FIELD OF THE INVENTION
The present invention relates generally to the field of network security. More particularly, the present invention is related to methods for analysis of cyber network interactions among attackers, passive network sensors, and active network sensors using three-sided games, where each side can have multiple participants sharing the same goal. The method provides network security based on the analysis.
BACKGROUND
Network attacks include one-to-one attacks, one-to-many attacks, and many-to-one attacks. Existing network security methods suffer from high false positives, difficulty in detecting highly complex attacks, and the inability to adapt for detecting new types of attacks. Moreover, existing methods often perform attack identification in a passive manner by using only available alerts instead of actively seeking and prioritizing the most useful alerts to mitigate. Another aspect that is lacking with current methods is the inability to provide effective mitigation of network threats, predicting future attacks, and resolving multiple simultaneous attacks. For current methods, the recommendation of mitigation is usually provided in an ad hoc and heuristic manner, often independent of the situation awareness (SA) process, the user, or the importance of the network for operational considerations.
SUMMARY OF THE EMBODIMENTS
It is a feature of the present invention to provide network security in the form of three-sided game-theoretic analysis of the cyber network interactions among attackers, passive network sensors, and active network sensors. A honey net (e.g., including active network sensors) can act as a supportive side, which can be camouflaged in the network to help passive sensors detect and track cyber network attacks.
In accordance with an additional feature of the present invention, a system is provided that includes a computer programmed for three-side game-theoretic analysis of cyber network interactions among attackers, passive network sensors, and active network sensors. A honey net acts as a support side, which can be camouflaged in the network to help passive network sensors detect and track cyber network attacks, and which generally originate from attacking servers. Game theory is relatively a new application for cyber research, and the use of a honey net provides a unique aspect of the work that enhances game-theoretic developments over passive network sensors and active network sensors.
It is yet another feature of the present invention to utilize a geometry method based on three-dimensional action curves to numerically solve the uniquely three-side game modeled cyber security problem. The numerical game solution includes four features: first, it can quickly determine whether the game problem has one Nash equilibrium, multiple Nash equilibriums, or no Nash equilibrium; second, it can efficiently check if the equilibrium is a mixed or pure Nash; third, it can timely compute the (mixed) Nash equilibriums; and fourth, it also follows a Fictitious Play Concept. These four features provide an adaptive solution and can be applied in any partially observed cyber security system.
BRIEF DECRIPTION OF THE DRAWINGS
FIG. 1 illustrates a block diagram of a system in accordance with features of the present invention;
FIG. 2 is a concept level block diagram of the three-side game engine for cyber network security problems;
FIG. 3 depicts the system level flowchart of the three-side game model and the geometric solutions;
FIG. 4 depicts an exemplary three-side game in a matrix format;
FIG. 5 is an exemplary action curve and surface intersection which has purse active sensor strategy;
FIG. 6 depicts another exemplary action curve and surface intersection which is a typical mixed Nash equilibrium;
FIG. 7 is a flowchart showing the block 33, “determine a cell and line segment”, of FIG. 3.
FIG. 8 depicts an exemplary cell and line segment to be searched for the intersection of action surface (of attacker) and action curve (defender).
FIG. 9 is a flowchart showing the main process of “current set contains MNE?” route 71 in FIG. 7.
FIG. 10 is a flowchart showing the “is p insider a triangle (p1, p2, p3)?” route 93 in FIG. 9.
FIG. 11 depicts an exemplary cell and line segment containing the intersection of action surface (of attacker) and action curve (defender).
DETAILED DESCRIPTION OF EMBODIMENTS
The purpose of this invention is to develop three-side game theory based innovative situation awareness systems and methods for active network security and impact mitigation of adversarial attacks against cyber networks.
Referring to FIG. 1, there is shown an implementation of a cyber-network security system according to the invention in a local network having the passive and active network sensors deployed. The local network comprises N production server 141 to 14N. The network traffic can be monitored by a Snort based passive network sensor (PNS) 12a, which can be controlled by the PNS engine 12b. Some network requests can be routed to an active network sensor (ANS) 13b, which can interact with remote users in a virtual way. The ANS can be deployed based on Honeypot and Address Resolution Protocol Daemon (ARPD). The interaction scripts and strategies can be reconfigured via the ANS engine 13b. The attacker 10 can launch cyber-attacks to the local network via the Internet 11. The PNS engine and ANS engine can follow the mixed Nash equilibrium of the three-side game model shown in FIG. 2.
