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Security Analysis of Network Protocols: Logical and Computational Methods

Security Analysis of Network Protocols: Logical and Computational Methods. John Mitchell Stanford University. ICALP and PPDP, 2005. Outline. Protocols Some examples, some intuition Symbolic analysis of protocol security Models, results, tools Computational analysis

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Security Analysis of Network Protocols: Logical and Computational Methods

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  1. Security Analysis of Network Protocols: Logical and Computational Methods John Mitchell Stanford University ICALP and PPDP, 2005

  2. Outline • Protocols • Some examples, some intuition • Symbolic analysis of protocol security • Models, results, tools • Computational analysis • Communicating Turing machines, composability • Combining symbolic, computational analysis • Some alternate approaches • Protocol Composition Logic (PCL) • Symbolic and computational semantics

  3. Many Protocols • Authentication • Kerberos • Key Exchange • SSL/TLS handshake, IKE, JFK, IKEv2, • Wireless and mobile computing • Mobile IP, WEP, 802.11i • Electronic commerce • Contract signing, SET, electronic cash, …

  4. IPv6 Mobile IPv6 Architecture • Authentication is a requirement • Early proposals weak Mobile Node (MN) Direct connection via binding update Corresponding Node (CN) Home Agent (HA)

  5. EAP/802.1X/RADIUS Authentication Data Communication 802.11i Wireless Authentication Supplicant UnAuth/UnAssoc 802.1X Blocked No Key Supplicant Auth/Assoc 802.1X UnBlocked PTK/GTK 802.11 Association MSK 4-Way Handshake Group Key Handshake

  6. m1 m2 IKE subprotocol from IPSEC A, (ga mod p) B, (gb mod p) , signB(m1,m2) signA(m1,m2) A B Result: A and B share secret gab mod p Analysis involves probability, modular exponentiation, complexity, digital signatures, communication networks

  7. Needham-Schroeder Protocol {A, NonceA} {NonceA, NonceB } { NonceB} Kb A B Ka Kb Result: A and B share two private numbers not known to any observer without Ka-1, Kb-1

  8. Anomaly in Needham-Schroeder [Lowe] { A, Na } Ke A E { Na, Nb } Ka { Nb } Ke { A, Na } { Na, Nb } Evil agent E tricks honest A into revealing private key Nb from B. Kb Ka B Evil E can then fool B.

  9. Initiate Respond Attacker C D Run of a protocol B A Correct if no security violation in any run

  10. Protocol analysis methods • Cryptographic reductions • Bellare-Rogaway, Shoup, many others • UC [Canetti et al], Simulatability [BPW] • Prob poly-time process calculus [LMRST…] • Symbolic methods • Model checking • FDR [Lowe, Roscoe, …], Murphi [M, Shmatikov, …], • Symbolic search • NRL protocol analyzer [Meadows] • Theorem proving • Isabelle [Paulson …], Specialized logics [BAN, …] See papers in PPDP, ICALP proceedings for references

  11. “The” Symbolic Model • Messages are algebraic expressions • Nonce, Encrypt(K,M), Sign(K,M), … • Adversary • Nondeterministic • Observe, store, direct all communication • Break messages into parts • Encrypt, decrypt, sign only if it has the key • Example: K1, Encrypt(K1, “hi”)   K1, Encrypt(K1, “hi”)  “hi” • Send messages derivable from stored parts

  12. Many formulations • Word problems [Dolev-Yao, Dolev-Even-Karp, …] • Each protocol step is symbolic function from input message to output message; cancellation law dkekx = x • Rewrite systems [CDLMS] • Each protocol step is symbolic function from state and input message to state and output message • Logic programming [Meadows NRL Analyzer] • Each protocol step can be defined by logical clauses • Resolution used to perform reachability search • Constraint solving [Amadio-Lugiez, … ] • Write set constraints defining messages known at step i • Strand space model [MITRE] • Partial order (Lamport causality), reasoning methods • Process calculus [CSP, Spi-calculus, applied , …) • Each protocol step is process that reads, writes on channel • Spi-calculus: use  for new values, private channels, simulate crypto

  13. Complexity results (see [Cortier et al]) Additional results for variants of basic model (AC, xor, modular exp, …)

  14. Many protocol case studies • Murphi [Shmatikov, He, …] • SSL, Contract signing, 802.11i, … • Meadows NRL tool • Participation in IETF, IEEE standards • Many important examples • Paulson inductive method; Scedrov et al • Kerberos, SSL, SET, many more • Protocol logic • BAN logic and successors (GNY, SvO, …) • DDMP …

  15. Computational model I “Alice” “Bob” oracle tape oracle tape Adversary input tape work tape [Bellare-Rogaway, Shoup, …]

  16. Computational model II Turing machine Turing machine Adversary Turing machine Turing machine [Canetti, …]

  17. Computational security: encryption • Passive adversary • Semantic security • Chosen ciphertext attacks (CCA1) • Adversary can ask for decryption before receiving a challenge ciphertext • Chosen ciphertext attacks (CCA2) • Adversary can ask for decryption before and after receiving a challenge ciphertext

