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H.W. Chan, CSE Dept., CUHK1 Quantitative Evaluation for Operational Security - an Experiment [Ortalo et al., IEEE Transactions on Software Engineering, Sept/Oct 1999] Group Meeting, Mar 7, 2000

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H.W. Chan, CSE Dept., CUHK2 Outline n Introduction n The Approach: – Privilege graphs – Attack state graphs – Mathematical model n The experiment – setup and results n Discussion

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H.W. Chan, CSE Dept., CUHK3 Introduction n System security has been usually discussed in terms of security requirements and policy – requires cooperation of all users – difficult for ordinary users to comprehend n A quantitative measure for system security is easier to comprehend – a figure representing the ‘degree of security’ of the system can be useful

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H.W. Chan, CSE Dept., CUHK4 Quantifying security n Borrowing software reliability theory: – In reliability, a piece of software fails upon time of usage; the Mean Time To Failure quantify the reliability of the software – Similar, in security, a system can be breached upon effort of attacks; the Mean Effort to Breach can quantify the security of the system

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H.W. Chan, CSE Dept., CUHK5 The Approach n Privilege graph: – node: a set of privileges owned by a user or set of users (e.g., a group in Unix) – arc: a vulnerability that cause a user owning one privilege to obtain another, e.g., X Y There is a method allowing a user owning privilege X to obtain privilege Y.

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H.W. Chan, CSE Dept., CUHK6 Examples of vulnerabilities n Privilege subsets directly issued from the protection scheme n Direct security flaws, e.g., Trojan horse n System features exploited for attack –.rhosts,.xinitrc, setuid programs hwchan1 gds

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H.W. Chan, CSE Dept., CUHK7 Privilege graph - example A X admin B P Finsider Key 1: Y’s.rhosts is writable by X 2: X can guess Y’s password 3: X can modify Y’s.tcshrc 4: X is a member of Y 5: Y uses a program managed by X 6: X can modify a setuid program owned by Y 7: X is in Y’s.rhosts Key 1: Y’s.rhosts is writable by X 2: X can guess Y’s password 3: X can modify Y’s.tcshrc 4: X is a member of Y 5: Y uses a program managed by X 6: X can modify a setuid program owned by Y 7: X is in Y’s.rhosts

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H.W. Chan, CSE Dept., CUHK8 Quantifying vulnerabilities n Each arc in the privilege graph should be assigned a weight to quantify the effort required for exploiting the vulnerability n Different factors should be considered, e.g., expertise, time and equipment n No good methods to do this yet!

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H.W. Chan, CSE Dept., CUHK9 Attacker behavior n In an attack, an attacker begins with some minimal privileges, and wants to obtain some protected privileges. n In a privilege graph, the path from the attacker node to the target node describes the progress of attack: attacker target

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H.W. Chan, CSE Dept., CUHK10 n There can be more than one paths from the attacker node to the target node – assumption: attacker does not know the shortest path n Two assumptions for attacker behavior – Total memory (TM): all possibilities of attack are considered at any stage of attack – Memoryless (ML): at each newly visited node, only attacks possible from that node are considered

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H.W. Chan, CSE Dept., CUHK11 Attack state graphs (ML) IFI BFIX ABFIPX BFIPX FIX IP AIP AFIX

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H.W. Chan, CSE Dept., CUHK12 Attack state graph (TM) IFI BFIX ABFIPX BFIPX FIX IP AIP AFIX FIP AFIP

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H.W. Chan, CSE Dept., CUHK13 Mathematical Model n Assume the Markov model: – Probability of success in an attack before an amount of effort ‘e’ is spent is: P(e) = 1 - exp(-Le) – L is the rate of attack, and can be assigned as the weight of the vulnerability – thus, mean effort to succeed is 1/L

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H.W. Chan, CSE Dept., CUHK14 – mean effort spent in state j is E j = 1/summation(L ji ), for all i belongs to out(j) – Mean Effort To security Failure (METF) from initial state k to state i is METF k = E k + summation(L ki *E k *METF i ), for all i belongs to out(k)

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H.W. Chan, CSE Dept., CUHK15 The experiment n Setup: – Several hundred different workstations – 700 users sharing one global file system – privilege graphs, attacker state graph and METF computed every day from June 95 to Mar 97 (674 days) – vulnerabilities are classified into four levels and given rates 10^-1, 10^-2, 10^-3, 10^-4

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H.W. Chan, CSE Dept., CUHK16 Results

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H.W. Chan, CSE Dept., CUHK17 Conclusion and discussion n A preliminary investigation about the security evaluation of operational systems n The assignment of rates of the vulnerabilities is pretty arbitrary, but is key to the validity of the measurement

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