CN110278108B - Simulated annealing algorithm-based multi-autonomous-body network intrusion tolerance capability assessment method - Google Patents

Abstract

The invention discloses a simulated annealing algorithm-based multi-autonomous-body network intrusion resistance evaluation method, which applies a simulated annealing technology to the field of network intrusion resistance evaluation, and simultaneously comprehensively considers three alternative states introduced during updating of a network robustness calculation subset pair on the basis of the traditional simulated annealing method, so that the subset pair update has higher sampling randomness. The method has the advantage of overcoming the problem that the large-scale multi-autonomous-body network intrusion-tolerant capability assessment cannot be solved due to NP difficulty.

Description

Simulated annealing algorithm-based multi-autonomous-body network intrusion tolerance capability assessment method

Technical Field

The invention relates to the technical field of network intrusion tolerance assessment, in particular to a multi-autonomous-body network intrusion tolerance assessment method based on a simulated annealing algorithm.

Background

The multi-autonomous system refers to a large-scale network system composed of a plurality of autonomous bodies with sensing, communication, computing and executing capabilities, and is widely used as an implementation carrier of a distributed cooperation algorithm. The multi-autonomous system not only has the advantages of resource sharing, good coordination, strong autonomy and the like of a general distributed system, but also has strong robustness and reliability because each autonomous body can solve the problem of large-scale complexity through coordination and cooperation. However, in recent years, with the network security risk becoming more prominent, network designers pay more attention to the evaluation of their network intrusion-tolerant capability in the process of constructing a multi-autonomous system. Network topology (r, s) -robustness is an effective index for measuring the intrusion tolerance capability of a multi-autonomous network at present.

The existing evaluation methods for the robustness of the network topology, such as exhaustion, graph construction, linear programming, functional relationship and the like, evaluate two values of (r, s) of the network topology, which are obtained through an exhaustion and traversal algorithm, need to acquire link information of the network communication topology overall situation. However, it has been documented that evaluating the decision on the value pairs (r, s) in robustness is an NP-hard problem. Therefore, the conventional method is only suitable for a small-sized multi-host network with a small number of nodes, and cannot be applied to a large-scale network with a large number of nodes.

Disclosure of Invention

The invention provides a network intrusion tolerance assessment method which is simple, easy to implement and suitable for a large-scale multi-autonomous system with a large number of nodes, aiming at overcoming the defects of the existing assessment technology.

The technical scheme adopted by the invention for solving the technical problems is as follows:

a simulated annealing algorithm-based multi-autonomous-body network intrusion tolerance capability assessment method comprises the following steps:

1) setting conditions: nodes in the graph theory are adopted to represent a plurality of autonomous bodies, and edges in the graph theory represent communication links between autonomous bodies; giving a directed graph D ═ (V, E), where V is a set of nodes and E is a set of edges; let A (D) be an adjacency matrix of a directed graph D, and then give an initial temperature of T₀Termination temperature of T_fThe temperature reduction temperature is delta T, the iteration number q is obtained, and the real-time temperature T is enabled_tIs an initial temperature T₀(ii) a Setting an initial robustness value to (r)_min，s_min) (ii) a Let r be_min＝min{δⁱⁿ(D)，[n/2]}，s_minN, where δⁱⁿ(D) Representing the minimum in-degree of the directed graph D, wherein n represents the number of nodes in the directed graph;

2) obtaining a primary solution: randomly generating a pair of non-empty disjoint subsets S in a set of nodes V₁,S₂Performing robustness calculation f (A), (D), S₁，S₂，r_min，s_min) Obtaining a subset pair S₁,S₂An optimum robustness value (r, s) is satisfied;

3) generating a new solution: update the subset pair S₁,S₂Form a new subset pair S'₁，S’₂Robustness calculation f (A (D), S 'is performed again'₁，S’₂，r_min，s_min) To obtain a subset pair S'₁，S’₂An optimum robustness value (r ', s') satisfied;

4) comparing the initial solution with the new solution, and calculating by taking the value of delta r as (r '-r) multiplied by n + (s' -s); if the new solution is better than the initial solution, i.e. Δ r < 0, the new solution (S 'is directly accepted'₁，S’₂R ', s'); if the new solution is inferior to the initial solution and delta r is more than or equal to 0, the new solution (S ') is accepted according to the Metropolis criterion'₁，S’₂，r’，s’)；

The Metropolis criteria includes the following steps:

(4.1) generating a random number xi epsilon U (0, 1);

(4.2) if exp (- Δ r/Tt)>ξ, receiving a new solution (S'₁，S’₂R ', s'); otherwise, the initial solution (S) is maintained₁，S₂，r，s)；

5)(r_min，s_min) And (3) updating the numerical value: if the result obtained in step 4) is a new solution, let r_min＝r’，s_minS'; if the result obtained in step 4) is the initial solution, let r_min＝r，s_min＝s；

6) When the iteration number reaches the set upper limit, the real-time temperature is reduced by delta T, namely T_t←T_t- Δ T, go to step 7); otherwise, turning to the step 2);

7) when real-time temperature T_tGreater than algorithm end temperature T_fTurning to step 2); otherwise, the operation is finished.