FIG. 2 shows the concept level framework of the three-side game engine. Attacker 2 may launch various cyber-attack weapons 21a, which are inputs to the game model. Attacks will get rewards 21b, which depend on the game model parameters 23, PNS strategies 25a, and ANS strategies 26a. Similarly, PNS 27 and ANS 28 can obtain their rewards 25b and 26b respectively. Their values are also partially determined by the attacker's choices. This reward dependence is the main modeling merit of game theory method: decisions should be made with the consideration of the opponents. To obtain the game solution of Mixed Nash equilibrium (MNE), the invention presents a geometric way 24 to determine and calculate the intersection point of attacker's action surface and defender's action curve. The action surface or action curve is set of one side's best response actions for his opponents' possible choices. In the three cyber game model, the ANS and PNS are coordinated to defend attackers. Therefore, given a combined PNS and ANS choices (hk, sk), the attacker will compute his best response rk. Since hk, sk and rk are all scalar values, the attacker's best response set is a surface, which is called an action surface. Similarly, for ANS and PNS, their combined best response is a curve, called an action curve.
FIG. 3 shows the system level flowchart of the invention. Block 30 creates a three-side game model based on a scenario or problem. For the general scenario in FIG. 1, the system states are defined as the probability vector of N servers:
(p11|1, p11|0, p21|1, p21|0, . . . pN1|1, pN1|0) (1)
where pi1|1 is the detection rate (DR), which is the probability that server i is flagged as attacked when it is actually attacked, pi1|0 is the false positive rate (FPR), which is the probability that server i is flagged as attacked when it is actually NOT attacked.
Given the system state vector p=(p11|1, p11|0, p21|1, p2 1|0, . . . )′, the reward functions for the attacker and defender are defined as
J
d(p)=Σi=1:N(ci1pi1|1−ci2pi0|1−ci3pi1|0) (2)
J
a(p)=Σi=1:N(vi1pis−vi2pif) (3)
where ci1, ci2, ci3 are the positive constants for server i; pi0|1=1−pi1|1 is the miss detection probability; vi1, vi2 are the value of server i and the cost of attacking server i; pis is the probability of successfully penetrate server i. The model includes pis=pi0|1pa(j), where pa (j) is the success rate of the selected attack (j). pif is the probability that an attack on server i is failed and pif=pi1|1+pi0|1(1−pa(j)). The three-side interaction is modeled as a matrix game. FIG. 4 depicts an exemplary three-side game in a matrix format. The game size (shown by 40) is determined by the possible strategies of the three sides. After all sides choose their strategies, a special 3D action curve or cube can be picked. For example, if attacker chooses r3, ANS chooses h3, and PNS chooses s3, then cube 41 is picked. Square 43 is the coordinated strategy of PNS and ANS. Square 42 tells the chosen attacker strategy. In the cube 41, there are two values obtained from equation (2) and (3), respectively.
The game in FIG. 4 is played by three sides in such a way that attacker chooses his strategy to maximize the Ja (eq. 3) in the picked cube (for example cube 41 in FIG. 4), while PNS and ANS choose their coordinated strategies to maximize the Jd (eq. 2) in the same cube, which depends on both attacker's and PNS/ANS combined choices.
To solve the three-sided game problem, this invention presents a geometric game solution to compute MNEs. The action curve (surface) based solution is depicted in block 31-34 of FIG. 3. Block 31 computes the action curve of PNS and ANS. For all possible attacker strategies, eq. (2) is maximized by choosing the coordinated PNS and ANS strategies. By connecting all these best responses of coordinated strategies, along with the chosen attacker strategies, block 31 obtains the defender action curve.
Block 32 computes the action surface of attacker. For any possible coordinated PNS and ANS strategies, eq. (3) is maximized by choosing the attacker strategy. Then block 32 connects these best responses of attacking strategies, along with the chosen coordinated defender strategies, to obtain the attacker action surface.