  18. m0, m1 E(mi) guess 0 or 1 Passive Adversary Challenger Attacker

  19. c D(c) m0, m1 E(mi) guess 0 or 1 Chosen ciphertext CCA1 Challenger Attacker

  20. c D(c) m0, m1 E(mi) c  E(mj) D(c) guess 0 or 1 Chosen ciphertext CCA2 Challenger Attacker

  21. Z input input P2 P1 S A P4 attacker P3 simulator F output Ideal functionality output Z Slide: R Canetti Protocol execution Protocol security P2 P1  P4 P3

  22. For every real adversary A there exists an adversary S Protocol interaction Trusted party Slide: Y Lindell Universal composability also “reactive simulatability” [BPW], … see [DKMRS]  REAL IDEAL

  23. Can we have best of both worlds?

  24. Some relevant approaches • Simulation framework • Backes, Pfitzmann, Waidner • Correspondence theorems • Micciancio, Warinschi • Kapron-Impagliazzo logics • Abadi-Rogaway passive equivalence  (K2,{01}K3) ,  {({101}K2,K5 )}K2, {{K6}K4}K5    (K2,  ) ,  {({101}K2,K5 )}K2, {  }K5    (K1,  ) ,  {({101}K1,K5 )}K1, {  }K5    (K1,{K1}K7) ,  {({101}K1,K5 )}K1, {{K6}K7}K5  Proposed as start of larger plan for computational soundness … … [Abadi-Rogaway00, …, Adao-Bana-Scedrov05]

  25. Symbolic methods  comp’l results • Pereira and Quisquater, CSFW 2001, 2004 • Studied authenticated group Diffie-Hellman protocols • Found symbolic attack in Cliques SA-GDH.2 protocol • Proved no protocol of certain type is secure, for >3 participants • Micciancio and Panjwani, EUROCRYPT 2004 • Lower bound for class of group key establishment protocols using purely Dolev-Yao reasoning • Model pseudo-random generators, encryption symbolically • Lower bounds is tight; matches a known protocol

  26. Rest of talk: Protocol composition logic Protocol Honest Principals, Attacker • Alice’s information • Protocol • Private data • Sends and receives Private Data Send Receive Logic now has symbolic and computational semantics

  27. Example { A, Noncea } { Noncea, … } Kb A B Ka • Alice assumes that only Bob has Kb-1 • Alice generated Noncea and knows that some X decrypted first message • Since only X knows Kb-1, Alice knows X=Bob

  28. More subtle example: Bob’s view { A, Noncea } { Noncea, B, Nonceb } { Nonceb} Kb A B Ka Kb • Bob assumes that Alice follows protocol • Since Alice responds to second message, Alice must have sent the first message

  29. Execution model • Protocol • “Program” for each protocol role • Initial configuration • Set of principals and key • Assignment of 1 role to each principal • Run Position in run x {x}B A ({z}B) ({x}B) decr B {z}B z C

  30. Formulas true at a position in run • Action formulas a ::= Send(P,m) | Receive (P,m) | New(P,t) | Decrypt (P,t) | Verify (P,t) • Formulas  ::= a | Has(P,t) | Fresh(P,t) | Honest(N) | Contains(t1, t2) |  | 1 2 | x  |  |  • Example After(a,b) = (b a) Notation in papers varies slightly …

  31. Modal Formulas • After actions, condition [ actions ] P where P = princ, role id • Before/after assertions  [ actions ] P  • Composition rule  [ S ] P  [ T ] P   [ ST ] P Logic formulated: [DMP,DDMP] Related to: BAN, Floyd-Hoare, CSP/CCS, temporal logic, NPATRL

  32. msg1 msg3 Example: Bob’s view of NSL • Bob knows he’s talking to Alice [ receive encrypt( Key(B), A,m ); new n; send encrypt( Key(A), m, B, n ); receive encrypt( Key(B), n ) ] B Honest(A)  Csent(A, msg1)  Csent(A, msg3) where Csent(A, …)  Created(A, …)  Sent(A, …)

  33. Proof System • Sample Axioms: • Reasoning about possession: • [receive m ]A Has(A,m) • Has(A, {m,n})  Has(A, m)  Has(A, n) • Reasoning about crypto primitives: • Honest(X)  Decrypt(Y, enc(X, {m}))  X=Y • Honest(X)  Verify(Y, sig(X, {m}))   m’ (Send(X, m’)  Contains(m’, sig(X, {m})) • Soundness Theorem: • Every provable formula is valid in symbolic model

  34. Modal Formulas • After actions, condition [ actions ] P where P = princ, role id • Before/after assertions  [ actions ] P  • Composition rule  [ S ] P  [ T ] P   [ ST ] P

  35. Application DH + CR = ISO 9798-3 • Initiator role of DH [ new a ] I Fresh(I, ga)  HasAlone(I, a) • Initiator role of CR Fresh(I, m) [send … receive … B… send] Honest(B)  ActionsInOrder(…) • Combination • Substitute ga for m in CR • Apply composition rule, persistence • Obtain assertion about ISO initiator

  36. Additional issues • Reasoning about honest principals • Invariance rule, called “honesty rule” • Preserve invariants under composition • If we prove Honest(X)   for protocol 1 and compose with protocol 2, is formula still true?