Preferably, the optimal robustness calculation method satisfied by the subset pairs in the steps 2) and 3) comprises the following steps:

(2.1) given that n represents the number of nodes in FIG. D, let r be r_min，s＝s_min；

(2.2) if the robustness value r > 0, then perform the robustness valid function RobustHolds (A (D)), S₁，S₂R, s) determination; if the result of the determination is true, the current robustness value (r, S) is the node subset pair S₁,S₂An optimal robustness value is satisfied; if the judgment result is false, the robustness value s is reduced by 1, and the value r is unchanged; when the value s is decreased to 0, the robustness value r is decreased by 1, and the value s becomes n; if the value r is equal to 0, the operation is ended;

the method for judging RobustHolds in the step (2.2) mainly comprises the following steps:

(2.2.1) computing the non-empty subset S₁The number of nodes with the number of the adjacent nodes with the degree of attack being more than or equal to r is counted by k₁；

(2.2.2) computing the non-empty subset S₂The number of nodes with the number of the adjacent nodes with the degree of attack being more than or equal to r is counted by k₂。

(2.2.3) when k₁＝S₁Or k₂＝S₂Or (k)₁+k₂)>When the judgment result is s, the RobustHolds judges that the judgment result is true, otherwise, the judgment result is false.

Preferably, in step 3), the updating method of the subset pair S1 and S2 includes:

(3.1) initialization S₁S of_neighbors；

(3.2) generating a random number xi epsilon U (0, 1); when the random number xi is less than 1/3, from S₁In the method, a node is randomly selected and replaced by a slave S_neighborsRandomly selecting one node; when the random number xi is equal to or greater than 1/3 and less than 2/3, from S_neighborsRandomly selecting a node to add to the set S₁Performing the following steps; when the random number xi is equal to or greater than 2/3 and less than 1, the random number is S₁Deleting a node;

(3.3) from the set S₁Is sampled to obtain a new S₂And (4) collecting.

The annealing simulation method is a method for solving an approximate optimal solution, is firstly used for simulating a metal melting process in physics to find the optimal solution, and is widely applied to various fields such as a traveler problem and an influence maximization problem.

The simulated annealing technology is applied to the field of network intrusion tolerance capability evaluation, and three alternative states are comprehensively considered on the basis of the traditional simulated annealing method when the network robustness calculation subset pair is updated, so that the subset pair update has higher sampling randomness.

The method has the advantage of overcoming the problem that the large-scale multi-autonomous-body network intrusion-tolerant capability assessment cannot be solved due to NP difficulty.

Drawings

FIG. 1 is a flow chart of the present invention.

Fig. 2 is a flow chart of specific steps.

Detailed Description

The invention is further described below with reference to the accompanying drawings of the specification:

a simulated annealing algorithm-based multi-autonomous-body network intrusion tolerance capability assessment method comprises the following steps:

1) setting conditions: for convenience in explaining the invention, the multi-autonomous network model is described by means of mathematical graph theory, nodes in the graph theory are used for representing multi-autonomous entities, and edges in the graph theory are used for representing communication links between autonomous entities. Given a directed graph D ═ V, E, where V is the set of nodes and E is the set of edges. Let A (D) be an adjacency matrix of a directed graph D, and then give an initial temperature of T₀Termination temperature of T_fThe temperature reduction temperature is delta T, the iteration number q is obtained, and the real-time temperature T is enabled_tIs an initial temperature T₀. Setting an initial robustness value to (r)_min，s_min). Let r be_min＝min{δⁱⁿ(D)，[n/2]}，s_minN, where δⁱⁿ(D) The minimum in-degree of the directed graph D is shown, and n represents the number of nodes in the directed graph.

2) Obtaining a primary solution: randomly generating a pair of non-empty disjoint subsets S in a set of nodes V₁,S₂Performing robustness calculation f (A), (D), S₁，S₂，r_min，s_min) Obtaining a subset pair S₁,S₂The satisfied optimal robustness value (r, s).

