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PREDICTING ZERO-DAY SOFTWARE VULNERABILITIES THROUGH DATA

MINING--SECOND PRESENTATION

Su Zhang

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Quick Review. Data Source – NVD. Six Most Popular/Vulnerable Vendors For Our

Experiments. Why The Six Vendors Are Chosen. Data Preprocessing. Functions Available For Our Approach. Statistical Results Plan For Next Phase.

Outline

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Quick Review

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National Vulnerability Database◦ U.S. government repository of standards based

vulnerability management data.◦ Data included in each NVD entry

Published Date Time Vulnerable software’s CPE Specification

◦ Derived data Published Date Time Month Published Date Time Day Two adjacent vulnerabilities’ CPE diff (v1,v2)Version diff CPE Specification Software Name Adjacent different Published Date Time ttpv Adjacent different Published Date Time ttnv

Source Database – NVD

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Linux: 56925 instances Sun: 24726 instances Cisco: 20120 instances Mozilla: 19965 instances Microsoft: 16703 instances Apple: 14809 instances.

Six Most Vulnerable/Popular Vendors

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r e s t

Adob

eIB

MPh

p

Appl

e

Micro

soft

Moz

illa

Cisco Su

nLinu

x0

10000

20000

30000

40000

50000

60000

Instances Table

Instances

Why We Only Choose Instances Of Pop Vendors—Instances Table

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r e s tHP

Linu

x

Moz

ila

Cisco

Oracle

IBMAp

ple

Sun

Micro

soft

0

500

1000

1500

2000

2500

Vulnerability Table

Vul_Num

Why We Only Choose Instances Of Pop Vendors—Vulnerability Table

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Huge size of nominal types (vendors and software) will result in a scalability issue.

Top six take up 43.4% of all instances.

We have too many vendors(10411) in NVD.

The seventh most popular/vulnerable vendor is much less than the sixth.

Vendors are independent for our approach.

Why We Only Choose Instances Of Pop Vendors

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NVD data—Training/Testing dataset◦ Starting from 2005 since before that the data

looks unstable.◦ Correct some obvious errors in NVD(e.g.

“cpe:/o:linux:linux_kernel:390”).

Attributes◦ Published time : Only use month and day. ◦ Version diff: A normalized difference between two

versions.◦ Vendor: Removed.

Data Preprocessing

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Attributes◦ “Group” vulnerabilities published at the same

day- we can guarantee ttnv/ttpv are non-zero values.

◦ ttnv is the predicted attribute.

For each software◦ Delete its first bunch of instances.◦ Delete its last bunch of instances.

Data Preprocessing(cont)

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v1= 3.6.4; v2 = 3.6; MaxVersionLength=4; v1= expand ( v1, 4 ) = 3.6.4.0 v2 =expand ( v2, 4 ) = 3.6.0.0 diff(v1, v2) = (3-3) * 1000 +(6-6) * 100-1

+(4-0) * 100-2

+(0-0) * 100-3 = 4 E -4

version diff Calculation

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Vendor, soft, version, month, day, vdiff, ttpv, ttnv linux,kernel,2.6.18, 05, 02, 0, 70, 5 linux,kernel,2.6.19.2, 05, 07,1.02E-4,5, 281

An Example

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Least Mean Square. Linear Regression Multilayer Perceptron. SMOreg. RBF Network. Gaussian Processes.

Functions Available For Our Approach On Weka

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Function: Linear Regression Training Dataset: 66% Linux(Randomly

picked since 2005). Test Dataset: the rest 34% Test Result:

◦ Correlation coefficient 0.5127◦ Mean absolute error 11.2358◦ Root mean squared error 25.4037◦ Relative absolute error 107.629 %◦ Root relative squared error 86.0388 %◦ Total Number of Instances 17967

Several Statistical Results

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Correlation Coefficient

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Mean absolute error :

Root mean square error:

Several Definitions About “Error”

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Relative absolute error:

Root relative squared error:

Several Definitions About “Error”(Cont)

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Function: Least Mean Square Training Dataset: 66% Linux(Randomly

picked since 2005). Test Dataset: the rest 34% Test Result:

◦ Correlation coefficient -0.1501◦ Mean absolute error 7.6676◦ Root mean squared error 30.6038◦ Relative absolute error 73.449 %◦ Root relative squared error 103.6507 %◦ Total Number of Instances 17967

Several Statistical Results

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Function: Multilayer Perceptron Training Dataset: 66% Linux(Randomly

picked since 2005). Test Dataset: the rest 34% Test Result:

◦ Correlation coefficient 0.9886◦ Mean absolute error 0.4068◦ Root mean squared error 4.6905◦ Relative absolute error 3.7802 %◦ Root relative squared error 15.1644 %◦ Total Number of Instances 17967

Several Statistical Results

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Function: RBF Network Training Dataset: 66% Linux(Randomly picked since

2005). Test Dataset: the rest 34% Test Result:

◦ Linear Regression Model ttnv = -15.3206 * pCluster_0_1 + 21.6205

◦ Correlation coefficient 0.1822◦ Mean absolute error 10.5857◦ Root mean squared error 29.048 ◦ Relative absolute error 101.4023 %◦ Root relative squared error 98.3814 %◦ Total Number of Instances 17967

Several Statistical Results

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Linear Regression: Not accurate enough but looks promising (correlation coefficient: 0.5127).

Least Mean Square: Probably not good for our approach(negative correlation coefficient).

Multilayer Perceptron: Looks good but it couldn’t provide us with a linear model.

Summary Of Current Results

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SMOreg: For most vendors, it takes too long time to finish (usually more than 80 hours).

RBF Network: Not very accurate.

Gaussian Processes: Runs out of heap memory for most of our experiments.

Summary Of Current Results (Cont)

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Adding CVSS metrics as predictive attributes.

Binarize our predictive attributes (e.g. divide ttnv/ttpv into several categories.)

Use regression SVM with multiple kernels.

Possible Ways To Improve The Accuracy Of Our Models.

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Try to find out an optimal model for our prediction.

Try to investigate how to apply it with MulVAL if we get a good model. Otherwise, find out the reason why it is not accurate enough.

Plan For Next Phase

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Thank you!