms as described in claim 5, characterized in that: The parallel construction strategy for multiple linear paths specifically involves: searching for multiple linear paths, solving them in batches, and combining and statistically analyzing the multiple linear paths.

7. The automated linear path analysis method for ARX-type cryptographic algorithms as described in claim 5, characterized in that: The linear aggregation analysis strategy is as follows: with fixed input and output masks, find all linear paths that satisfy the correlation condition, and calculate the probability of the aggregated path based on the path set.

8. The automated linear path analysis method for ARX-type cryptographic algorithms as described in claim 5, characterized in that: The linear path filtering strategy specifically involves filtering linear paths based on constraints such as rounds or weight conditions.

9. An automated linear path analysis system for ARX-type cryptographic algorithms, characterized in that: To implement the method as described in any one of claims 1 to 8, the method includes the following modules: Front-end modeling module: used to visualize the round function structure of cryptographic algorithms and configure linear analysis targets; Linear mask propagation module: used to perform linear mask initialization on the round function structure and establish the association between mask variables between rounds; Backend parsing module: used to generate linear approximation models and calculate the correlation expression of linear paths; Parallel construction module for multiple linear paths: used to search and output multiple linear paths; Linear Aggregation Analysis Module: Used to find linear paths that meet certain conditions and perform aggregation analysis under fixed input and output masks; Linear path filtering module: used to filter linear paths under preset constraints; Constraint generation module: used to convert the global linear approximation model and linear path search strategy into constraint descriptions that can be recognized by the constraint solver; Solver Call Module: Used to call the constraint solver to solve for linear paths that meet the conditions; Parsing Feedback Module: Used to parse the results of linear paths and feed the path information back to the system front end.

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