3) Generating a new solution: update the subset pair S₁,S₂Form a new subset pair S'₁，S’₂Robustness calculation f (A (D), S 'is performed again'₁，S’₂，r_min，s_min) To obtain a subset pair S'₁，S’₂The optimum robustness value (r ', s') is satisfied.

4) The initial solution is compared with the new solution and calculated, and the Δ r ═ r '-r × n + (s' -s). If the new solution is better than the original solution (. DELTA.r < 0), the new solution (S 'is directly accepted'₁，S’₂R ', s'); if the new solution is inferior to the initial solution (delta r is more than or equal to 0), the new solution (S 'is accepted according to the Metropolis criterion'₁，S’₂R ', s'). The Metropolis criteria includes the following steps:

(4.1) generating a random number xi ∈ U (0, 1).

(4.2) if exp (- Δ r/Tt)>ξ, receiving a new solution (S'₁，S’₂R ', s'); otherwise, the initial solution (S) is maintained₁，S₂，r，s)。

5)(r_min，s_min) And (3) updating the numerical value: if the result obtained in step 4) is a new solution, let r_min＝r’，s_minS'; if the result obtained in step 4) is the initial solution, let r_min＝r，s_min＝s。

6) When the iteration number reaches the set upper limit, the real-time temperature is reduced by delta T, namely T_t←T_t- Δ T, go to step 6); otherwise, turning to the step 2).

7) When real-time temperature T_tGreater than algorithm end temperature T_fTurning to step 2); otherwise, the operation is finished.

Further, the optimal robustness calculation method satisfied by the subset pairs in the steps 2) and 3) comprises the following steps:

(2.1) given that n represents the number of nodes in FIG. D, let r be r_min，s＝s_min。

(2.2) if the robustness value r > 0, then RobustHolds (A (D)), S₁，S₂R, s). If the result of the determination is true, the current robustness value (r, S) is the node subset pair S₁,S₂An optimal robustness value is satisfied; if the result of the determination is false, the robustness value s is decreased by 1 and the value r is unchanged. When the value s is reduced to 0, the robustness value r is reduced by 1 and the value s becomes n. If the value r is equal to 0, the operation is ended;

the method for judging RobustHolds in the step (2.2) mainly comprises the following steps:

(2.2.1) computing the non-empty subset S₁The number of nodes with the number of the adjacent nodes with the degree of attack being more than or equal to r is counted by k₁。

(2.2.2) computing the non-empty subset S₂The number of nodes with the number of the adjacent nodes with the degree of attack being more than or equal to r is counted by k₂。

(2.2.3) when k₁＝S₁Or k₂＝S₂Or (k)₁+k₂)>When is equal to sAnd judging that RobustHolds is true, otherwise, judging that the RobustHolds is false. Further, in step 3), the updating method of the subset pair S1 and S2 includes:

(3.1) initialization S₁S of_neighbors。

(3.2) generating a random number xi ∈ U (0, 1). When the random number xi is less than 1/3, from S₁In the method, a node is randomly selected and replaced by a slave S_neighborsRandomly selecting one node; when the random number xi is equal to or greater than 1/3 and less than 2/3, from S_neighborsRandomly selecting a node to add to the set S₁Performing the following steps; when the random number xi is equal to or greater than 2/3 and less than 1, the random number is S₁One node is deleted.

(3.3) from the set S₁Is sampled to obtain a new S₂And (4) collecting.

The annealing simulation method is a method for solving an approximate optimal solution, is firstly used for simulating a metal melting process in physics to find the optimal solution, and is widely applied to various fields such as a traveler problem and an influence maximization problem. The simulated annealing technology is applied to the field of network intrusion tolerance capability evaluation, and three alternative states are comprehensively considered on the basis of the traditional simulated annealing method when the network robustness calculation subset pair is updated, so that the subset pair update has higher sampling randomness.

The embodiments of the present invention are described in detail with reference to the prior art, and the description thereof is not limited thereto.

The above specific implementation is a specific support for the technical idea of the multi-autonomous-network intrusion-tolerance capability evaluation method based on the simulated annealing algorithm, and the protection scope of the present invention cannot be limited thereby, and any equivalent changes or equivalent changes made on the basis of the technical scheme of the present invention according to the technical idea of the present invention still belong to the protection scope of the technical scheme of the present invention.

