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Anonymity Analysis of Onion Routing in the Universally Composable Framework

This workshop paper presents an analysis of onion routing protocols within the Universally Composable (UC) framework to establish provable privacy guarantees. It builds on previous models, such as I/O-automata and abstract models, offering both possibilistic and probabilistic anonymity analyses. We aim to formalize the abstract model in the UC framework and examine the integrity of information leakage throughout the routing process. The results enhance our understanding of how onion routing can maintain anonymity under adverse conditions.

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Anonymity Analysis of Onion Routing in the Universally Composable Framework

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  1. Anonymity Analysis of Onion Routing in the Universally ComposableFramework Joan Feigenbaum Aaron Johnson Paul Syverson Yale University U.S. Naval Research Laboratory Provable Privacy Workshop July 9, 2012

  2. Problem • [FJS07a] - Onion-routing I/O-automata model - Possibilistic anonymity analysis • [FJS07b] - Onion-routing abstract model - Probabilistic anonymity analysis • […] - How do we apply results in standard cryptographic models? • [CL05] - “Onion routing” formalized with Universal Composability (UC) - No anonymity analysis • [BGKM12] - Onion routing formalized with UC - Our work will provide anonymity

  3. Solution • Formalize abstract (black-box) model of onion routing in UC framework • Focus on information leaked • Anonymity analysis on earlier abstract model is inherited by UC version

  4. Problem • [FJS07a] - Onion-routing I/O-automata model - Possibilistic anonymity analysis • [FJS07b] - Onion-routing abstract model - Probabilistic anonymity analysis • […] - How do we apply results in standard cryptographic models? • [CL05] - “Onion routing” formalized with Universal Composability (UC) - No anonymity analysis • [BGKM12] - Onion routing formalized with UC - Our work will provide anonymity

  5. I/O-automata model Adversary controls relays 1 2 u d 3 5 User u running client Internet destination d 4 Onion routing relays Encrypted onion-routing hop Unencrypted onion-routing hop

  6. I/O-automata model 1 2 u d 3 5 4 u 1 2 Main theorem: Adversary can only determine parts of a circuit it controls or is next to.

  7. I/O-automata model u 1 2 d v e 3 5 4 w f

  8. I/O-automata model u 1 2 d v e 3 5 4 w f • First router compromised

  9. I/O-automata model u 1 2 d v e 3 5 4 w f • First router compromised • Last router compromised

  10. I/O-automata model u 1 2 d v e 3 5 4 w f • First router compromised • Last router compromised • First and last compromised

  11. I/O-automata model u 1 2 d v e 3 5 4 w f • First router compromised • Last router compromised • First and last compromised • Neither first nor last compromised

  12. Problem • [FJS07a] - Onion-routing I/O-automata model - Possibilistic anonymity analysis • [FJS07b] - Onion-routing abstract model - Probabilistic anonymity analysis • […] - How do we apply results in standard cryptographic models? • [CL05] - “Onion routing” formalized with Universal Composability (UC) - No anonymity analysis • [BGKM12] - Onion routing formalized with UC - Our work will provide anonymity

  13. Black-box Abstraction u d v e w f

  14. Black-box Abstraction u d v e w f • Users choose a destination

  15. Black-box Abstraction u d v e w f • Users choose a destination • Some inputs are observed

  16. Black-box Abstraction u d v e w f • Users choose a destination • Some inputs are observed • Some outputs are observed

  17. Black-box Anonymity u d v e w f • The adversary can link observed inputs and outputs of the same user.

  18. Black-box Anonymity u d v e w f • The adversary can link observed inputs and outputs of the same user. • Any configuration consistent with these observations is indistinguishable to the adversary.

  19. Black-box Anonymity u d v e w f • The adversary can link observed inputs and outputs of the same user. • Any configuration consistent with these observations is indistinguishable to the adversary.

  20. Black-box Anonymity u d v e w f • The adversary can link observed inputs and outputs of the same user. • Any configuration consistent with these observations is indistinguishable to the adversary.

  21. Probabilistic Black-box u d v e w f

  22. Probabilistic Black-box u d v e w f pu • Each user v selects a destination from distribution pv

  23. Probabilistic Black-box u d v e w f pu • Each user v selects a destination from distribution pv • Inputs and outputs are observed independently with probability b

  24. Problem • [FJS07a] - Onion-routing I/O-automata model - Possibilistic anonymity analysis • [FJS07b] - Onion-routing abstract model - Probabilistic anonymity analysis • […] - How do we apply results in standard cryptographic models? • [CL05] - “Onion routing” formalized with Universal Composability (UC) - No anonymity analysis • [BGKM12] - Onion routing formalized with UC - Our work will provide anonymity

  25. Problem • [FJS07a] - Onion-routing I/O-automata model - Possibilistic anonymity analysis • [FJS07b] - Onion-routing abstract model - Probabilistic anonymity analysis • [FJS12] – Onion-routing UC formalization - “Free” probabilistic anonymity analysis • [CL05] - “Onion routing” formalized with Universal Composability (UC) - No anonymity analysis • [BGKM12] - Onion routing formalized with UC - Our work will provide anonymity

  26. Onion-Routing UC Ideal Functionality Upon receiving destination d from user U u with probability b øwith probability 1-b x d with probability b øwith probability 1-b y Send (x,y) to the adversary. FOR

  27. Black-box Model • Ideal functionality FOR • Environment assumptions • Each user gets a destination • Destination for user u chosen from distribution pu • Adversary compromises a fraction b of routers before execution

  28. UC Formalization • Captures necessary properties of any crytographic implementation • Easy to analyze resulting information leaks • Functionality is a composable primitive • Anonymity results are valid in probabilistic version of I/O-automata model

  29. Anonymity Analysis of Black Box • Can lower bound expected anonymity with standard approximation: b2 + (1-b2)pud • Worst case for anonymity is when user acts exactly unlike or exactly like others • Worst-case anonymity is typically as if √b routers compromised: b + (1-b)pud • Anonymity in typical situations approaches lower bound

  30. Future Extensions • Compromised links • Non-uniform path selection • Heterogeneous path selection • Anonymity over time

  31. Problem • [FJS07a] - Onion-routing I/O-automata model - Possibilistic anonymity analysis • [FJS07b] - Onion-routing abstract model - Probabilistic anonymity analysis • [FJS12] – Onion-routing UC formalization - “Free” probabilistic anonymity analysis • [CL05] - “Onion routing” formalized with Universal Composability (UC) - No anonymity analysis • [BGKM12] - Onion routing formalized with UC - Our work will provide anonymity

  32. [BGKM12] Ideal Functionality • Functionality can actually send messages • Needs wrapper to hide irrelevant circuit-building options • Shown to UC-emulate FOR

  33. References [BGKM12] Provably Secure and Practical Onion Routing,by Michael Backes, Ian Goldberg, Aniket Kate, and EsfandiarMohammadi, in CSF12. [CL05] A Formal Treatment of Onion Routing, by Jan Camenisch and Anna Lysyanskaya, in CRYPTO 05. [FJS07a] A Model of Onion Routing with Provable Anonymity,by Joan Feigenbaum, Aaron Johnson, and Paul Syverson, in FC07. [FJS07b] Probabilistic Analysis of Onion Routing in a Black-box Model, id., in WPES07. [FJS12] A Probabilistic Analysis of Onion Routing in a Black-box Model, id.in TISSEC (forthcoming)

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