For the three-side game, an intersection of action curve and surface is a Nash strategy. If the intersection located exactly on these best response points, then the Nash strategy is a pure Nash equilibrium (PNE). Otherwise it is a mixed Nash equilibrium (MNE). PNE can be seemed a special case of MNE, so in this invention, MNEs can be used to solve the three-side game engine. Another advantage of MNE is that at least one MNE always exists for the three-side game model for cyber network security.
FIG. 5 is an exemplary action curve and surface intersection which has a pure active sensor strategy. 5100 is the point at attacker action surface when ANS and PNS choose the coordinated strategy (0, 0). 51a2 is the point at attacker action surface when ANS and PNS choose the coordinated strategy (10, 2). 507 is the point at the defender action curve when attacker takes no. 7 strategy. 505 is the point at the defender action curve when attacker takes no. 5 strategy. 52a and 525 are the contour lines of the attacker action surface when the attacking rate is 50% and 100% of the maximum attacking speed. From the plot in FIG. 5, it is obvious that PNS will play his No. 10 strategy and the intersection occurs between 504 and 505 at the action curve.
FIG. 6 depicts another exemplary action curve and action surface intersection which is a typical mixed Nash equilibrium. From the plot in FIG. 6, it is difficult to find location of the intersection. Therefore, the invention presents a geometric way (FIG. 7) to find cells in action surface and the related line segments in action curve so that they contains the intersection points.
FIG. 7 is a flowchart showing the “determine a cell and line segment” block 33 in the process of FIG. 3. Block 70 is to initialize the searching by setting the sizes of the attacker action set, the PNS action set, and the ANS action set. It also set the initial position of the searching. Block 71 is to test whether current action surface cell and action curve segment contain the intersection. The details of this block are described in FIG. 8. Block 72 saves the current decision set if it contains the intersection. Otherwise, the process will search next set (surface cell and curve segment). This decision can be decomposed in Block 73-77. After all sets are searched, the process will exit (Block 78) with saved sets containing the intersection points, which are MNEs. The invention will further calculate the MNEs in Block 34 of FIG. 3.
FIG. 8 depicts an exemplary cell and line segment to be searched for the intersection of action surface (of attacker) and action curve (defender). 801-804 determine the action surface cell projected to ANS and PNS strategy space (like 43 in FIG. 4). 811 and 812 define the action curve segment, where r1 and r2 are the consecutive attacker strategies. Since all 6 points are on the action surface or action curve, the locations in 3-D spaces can be determined. This problem, of whether the set contains an intersection point, can be solved via the following way:
- if r1r2 go through Δ123, true, exit;
- else if r1r2 go through Δ124, true, exit;
- else if r1r2 go through Δ134, true, exit;
- else if r1r2 go through Δ234, true, else false;
where Δ123 is the triangle determined by points 801, 802, and 803. Similar notes for Δ124, Δ134, and Δ234. The geometric way to test whether a line segment go through a triangle is presented in FIG. 9.
FIG. 9 is a flow chart of testing whether a line segment goes through a triangle. This part is the main process of “current set contains MNE?” route 71 in FIG. 7. Block 90 specifies the input and output structure. The inputs are the three points of the triangle and the line segment. The output is yes or no. Block 91 calculates the intersection point of the plane, which contains the triangle, and the line, which contains the line segment. The detail algorithm is listed as follows:
n=cross((p2−p1), (p3−p1)); % calculate the normal vector
if (n′*(pt−ps)==0), return false; % no intersection
r=n′*(p1−ps)/(n′*(pt−ps)); % calculate the ratio on the normal vector
p=ps+r*(pt−ps); % calculate the intersection point based on the ratio
Note that the intersection may not be located in the triangle or in the line segment even if the intersection point exists. Therefore, blocks 92-95 are used here to further test whether the intersection point is in the triangle AND in the line segment. Block 92 is clear while block 93 needs to be expanded and explained in FIG. 10.
FIG. 10 is a flow chart showing the “is p insider a triangle (p1, p2, p3)?” route 93 in FIG. 9. Block 100 is to specify the input structure, which contains the three points of the triangle and a point to be tested. Given that the p and triangle are in the same plane (since p is the intersection point, p is in the plane contains the triangle), the geometric test method is based on the following observation. A point p is in the triangle (pl,p2,p3), if and only if
p and p1 on the same side of the line through p2 and p3, AND
p and p2 on the same side of the line through p1 and p3, AND
p and p3 on the same side of the line through p1 and p2.
