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Current issue : #57 | Release date : 2001-11-08 | Editor : Phrack Staff
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                             ==Phrack Inc.==

               Volume 0x0b, Issue 0x39, Phile #0x0c of 0x12

|=-----------------=[ Network Intrusion Detection System ]=--------------=|
|=--------------=[ On Mass Parallel Processing Architecture ]=-----------=|
|=------------=[ Wanderley J. Abreu Jr.  <storm@stormdev.net> ]=---------=|


"Nam et Ipsa Scientia Potestas Est" - Francis Bacon 


1 ----|Introduction:

	One of the hardest challenges of the security field is to detect with
a 100% certainty malicious attacks while they are occuring, and taking the
most effective method to log, block and prevent it from happening again.
	The problem was solved, partially. About 19 years ago, Intrusion 
Detection System concept came to fit the market wishes to handle security 
problems concerning Internal/External attacks, with a low or medium cost, 
without major needs for trained security personnel, since any network 
administrator "seems" to manage them well.
	But then we came across some difficulties with three demands of 
anomaly and policy based IDS which are: effectiveness, efficiency and ease 
of use.
	This paper focuses on enhancing the bayesian detection rate by 
constructing a Depth-Search algorithm based IDS on a mass parallel processing 
(MPP) environment and give a mathematical aproach to effectiveness of this 
model in comparision with other NIDS.
	One Problem with building any software on such an expensive 
environment,like most MPPs, is that it is limited to a very small portion 
of computer community, thus we'll focus on High Performance Computer
Cluster called "Class II - Beowulf Class Cluster" which is a set of 
tools developed by NASA. These tools are used to emulate MPP environment 
built of x86 computers running under Linux Based Operating Systems.         
	The paper does not intend to offer the absolute solution for false 
positives and false negatives generated by Network-Based IDS, but it gives one 
more step towards the utopia.



2 -----|Bayesian Detection Rate (BDR):


		In 1761, Reverend Thomas Bayes brought us a concept for 
govern the logical inference, determining the degree of confidence we may 
have, in various possible conclusions, based on the body of 
evidence available. Therefore, to arrive at a logically defensible prediction
one must use Bayes theorem.
		The Bayesian Detection Rate was first used to measure IDS 
effectiveness in Mr. Stefan Axelson paper "The Base-Rate Fallacy and its 
Implications for the Difficulty of Intrusion Detection" presented on RAID 99 
which gives a realistic perspective on how "False Alarm" rate can limit 
the performance of an IDS.
		As said, the paper aims to increase the detection rate 
reducing false alarms on the IDS model, therefore we must know the principles
of Bayesian Detection Rate (BDR):
		
				P(D|H)P(H)
		 P(H|D) = -------------------------
			 P(D|H)P(H) + P(D|H')P(H')

Let's use a simple example to ilustrate how Bayes Theorem Works:

		Suppose that 2% of people your age and heredity have cancer. 
		Suppose that a blood test has been developed that correctly 
gives a positive test result in 90% of people with cancer, and gives a false
positive in 10% of the cases of people without cancer. Suppose you take
the test, and it is positive. What is the probability that you actually 
have cancer, given the positive test result? 
		First, you must identify the Hypothesis, H, the Datum, D, 
and the probabilities of the Hypothesis prior to the test, and the hit rate
and false alarm rates of the test. 

H = the hypothesis; in this case H is the hypothesis that you have cancer, 
and H' is the hypothesis that you do not.

D = the datum; in this case D is the positive test result.

P(H) is the prior probability that you have cancer, which was given in 
the problem as 0.02.

P(D|H) is the probability of a positive test result GIVEN that you have cancer.
This is also called the HIT RATE, and was given in the problem as 0.90.

P(D|H') is the probability of a positive test result GIVEN that you do not 
have cancer. This is also called the FALSE ALARM rate, and was given as 0.10. 

P(H|D) is the probability that you have cancer, given that the test was 
positive. This is also called the posterior probability or Bayesian Detection 
Rate. 

In this case it was 0.155(16% aprox., i'd not bet the rest of my days on 
this test). 