Claims (2)

1. A simulated annealing algorithm-based multi-autonomous-body network intrusion tolerance capability assessment method is characterized by comprising the following steps: the method comprises the following steps:

1) setting conditions: nodes in the graph theory are adopted to represent a plurality of autonomous bodies, and edges in the graph theory represent communication links between autonomous bodies; giving a directed graph D ═ (V, E), where V is a set of nodes and E is a set of edges; let A (D) be an adjacency matrix of a directed graph D, and then give an initial temperature of T₀Termination temperature of T_fThe temperature reduction temperature is delta T, the iteration number q is obtained, and the real-time temperature T is enabled_tIs an initial temperature T₀(ii) a Setting an initial robustness value to (r)_min，s_min) (ii) a Let r be_min＝min{δⁱⁿ(D)，[n/2]}，s_minN, where δⁱⁿ(D) Representing the minimum in-degree of the directed graph D, wherein n represents the number of nodes in the directed graph;

2) obtaining a primary solution: randomly generating a pair of non-empty disjoint subsets S in a set of nodes V₁,S₂Performing robustness calculation f (A), (D), S₁，S₂，r_min，s_min) Obtaining a subset pair S₁,S₂An optimum robustness value (r, s) is satisfied;

the optimal robustness calculation method satisfied by the subset pair comprises the following steps:

(2.1) given that n represents the number of nodes in FIG. D, let r be r_min，s＝s_min；

(2.2) if the robustness value r > 0, then perform the robustness valid function RobustHolds (A (D)), S₁，S₂R, s) determination; if the result of the determination is true, the current robustness value (r, S) is the node subset pair S₁,S₂An optimal robustness value is satisfied; if the judgment result is false, the robustness value s is reduced by 1, and the value r is unchanged; when the value s is decreased to 0, the robustness value r is decreased by 1, and the value s becomes n; if the value r is equal to 0, the operation is ended;

the method for judging RobustHolds in the step (2.2) mainly comprises the following steps:

(2.2.1) computing the non-empty subset S₁The number of nodes with the number of the adjacent nodes with the degree of attack being more than or equal to r is counted by k₁；

(2.2.2) computing the non-empty subset S₂The number of nodes with the number of the adjacent nodes with the degree of attack being more than or equal to r is counted by k₂；

(2.2.3) when k₁＝S₁Or k₂＝S₂Or (k)₁+k₂)>When the signal is s, the RobustHolds judges that the signal is true, otherwise, the signal is judged to be false;

3) generating a new solution: update the subset pair S₁,S₂Form a new subset pair S'₁，S’₂Robustness calculation f (A (D), S 'is performed again'₁，S’₂，r_min，s_min) To obtain a subset pair S'₁，S’₂An optimum robustness value (r ', s') satisfied;

4) comparing the initial solution with the new solution, and calculating by taking the value of delta r as (r '-r) multiplied by n + (s' -s); if the new solution is better than the initial solution, i.e. Δ r < 0, the new solution (S 'is directly accepted'₁，S’₂R ', s'); if the new solution is inferior to the initial solution, namely delta r is more than or equal to 0, the new solution (S 'is accepted according to the Metropolis criterion'₁，S’₂，r’，s’)；

The Metropolis criteria includes the following steps:

(4.1) generating a random number xi epsilon U (0, 1);

(4.2) if exp (- Δ r/Tt)>ξ, receiving a new solution (S'₁，S’₂R ', s'); otherwise, the initial solution (S) is maintained₁，S₂，r，s)；

5)(r_min，s_min) And (3) updating the numerical value: if the result obtained in step 4) is a new solution, let r_min＝r’，s_minS'; if the result obtained in step 4) is the initial solution, let r_min＝r，s_min＝s；

6) When the iteration number reaches the set upper limit, the real-time temperature is reduced by delta T, namely T_t←T_t- Δ T, go to step 7); otherwise, turning to the step 2);

7) when real-time temperature T_tGreater than algorithm end temperature T_fTurning to step 2); otherwise, the operation is finished.

2. The method for evaluating the intrusion tolerance capability of the multi-autonomous body network based on the simulated annealing algorithm according to claim 1, wherein: in step 3), the updating method of the subset pair S1 and S2 includes:

(3.1) initialization S₁S of_neighbors；

(3.2) generating a random number xi epsilon U (0, 1); when the random number xi is less than 1/3, from S₁In the method, a node is randomly selected and replaced by a slave S_neighborsRandomly selecting one node; when the random number xi is equal to or greater than 1/3 and less than 2/3, from S_neighborsRandomly selecting a node to add to the set S₁Performing the following steps; when the random number xi is equal to or greater than 2/3 and less than 1, the random number is S₁Deleting a node;

(3.3) from the set S₁Is sampled to obtain a new S₂And (4) collecting.

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