The invention uses the following geometric algorithm to test where two points (p1, and p) on the same side of a line (p2, p3):
cp1=cross(p2−p3, p−p3); % calculate the cross product
cp2=cross(p2−p3, p1−p3); % calculate the cross product
IF cp1′*cp2>=0, same side, ELSE different side.
Blocks 101-106 depict the whole test processing of whether p insider a triangle (p1, p2, p3).
The next step (block 34 of FIG. 3) is to compute the MNE for a given action surface cell and action curve segment, which contains the intersection point. FIG. 11 depicts an exemplary cell and line segment containing the intersection of action surface (of attacker) and action curve (defender). Points 1101-1104 define the cell and point 111 is the intersection point. The exact position (in three dimensions: PNS s*, ANS h*, and Attacker r*, see FIG. 4 for visual illustration) of 111 can be formulated as
S*=λ
1
s
1+λ2s2+λ3s3+(1−λ1−λ2−λ3)s4 (4)
h*=λ
1
h
1
+λ
2
h
2+λ3h3+(1−λ1−λ2−λ3)h4 (5)
r*=κ
1
r
1+(1−κ1)r2 (6)
where 0≦λi≦1, 0≦(λ1+λ2+λ3)≦1, and 0≦κ1≦1. r1 and r2 are the attacking strategies of the two end points of active curve segment. Then the rewards, J, are
J*
d
=J
d (s*, h*, r*)=fd(λ1, λ2, λ3, κ1) (7)
J*
a
=J
a (s*, h*, r*)=fa(λ1, λ2, λ3, κ1) (8)
Since (s*, h*, r*) is a mixed Nash equilibrium, the following equations apply:
∂fd/∂λ1=0 (9)
∂fd/∂λ2=0 (10)
∂fd/∂λ3=0 (11)
∂fa/∂κ1=0 (12)
where λ1, λ2, λ3, and κ1 can be obtained by solving the equations (9-12). Then the MNE can be computed by eq. 4-6.
Block 35 of FIG. 3 is implemented the obtain MNE. For the defender side, the PNS will play s1 strategy with probability λ1, s2 strategy with probability λ2, s3 strategy with probability λ3, and s4 strategy with probability 1−λ1−λ2−λ3. The ANS will play h1 strategy with probability λ1, h2 strategy with probability λ2, h3 strategy with probability λ3, and h4 strategy with probability 1−λ1−λ2−λ3. Similarly, for the attacker side, the attacker will play the r1 strategy with probability κ1, and the r2 strategy with probability 1−κ1. To implement the MNE, two uniformly distributed random variables over [0, 1], Xd for defender and Xa for attacker, will be created. Each time, the random values will be used to determine which pure strategy to use. If Xd∈[0, λ1], then PNS takes s1 and ANS take h1. If Xd∈(λ1, λ1+λ2], PNS takes s2 and ANS take h2. If Xd∈(λ1+λ2, λ1+λ2+λ3], PNS takes s3 and ANS take h3. If Xd∈(λ1+λ2+λ3, 1], PNS takes s4 and ANS take h4. Similar, if Xa∈[0, κ1], the attacker will apply the r1 strategy. If Xa∈[κ1, 1], the attacker will apply the r2 strategy.
Block 36 and 37 of FIG. 3 are designed to let system update the states defined in eq. (1). Then the game can be updated with the new system states. Accordingly, the three-sided game solution can be calculated using the geometric method of the present invention, which provides a closed loop control paradigm.
For cyber applications, game theory is a relatively new concept and the use of a honey net is a unique aspect of the work that enhances game-theoretic developments over active and passive sensors. To numerically solve the uniquely three-side game modeled cyber security problem, a geometry method based on action surface and action curve is developed. To summarize, the present numerical game solution has four features: first, it can quickly determine whether the game problem has one Nash equilibrium, multiple Nash equilibriums, or no Nash equilibrium; second, it can efficiently check the equilibrium is a mixed or pure Nash; third, it can timely compute the (mixed) Nash equilibriums; and fourth, it also follows a Fictitious play concept, from which the solution is an adaptive one and can be applied for any partially observed cyber security system.
Patent Application
20170257396