  37. Composing protocols  ’ DHHonest(X)  … CRHonest(X)  … ’ |- Authentication  |- Secrecy ’ |- Secrecy ’ |- Authentication ’ |- Secrecy  Authentication [additive] DH  CR’[nondestructive] = ISOSecrecy  Authentication

  38. Main results in ICALP Proceedings • Computational PCL • Symbolic logic for proving security properties of network protocols using public-key encryption • Soundness Theorem: • If a property is provable in CPCL, then property holds in computational model with overwhelming asymptotic probability. • Benefits • Symbolic proofs about computational model • Computational reasoning in soundness proof (only!) • Different axioms rely on different crypto assumptions

  39. PCL  Computational PCL • Syntax, proof rules mostly the same • But not sure about propositional connectives… • Significant difference • Symbolic “knowledge” • Has(X,t) : X can produce t from msgs that have been observed, by symbolic algorithm • Computational “knowledge” • Possess(X,t) : can produce t by ppt algorithm • Indistinguishable(X,t) : can distinguish from random in ppt • More subtle system: some axioms rely on CCA2, some are info-theoretically true, etc.

  40. Complexity-theoretic semantics • Q |=  if  adversary A  distinguisher D  negligible function f  n0 n > n0 s.t. Fraction represents probability [[]](T,D,f(n))|/|T| > 1 – f(n) • Fix protocol Q, PPT adversary A • Choose value of security parameter n • Vary random bits used by all programs • Obtain set T=T(Q,A,n) of equi-probable traces T(Q,A,n) [[]](T,D,f)

  41. Inductive Semantics • [[1  2]] (T,D,) = [[1]] (T,D,) [[2]] (T,D,) • [[1  2]] (T,D,) = [[1]] (T,D,) [[2]] (T,D,) • [[ ]] (T,D,) = T - [[]] (T,D,) Implication uses conditional probability • [[1  2]] (T,D,) = [[1]] (T,D,)  [[2]] (T’,D,) where T’ = [[1]] (T,D,) Formula defines transformation on probability distributions over traces

  42. Soundness of proof system • Example axiom • Source(Y,u,{m}X)  Decrypts(X, {m}X)  Honest(X,Y)  (Z  X,Y)  Indistinguishable(Z, u) • Proof idea: crypto-style reduction • Assume axiom not valid:  A  D  negligible f  n0  n > n0 s.t. • [[]](T,D,f)|/|T| < 1 –f(n) • Construct attacker A’ that uses A, D to break IND-CCA2 secure encryption scheme • Conditional implication essential Parts of proof are similar to [Micciancio, Warinschi]

  43. Applications of PCL • IKE, JFK family key exchange • IKEv2 in progress • 802.11i wireless networking • SSL/TLS, 4way handshake, group handshake • Kerberos v5 [Cervesato et al] • GDOI [Meadows, Pavlovic] • Future work • Use CPCL to understand computational security of these protocols, reliance on specific crypto properties

  44. Advantages of Computational PCL • High-level reasoning • Prove properties of protocols without explicit reasoning about probability, asymptotic complexity • Sound for “real crypto” • Composability • PCL is designed for protocol composition • Identify crypto assumptions needed

  45. Future Work • Investigate nature of propositional fragment • Non-classical;  involves some conditional probability • complexity-theoretic reductions • connections with probabilistic logics (e.g. Nilsson86) • Generalize reasoning about secrecy • Extend logic • More primitives: signature, hash functions,… • Remove current syntactic restrictions on formulas • Information-theoretic semantics (thanks to A Scedrov) • Only probability; no complexity • Other fundamental problems • See Kapron-Impagliazzo, etc.

  46. Conclusion • Symbolic model supports useful analysis • Tools, case studies, high-level proofs • Computational model more “correct” • More accurately reflects realistic attack • Two approaches can be combined • Several current projects and approaches • One example: computational semantics for symbolic protocol logic

  47. Credits • Collaborators • M. Backes, A. Datta, A. Derek, N. Durgin, C. He, R. Kuesters, D. Pavlovic, A. Ramanathan, A. Roy, A. Scedrov, V. Shmatikov, M. Sundararajan, V. Teague, M. Turuani, B. Warinschi, … • More information • References in PPDP, ICALP proceedings • Web page on Protocol Composition Logic • http://www.stanford.edu/~danupam/logic-derivation.html • My web site for related projects not discussed Science is a social process

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