		Applying it to Intrusion Detection Let's say that:
			Ii -> Intrusion behaviour
			Ij -> Normal behaviour
			Ai -> Intrusion Alarm
			Aj -> No Alarm

		Now, what a IDS is meant to do is alarm us when log pattern
really indicates an intrusion, so what we want is P(Ii|Ai), or the Bayesian 
Detection Rate.


		 	           P(Ii) P(Ai|Ii)	
  	        P(Ii|Ai) = ----------------------------------
			    P(Ii) P(Ai|Ii) + P (Ij) P(Ai|Ij)

Where:


True Positive Rate P(Ai|Ii):
			
		      Real Attack-Packets Detected 	
         P(Ai|Ii) = ----------------------------------
		      Total Of Real Attack-Packets		
			
False Positive Rate P(Ai|Ij):
			
			          False Attack-Packets Detected	
	 P(Ai|Ij) =  -------------------------------------------------------
	 	      (Total Of Packets) - (Total Of Real Attack-Packets) 	

			
Intrusive Behaviour P(Ii):
			
	                                 1
 	 P(Ii) = -------------------------------------------------------------  
		            	     Total of Packets
	   	    -----------------------------------------------------
		     (Number of Packets Per Attack) * (Number of Attacks)

Non-Intrusive Behaviour P(Ij):
			
	P(Ij) = 1 - P(Ii)


		By now you should realize that the Bayesian Detection Rate 
increases if the False Positive Rate decreases.
		


3 -----|Normal Distribution:

	To detect a raise on BDR we must know what is the standard BDR 
for actual Intrusion Detection Systems so we'll use a method called Normal 
Distribution.
	Normal distributions are a family of distributions that have the 
same general shape. They are symmetric with scores more concentrated in the
middle than in the tails. Normal distributions are sometimes described as
bell shaped. The area under each curve is the same. 
The height of a normal distribution can be specified mathematically in terms
of two parameters: 

	+the mean (m) and the standard deviation (s). 

	+The height (ordinate) of a normal curve is defined as: 

					1
   			f(x)= ------------------ * e ^(-(x-m)^2)/2s^2
			        /-------------|
			      \/    2*p*s^2

	Where m is the mean and s is the standard deviation, p is the 
constant 3.14159, and e is the base of natural logarithms and is equal 
to 2.718282. x can take on any value from -infinity to +infinity.

3.1 ---------| The Mean:

		     The arithmetic mean is what is commonly called the
average and it can be defined as:
	
		   x1 + x2 + x3 + ... + xn 
	       m = -----------------------
			    n

		Where n is the number of scores entered.


3.2 ---------| The Standard Deviation:
		
	 The Standard Deviation is a measure of how spread out a distribution
is. 
         It is computed as the average squared deviation of each number from
its mean:

		(x1 - m) ^2 + (x2 - m) ^2 + (x3 - m) ^2 + ... + (xn - m) ^2 	
         s^2 = -------------------------------------------------------------
		  		       n


	Where n is the number of scores entered.
	We'll define a experimental method in which X will be the BDR for
the most known IDS from market and we'll see how much our protype based on
MPP plataform will differ from their results with the Normal Distribution 
Method and with the Standard Deviation. 		



4 ------|Experimental Environment:

	Now we should gather experimental information to trace some standard
to IDS BDR:
	Let's take the default installation of 10 IDS plus our prototype, 11
in total running at this configuration:

		*Pentium 866 MHZ 
	   	*128 MBytes RAM
		*100 Mb/s fast Ethernet Adapter(Intel tulip based(2114X) )
		*1Megabyte of synchronous cache
		*Motherboard ASUS P3BF
		*Total of 30 gigabytes of HD capacity Transfer Rate of 15 Mb/s

