Detection of brute force attacks
The disclosed embodiments determine a plurality of anomaly indications for a plurality of corresponding time series. A multi-modal model is defined for each time series. A first distribution is compared against a time series when the time series values fall within a first range and a second distribution is compared against the time series when the time series values fall with a second range. Based on the comparison, an indication of anomaly is generated for the time series. The indicators of anomaly for each time series are then combined using Fisher's method in some embodiments. The resulting combined anomaly indication is used to determine whether a network is experiencing a brute force attack.
1. A method performed by hardware processing circuitry, comprising:
obtaining a first time series of operational parameter values of a device attached to a network;
comparing the operational parameter values of the first time series to a first parameter value range and a second parameter value range;
determining, based on the comparing, that the operational parameter values of the first time series are within the first parameter value range;
based on the determining, selecting, from a plurality of distributions, a first distribution;
comparing the first time series to the selected first distribution;
determining, based on the comparing the first time series, a first probability at which values of the operational parameter values in the first time series occur in the selected first distribution;
determining, based on the first probability, a likelihood of a brute force attack on the network;
based on the first time series, adjusting a boundary between the first parameter value range and the second parameter value range resulting in at least one of an updated first parameter value range or an updated second parameter value range; and
determining, based on the updated first parameter value range or the updated second parameter value range, a second likelihood of a brute force attack.
2. The method of claim 1 , further comprising performing, based on the likelihood, a mitigating action.
3. The method of claim 2 , wherein the mitigating action includes changing an access control policy of the network.
4. The method of claim 3 , wherein the changing of the access control policy comprises programmatically configuring a firewall of the network.
5. The method of claim 1 , wherein the adjusting of the boundary comprises updating a threshold value τ p defining the boundary between the first parameter value range and the second parameter value range, τ p defined according to:
τ p : =E [ Y|Y>Q p−1 ]
where:
E[ ] is an expected value function,
Y is the first time series,
t p is the threshold value between the first parameter value range and the second parameter value range or the updated first parameter value range and the updated second parameter value range, and
Q p is a qth quantile of a negative binomial distribution.
6. The method of claim 1 , wherein the adjusting of the boundary further comprises updating parameters defining the first distribution.
7. The method of claim 6 , wherein the parameters are updated via exponential smoothing and a grid of smoothing weights.
8. The method of claim 7 , where at least one parameter of the first distribution is updated according to:
Φ t+∈ =g Φ −1 [η t+∈ ],
where:
Φ t+∈ is the updated parameter,
g Φ is a link function for a parameter Φ,
η t+∈ ={tilde over (α)} θ *M Φ [y t+∈ |η t ]+(1−{tilde over (α)} θ ) *η t ,
where:
M Φ , is a central moment corresponding to the parameter Φ,
{tilde over (α)} θ is a smoothing weight,
η t is g Φ [Φ t ], and
y t+∈ is a sample value included in the first time series.
9. The method of claim 1 , further comprising:
determining a second time series for second operational parameter values of the device;
selecting, based on the second time series, a second distribution;
comparing the second time series to the selected second distribution;
determining, based on the comparing the second time series, a second probability at which second values in the second time series occur in the selected second distribution;
applying Fisher's method to the first probability and the second probability; and
based on the applying, generating a combined indicator of anomaly, wherein the determining of the likelihood of the brute force attack is further based on the combined indicator.
10. A system, comprising:
hardware processing circuitry;
one or more hardware memories storing instructions that when executed configure the hardware processing circuitry to perform operations comprising:
obtaining a first time series of operational parameter values of a device attached to a network;
comparing the operational parameter values of the first time series to a first parameter value range and a second parameter value range;
determining, based on the comparing, that the operational parameter values of the first time series are within the first parameter value range;
based on the determining, selecting, from a plurality of distributions, a first distribution;
comparing the first time series to the selected first distribution;
determining, based on the comparing the first time series, a first probability at which values of the operational parameter values in the first time series occur in the selected first distribution;
determining, based on the first probability, a likelihood of a brute force attack on the network;
based on the first time series, adjusting a boundary between the first parameter value range and the second parameter value range resulting in at least one of an updated first parameter value range or an updated second parameter value range; and
determining, based on the updated first parameter value range or the updated second parameter value range, a second likelihood of a brute force attack.
11. The system of claim 10 , the operations further comprising performing, based on the likelihood, a mitigating action.
12. The system of claim 11 , wherein the mitigating action includes changing an access control policy of the network.
13. The system of claim 12 , wherein the changing of the access control policy comprises programmatically configuring a firewall of the network.
14. The system of claim 10 , wherein the adjusting of the boundary comprises updating a threshold value τ p defining the boundary between the first parameter value range and the second parameter value range, τ p defined according to:
τ p : =E [ Y|Y>Q p−1 ]
where:
E[ ] is an expected value function,
Y is the first time series,
t p is the threshold value between the first parameter value range and the second parameter value range or the updated first parameter value range and the updated second parameter value range, and
Q p is a qth quantile of a negative binomial distribution.
15. The system of claim 10 , wherein the adjusting of the boundary further comprises updating parameters defining the first distribution.
16. The system of claim 15 , wherein the parameters are updated via exponential smoothing and a grid of smoothing weights.
17. The system of claim 16 , where at least one parameter of the first distribution is updated according to:
Φ t+∈ =g Φ −1 [η t+∈ ],
where:
Φ t+∈ is the updated parameter,
g Φ is a link function for a parameter Φ,
η t+∈ ={tilde over (α)} θ *M Φ [y t+∈ |η t ]+(1−{tilde over (α)} θ )*η t ,
where:
M Φ is a central moment corresponding to the parameter Φ,
{tilde over (α)} θ is a smoothing weight,
η t is g Φ [Φ t ], and
y t+∈ is a sample value included in the first time series.
18. The system of claim 10 , the operations further comprising modeling a distribution of the first time series as a finite mixture of distributions P1[Y| 1], . . . Pm[Y| m], where each parameter p is a stochastic process.
19. The system of claim 18 , wherein the first distribution is included in the finite mixture of distributions.
20. A non-transitory computer readable storage medium comprising instructions that when executed configure hardware processing circuitry to perform operations, comprising:
obtaining a first time series of operational parameter values of a device attached to a network;
comparing the operational parameter values of the first time series to a first parameter value range and a second parameter value range;
determining, based on the comparing, that the operational parameter values of the first time series are within the first parameter value range;
based on the determining, selecting, from a plurality of distributions, a first distribution;
comparing the first time series to the selected first distribution;
determining, based on the comparing the first time series, a first probability at which values of the operational parameter values in the first time series occur in the selected first distribution;
determining, based on the first probability, a likelihood of a brute force attack on the network;
based on the first time series, adjusting a boundary between the first parameter value range and the second parameter value range resulting in at least one of an updated first parameter value range or an updated second parameter value range; and
determining, based on the updated first parameter value range or the updated second parameter value range, a second likelihood of a brute force attack.