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Analysis of Onion Routing

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  1. Analysis of Onion Routing Presented in 294-4 by Jayanthkumar Kannan On 10/8/03

  2. Outline • Problem Definition, Assumptions • Background • An old (1981) solution: Chaumian mixes • Onion Routing • Security Analysis of Onion Routing

  3. Problem Definition • Set of infrastructure nodes • Set of clients • Client A wishes to talk to Client B without divulging its identity • Infrastructure provides this service to the clients

  4. Metrics and Assumptions • Metrics of Anonymity • Sender Anonymity: Not possible to identify sender of a given message • Receiver Anonymity • Sender Receiver Unlinkability: Not possible to establish correspondence. • Content Anonymity (Sender/Receiver) • The set of infrastructure nodes is fully connected (clique) • No node can snoop on links between other nodes • A public key infrastructure is in place

  5. Mixes Vs Freenet • Goal of Freenet: Anonymous Storage • Chaumian mixes & Onion routing: Anonymous Routing • Can implement one using the other • Not efficiently though • More about this later

  6. Outline • Problem Definition, Assumptions • Background • An old (1981) solution: Chaumian mixes • Onion Routing • Security Analysis of Onion Routing

  7. Chaumian Mixes • Seminal work that considers the off-line case: email. • Basic Idea: Encoded Source Routing • Notation • M1 | M2 = M1 concatenated with M2 • E(A,M) = Message M encrypted by A’s public key • Always padded with random bits: E(A,R|M) • S(A,M) = Message M signed by A’s private key • Always padded with constant: S(A,C|M)

  8. Protocol • A wishes to send M to B anonymously • Simple scheme: contacts through randomly chosen infrastructure node, say C • A sends E(C,E(B,M) | B) and sends to C • C decrypts message, finds destination B, and forwards E(B,M) to B • B uses its private key to decrypt message • B is unaware of A’s identity • Doesn’t work if C is an adversary

  9. Cascaded Mixes • A choses random path C1,C2,…,Cn (called “mixes”). • Sends E(C1,M1 | C2) to C1 • where M1 = E(C2,M2 | C3) and so on • Mn = E(B,M) | B • C1 strips off one layer, discovers next hop C2, and forwards M1 to C2 • C2 strips off additional layer, forwards M2 to C3. • Until B gets the message E(B,M) • More resilient to adversaries: each C aware of only the next and previous hop

  10. Traffic Analysis • Consider an adversary who can observe traffic on all links • Can he correlate input to mix to output? • Encryption prevents any content correlation • Eg: Mix uses FIFO • Eg: Different packet sizes • Defense: each relay point also “mixes” up its traffic: re-ordering: called “mix” • Batch up packets, send them in random order • Have to defend against duplicate packets using timestamps etc

  11. Chaumian Mixes • Offer return addresses for B to contact A • Basic idea: A fabricates an onion with its identity hidden under many layers • Also has to include public/symmetric key • Much like private triggers in I3 • Offer psuedonyms • User identified by public key • SFS uses same approach • Mixes not suitable for real-time however: due to batching etc

  12. Outline • Problem Definition, Assumptions • Background • An old (1981) solution: Chaumian mixes • Onion Routing • Security Analysis of Onion Routing

  13. Onion Routing • Objective: Support real-time, bi-directional traffic • For tunneling TCP (web traffic) etc • Simple modifications to Chaumian Mixes • Terminology: • COR: core onion router (infrastructure) • Clients connect to COR through Proxies • Clients do not have public keys • COR routers know each other’s public keys, topology

  14. Modifications • Proxy chooses random COR path C1,C2,….,Cn on behalf of client • Control plane setup similar to Mixes • Control setup also involves exchange of symmetric keys • Forward data path: Proxy sends E(K1,E(K2,E(…E(Kn,M)..)) where K1,..,Kn are symmetric keys • Ki divulged to Ci along with next hop in control setup, used to decrypt • Reverse data path: Ri divulged to Ci, used to encrypt reverse traffic • A finally uses R1,…,Rn to strip off all encryption • Bi-directional • No “mixing” : cover traffic, padding to fixed-size messages done. • Application level sanitation also done • (Does not) Scales similar to RON.

  15. Outline • Problem Definition, Assumptions • Background • An old (1981) solution: Chaumian mixes • Onion Routing • Security Analysis of Onion Routing

  16. Threat Model • Two configurations • Remote COR: Proxy runs on remote machine: have to trust it • Local COR: Proxy on local machine, stronger guarantees • Adversary Model • Single • Multiple: fixed subset compromised • Roving: bounded (c) subset compromised at any instant • Global: Nothing can be done • Unlinkability analyzed

  17. Remote-COR configuration • Given a route R, subset R’ is compromised • If C1 in R’, no sender anonymity (p = c/r) • If Cn in R’, no receiver anonymity (p = c/r) • C1 in R’ and Cn in R’, no unlinkability (p=(c/r)^2) • Long-lived connection: roving adversary can do better • Rs: first adversary on path • Re: last adversary on path • Adversary moves one step towards endpoint • Takes O(path length)

  18. Local-COR configuration • No attack possible unless the local COR is itself corrupted • No way to know whether C1 is relaying for itself or for someone else • Unless everyone else is corrupted • Other attacks might be possible in practice • Response time: if response comes back immediately, likely that C1 is an endpoint

  19. Onion Routing in P2P • Tarzan (Freedman et al) • Gossiping to discover all nodes in overlay • Public keys passed around during gossiping • Similar path setup • Involves lots of bells and whistles: cover traffic etc • Scalability • All current schemes require O(n) state • How do things work in incomplete graph? • Tradeoff between state required and anonymity • Pseudonyms useful for persistent communication • Reputation schemes needed to prevent DoS attacks • Sybil attack can be used to increase fraction of adversaries

  20. Mixes Vs Freenet • Implementing storage using routing • Easy to do in static situation • Choose Cn = hash(content) • C1,…,C(n-1) is randomly chosen • Harder to do in dynamic situation: Freenet • Implementing routing using storage • Mailbox at rendevzous point • Much the same way I3 generalized from storage in DHTs to routing