	The Experiment will run for 22 days. Each IDS will run separately 
for 2 days.
	We'll use 3 Separate Subnets here 192.168.0.0/26 Netmask 
255.255.255.192, 192.168.0.129/26 Netmask 255.255.255.192, And a Real IP 
Network, 200.200.200.x.
	The IDS can only differ on OS aspect and methods of detection, 
but must still mantain the same node configuration.
	We'll simulate, random network usage and 4 intrusion attacks 
(4 packets) until the amount of traffic reaches around 100,000 packets 
from diferent protocols.
	The gateway (host node) remains routing or seeing packets of the 
Internal network, Internet, WAN, etc.
                -------------------
                |      SWITCH     |
                -------------------
		       | |  |______DMZ ____>Firewall___>Router___> Internet
     	               | |          |
      		       | |_________ |  __________ LAN ____>
		       _____________|          | | |
    	  	       |                       -----     
    		     -----        HOST NODE    |   |      -------
   		     |   |      (login  node)  |   |      |     |---
 		     |   |                     |   | ---- |     |   |
    		     |   |                     -----      -------   |
    		     -----                     node       |ooooo|   _
    		      node                     one        |ooooo|  | |
                    two(IDS)                (gateway)     -------   -
                                                       Keyboard/Mouse
                                                           Monitor


4.1 -----|MPP Environment:

	Now we must define a network topology and a standard operating 
system for our prototype.
	The gateway host is in the three networks at the same time and it 
will handle the part of the software that will gather packet information, 
process a Depth-1st search and then transmit the supicious packets to the 
other hosts.
	The hardware will be:
	 	*3 Pentium II 400 MHZ 
		*128 Megabytes RAM
		----------------------	
		*1 Pentium III 550 MHZ
		*512 Megabytes RAM
		----------------------
		*Motherboard ASUS P3BF
		*Total of 30 gigabytes of HD capacity Transfer Rate of 15 Mb/s
		*1Megabyte of synchronous cache
		*100 Mb/s fast Ethernet Adapter ( Intel tulip based (2114X) )
	The OS will be the Extreme Linux distribution CD which comes with all 
the necessary components to build a Cluster.
	Note that we have the same processing capability of the other NIDS 
systems (866 MHZ), we'll discuss the cost of all environments later.
 	
              -------------------
              |      SWITCH     |
              -------------------
      __________|   |  | | |  |______DMZ ____>Firewall___>Router___> Internet
      |       ______|  | | |          |
      |       |      __| | |          |               __________ LAN ____>
      |       |      |     |          |              |
    -----   -----  -----   |          |		    -----     
    |   |   |   |  |   |  -----       |_____________|   |      -------
    |   |   |   |  |   |  |   |                     |   |      |     |---
    |   |   |   |  |   |  |   |        HOST NODE    |   | ---- |     |   |
    -----   -----  -----  |   |       (login  node) -----      -------   |
    node    node   node   -----                     node       |ooooo|   _
    five    four   three   node                     one        |ooooo|  | |
                           two                   (gateway)     -------   -
                                                             Keyboard/Mouse
                                                                Monitor

	
	
5 ------|The Experiment:

Tested NIDS Were:

+SNORT
+Computer Associates Intrusion Detection System
+Real Secure
+Shadow
+Network Flight Recorder 
+Cisco NetRanger
+EMERALD (Event Monitoring Enabling Response to Anomalous Live Disturbances)
+Network Associates CyberCop
+PENS Dragon Intrusion Detection System
+Network ICE
+MPP NIDS Prototype

5.1 ------|Results:


----|Snort


False positives - 7
False Negatives - 3
True  Positives - 1


                 1
P(Ii) = -------------------- = 2.5 * 10^-4 
               1*10^5
	      --------
	        1*4

P(Ij) = 1 - P(Ii) = 0.99975

P(Ai|Ii) = 1/4 = 0.25

P(Ai|Ij) = 7/99996 = 7.0 * 10^-5


                       (2.5 * 10^-4) * (2.5^-10) 	                
BDR =  ------------------------------------------------------------- = 0.4718
        (2.5 * 10^-4) * (2.5^-10) + (9.9975 * 10^-1) * (7.0 * 10^-5)




----|Computer Associates Intrusion Detection System


False positives - 5
False Negatives - 2
True  Positives - 2
 


                 1
P(Ii) = -------------------- = 2.5 * 10^-4 
               1*10^5
	      --------
	        1*4

P(Ij) = 1 - P(Ii) = 0.99975

P(Ai|Ii) = 2/4 = 0.50

P(Ai|Ij) = 5/99996 = 5.0 * 10^-5


                       (2.5 * 10^-4) * (5.0^-10) 	                
BDR =  ------------------------------------------------------------- = 0.7143
        (2.5 * 10^-4) * (5.0^-10) + (9.9975 * 10^-1) * (5.0 * 10^-5)



----|Real Secure


False positives - 6
False Negatives - 2
True  Positives - 2



                 1
P(Ii) = -------------------- = 2.5 * 10^-4 
               1*10^5
	      --------
	        1*4

P(Ij) = 1 - P(Ii) = 0.99975

P(Ai|Ii) = 2/4 = 0.50

P(Ai|Ij) = 6/99996 = 6.0 * 10^-5


                       (2.5 * 10^-4) * (5.0^-10) 	                
BDR =  ------------------------------------------------------------- = 0.6757
        (2.5 * 10^-4) * (5.0^-10) + (9.9975 * 10^-1) * (6.0 * 10^-5)


----|Network Flight Recorder 

False positives - 5
False Negatives - 1
True  Positives - 3



                 1
P(Ii) = -------------------- = 2.5 * 10^-4 
               1*10^5
	      --------
	        1*4

P(Ij) = 1 - P(Ii) = 0.99975

P(Ai|Ii) = 3/4 = 0.75

P(Ai|Ij) = 5/99996 = 5.0 * 10^-5


                       (2.5 * 10^-4) * (7.5^-10) 	                
BDR =  ------------------------------------------------------------- = 0.7895
        (2.5 * 10^-4) * (7.5^-10) + (9.9975 * 10^-1) * (5.0 * 10^-5)


----|Cisco NetRanger


False positives - 5
False Negatives - 3
True  Positives - 1


                 1
P(Ii) = -------------------- = 2.5 * 10^-4 
               1*10^5
	      --------
	        1*4

P(Ij) = 1 - P(Ii) = 0.99975

P(Ai|Ii) = 1/4 = 0.25

P(Ai|Ij) = 5/99996 = 5.0 * 10^-5


                       (2.5 * 10^-4) * (2.5^-10) 	                
BDR =  ------------------------------------------------------------- = 0.5556
        (2.5 * 10^-4) * (2.5^-10) + (9.9975 * 10^-1) * (5.0 * 10^-5)


----|EMERALD

False positives - 7
False Negatives - 3
True  Positives - 1



                 1
P(Ii) = -------------------- = 2.5 * 10^-4 
               1*10^5
	      --------
	        1*4

P(Ij) = 1 - P(Ii) = 0.99975

P(Ai|Ii) = 1/4 = 0.25

P(Ai|Ij) = 7/99996 = 7.0 * 10^-5


                       (2.5 * 10^-4) * (2.5^-10) 	                
BDR =  ------------------------------------------------------------ = 0.4718
        (2.5 * 10^-4) * (2.5^-10) + (9.9975 * 10^-1) * (7.0 * 10^-5)


----|CyberCop


False positives - 4
False Negatives - 2
True  Positives - 2



                 1
P(Ii) = -------------------- = 2.5 * 10^-4 
               1*10^5
	      --------
	        1*4

P(Ij) = 1 - P(Ii) = 0.99975

P(Ai|Ii) = 2/4 = 0.50

P(Ai|Ij) = 4/99996 = 4.0 * 10^-5


                       (2.5 * 10^-4) * (5.0^-10) 	                
BDR =  ------------------------------------------------------------ = 0.7576
        (2.5 * 10^-4) * (5.0^-10) + (9.9975 * 10^-1) * (4.0 * 10^-5)


----|PENS Dragon Intrusion Detection System

False positives - 6
False Negatives - 2
True  Positives - 2



                 1
P(Ii) = -------------------- = 2.5 * 10^-4 
               1*10^5
	      --------
	        1*4

P(Ij) = 1 - P(Ii) = 0.99975

P(Ai|Ii) = 2/4 = 0.50

P(Ai|Ij) = 6/99996 = 6.0 * 10^-5


                       (2.5 * 10^-4) * (5.0^-10) 	                
BDR =  ------------------------------------------------------------- = 0.6757
        (2.5 * 10^-4) * (5.0^-10) + (9.9975 * 10^-1) * (6.0 * 10^-5)


----|Network ICE

False positives - 5
False Negatives - 3
True  Positives - 1



                 1
P(Ii) = -------------------- = 2.5 * 10^-4 
               1*10^5
	      --------
	        1*4

P(Ij) = 1 - P(Ii) = 0.99975

P(Ai|Ii) = 1/4 = 0.25

P(Ai|Ij) = 5/99996 = 5.0 * 10^-5


                       (2.5 * 10^-4) * (2.5^-10) 	                
BDR =  ------------------------------------------------------------- = 0.5556
        (2.5 * 10^-4) * (2.5^-10) + (9.9975 * 10^-1) * (5.0 * 10^-5)


----|Shadow

False positives - 3
False Negatives - 2
True  Positives - 2



                 1
P(Ii) = -------------------- = 2.5 * 10^-4 
               1*10^5
	      --------
	        1*4

P(Ij) = 1 - P(Ii) = 0.99975

P(Ai|Ii) = 2/4 = 0.50

P(Ai|Ij) = 3/99996 = 3.0 * 10^-5


                       (2.5 * 10^-4) * (5.0^-10) 	                
BDR =  ------------------------------------------------------------- = 0.8065
        (2.5 * 10^-4) * (5.0^-10) + (9.9975 * 10^-1) * (3.0 * 10^-5)


----|MPP NIDS Prototype

False positives - 2
False Negatives - 1
True  Positives - 3



                 1
P(Ii) = -------------------- = 2.5 * 10^-4
               1*10^5
	      --------
	        1*4

P(Ij) = 1 - P(Ii) = 0.99975

P(Ai|Ii) = 3/4 = 0.75

P(Ai|Ij) = 2/99996 = 2.0 * 10^-5


                       (2.5 * 10^-4) * (7.5^-10) 	                
BDR =  ------------------------------------------------------------- = 0.9036
        (2.5 * 10^-4) * (7.5^-10) + (9.9975 * 10^-1) * (2.0 * 10^-5)



4.2 -------|Normal Distribution

	Using the normal distribuiton method let us identify, for a scale from
1 to 10, what's the score of our NIDS Prototype:


---|The Average BDR for NIDS test was:


          0.4718+0.7143+0.6757+0.7895+0.5556+0.4718+...+0.8065+0.9036
m(BDR) = -------------------------------------------------------------
				     11

m(BDR) =  0.6707


---|The Standard Deviation for NIDS test was:

	    (0.4718 - 0.6707)^2+(0.7143 - 0.6707)^2+...+(0.9036 - 0.6707)^2 	
s(BDR)^2 = ----------------------------------------------------------------
					11

s(BDR) = 0.1420

---|The Score

	The mean is 67.07(m) and the standard deviation is 14.2(s). Since 
90.36(X) is 23.29 points above the mean (X - m = 23.29) and since a standard 
deviation is 14.2 points,there is a distance of 1.640(z) standard deviations 
between the 67.07 and 90.36 (z=[23.29/14.2]) plus 0,005 for rounds and  
5.0 for our average standard score. The score (z) can be computed using the 
following formula:

	                             X - m
	                        Z = -------- 
                                       s
	
	If you get a positive number for Z  then  apply (z = z + 0.005 + 5.0)
	If you get a negative number for Z  then  apply (z = z - 0.005 + 5.0)
		
	You should consider just the two first decimal places:
	
	So for our prototype we'll get:
	z = 1.640 + 0.005 + 5.0
	z = 6.64
	
	Our prototype scored 6.64 in our test, at this point the reader is 
encouraged to make the same calculation for all NIDS, you'll see that our 
prototype achieved the best score of all NIDS we tested.


6 -------|Why?


	Why our prototype differs so much from the rest of the NIDS, if it
was built under almost the same concepts?
	
6.1 ---|E,A,D,R AND "C" Boxes
	
	Using the CIDF (Common Intrusion Detection Framework) we have 4 basic
boxes, which are:

	E - Boxes, or event generators, are the sensors; Their Job is to 
detect events and push out the reports.
	A - Boxes receive reports and do analysis. They might offer a 
prescription and recommend a course of action.
	D - Boxes are database components; They can determine wheter an 
IP address or an attack has been seen before, and they can do trend analysis
	R - Boxes can take the input of the E, A and D Boxes and Respond to 
the event

	Now what are the "C" - Boxes? They are Redundancy Check boxes, 
they use CRC methods to check if a True Positive is really a True Positive or 
not. 
	The C-Boxes can tell If an E - Box generates a rightful report or an 
A - Box generates a real true positive based on that report.
	Because we're dealing with a MPP Enviroment this node can be at all 
machines dividing the payload data by as much as boxes you have.

6.2 ---|CISL


   	Our prototype Boxes use a language called CISL (Common Intrusion 
Specification Language) to talk with one another and it convey the following 
kinds of information:
       +Raw event information: Audit Trail Records and Network Traffic
       +Analysis Results: Description of System Anomalies and Detected Attacks
       +Response Prescriptions: Halt Particular Activities or modify 
	component security specifications
	

6.3 ---|Transparent NIDS Boxes

	All but some E-Boxes will use a method comonly applied to firewalls 
and proxies to control in/out network traffic to certain machines. It's Called
"Box Transparency", it reduces the needs for software replacement and user
retain.
	It can control who or what is able to see the machine so all
unecessary network traffic will be reduced by a minimum.

6.4 ---|Payload Distribution And E-Box to A-Box Tunneling

	Under MPI (Message Passing Interface) programming environment, using
Beowulf as Cluster Plataform, we can distribute network payload traffic
parsing of A - Boxes every machine in the cluster, maximizing the A - Box 
perfomance and C - Box as well. 
	All other network traffic than the report data that come from E-Boxes
by a encrypted tunneling protocol, is blocked in order to maximize the cluster 
data transfer and the DSM (Distributed Shared Memory).


 
7 -------|Conclusions

	Altough Neither Attack Method nor the NIDS Detection Model were
considered on this paper, it's necessary to add that no one stays with a NIDS 
with their default configuration, so you can achieve best scores with your
well configured system. 
	You can also score any NIDS scope with this method and it gives
you a glimpse of how your system is doing in comparison with others.   
	Like it was said at the introduction topic, this paper is not a final 
solution for NIDS performance mesurement or a real panacea to false positive
rates (doubtfully any paper will be), but it gives the reader a relative easy
way to measure yours NIDS enviroment effectivess and it proposes one 
more way to perform this hard job.
		

8 -------|Bibliography

AMOROSO, Edward G. (1999), "Intrusion Detection", Intrusion NetBook, USA.

AXELSON, Stefan (1999) - "The Base-Rate Fallacy and its Implications for 
	the Difficulty of Intrusion Detection", 
	www.ce.chalmers.se/staff/sax/difficulty.ps, Sweden. 

BUNDY, Alan (1997), "Artificial Inteligence Techniques", Springer-Verlag 
	Berlin Heidelberg, Germany.   

BUYYA, Rajkumar (1999), "High Performance Cluster Computing: Architectures 
	and Systems", Prentice Hall, USA.

KAEO, Merike (1999), "Designing Network Security", Macmillan Technical 
	Publishing, USA.

LEORNARD, Thomas (1999), "Bayesian Methods: An Analysis for Statisticians 
	and Interdisciplinary Researchers", Cambridge Univ Press, UK.

NORTHCUTT, Stephen (1999), "Network Intrusion Detection: An Analyst's 
	Handbook", New Riders Publishing, USA.

PATEL, Jagdish K. (1996), "Handbook of the Normal Distribution", 
	Marcel Dekker, USA.

STERLING, Thomas L. (1999), "How to Build a Beowulf: A Guide to 
	the Implementation and Application of PC Clusters", MIT Press, USA. 


9 -------|Acknowlegments:

	#Segfault at IRCSNET, Thanks for all fun and moral support

	TICK, for the great hints on NIDS field and beign the first 
	one to believe on this paper potential

	VAX, great pal, for all those sleepless nights

	Very Special Thanks to GAMMA, for the great Text & Math hints

	SYD, for moral support and great jokes 

	All THC crew
	
	Michal Zalewski, dziekuje tobie za ostatnia noc

	My Girlfriend Carolina, you all Know why :)
	
	Storm Security Staff, for building the experimental environment
	
|=[ EOF ]=---------------------------------------------------------------=|

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