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**Universally Composable Symbolic Analysis of Cryptographic Protocols**

Ran Canetti and Jonathan Herzog 6 March 2006 The author's affiliation with The MITRE Corporation is provided for identification purposes only, and is not intended to convey or imply MITRE's concurrence with, or support for, the positions, opinions or viewpoints expressed by the author.

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**Universally Composable Automated Analysis of Cryptographic Protocols**

Ran Canetti and Jonathan Herzog 6 March 2006 The author's affiliation with The MITRE Corporation is provided for identification purposes only, and is not intended to convey or imply MITRE's concurrence with, or support for, the positions, opinions or viewpoints expressed by the author.

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Overview This talk: symbolic analysis can guarantee universally composable (UC) key exchange (Paper also includes mutual authentication) Symbolic (Dolev-Yao) model: high-level framework Messages treated symbolically; adversary extremely limited Despite (general) undecidability, proofs can be automated Result: symbolic proofs are computationally sound (UC) For some protocols For strengthened symbolic definition of secrecy With UC theorems, suffices to analyze single session Implies decidability!

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**Needham-Schroeder-Lowe protocol**

(Prev: A, B get other’s public encryption keys) A B EKB(A || Na) EKA(Na || Nb || B) K EKB(Nb) K Version 1: K = Na Version 2: K = Nb Which one is secure?

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**Two approaches to analysis**

Standard (computational) approach: reduce attacks to weakness of encryption Alternate approach: apply methods of the symbolic model Originally proposed by Dolev & Yao (1983) Cryptography without: probability, security parameter, etc. Messages are parse trees Countable symbols for keys (K, K’,…), names (A, B,…) and nonces (N, N’, Na, Nb, …) Encryption ( EK(M) ) pairing ( M || N ) are constructors Participants send/receive messages Output some key-symbol

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**The symbolic adversary**

Explicitly enumerated powers Interact with countable number of participants Knowledge of all public values, non-secret keys Limited set of re-write rules: M1, M2 M1 || M2 M, K EK(M) EK(M), K-1 M

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**‘Traditional’ symbolic secrecy**

Conventional goal for symbolic secrecy proofs: “If A or B output K, then no sequence of interactions/rewrites can result in K” Undecidable in general [EG, HT, DLMS] but: Decidable with bounds [DLMS, RT] Also, general case can be automatically verified in practice Demo 1: analysis of both NSLv1, NSLv2 So what? Symbolic model has weak adversary, strong assumptions We want computational properties! …But can we harness these automated tools? EG = Evan & Goldreich HT = Heintze & Tygar DLMS = Durgin, Lincoln, Mitchell, Scedrov RT = Rusinowitch & Turauni

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**What we’d like Symbolic protocol Symbolic key-exchange**

Simple, automated Natural translation for large class of protocols ‘Soundness’ (need only be done once) Would like Concrete protocol Computational key-exchange

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**Some previous work General area:**

[AR]: soundness for indistinguishability Passive adversary [MW, BPW]: soundness for general trace properties Includes mutual authentication; active adversary Many, many others Key-exchange in particular (independent work): [BPW]: (later) [CW]: soundness for key-exchange Traditional symbolic secrecy implies (weak) computational secrecy Abadi-Rogaway Micciancio-Warinschi

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**Limitations of ‘traditional’ secrecy**

Big question: Can ‘traditional’ symbolic secrecy imply standard computational definitions of secrecy? Unfortunately, no Counter-example: Demo: NSLv2 satisfies traditional secrecy Cannot provide real-or-random secrecy in standard models Falls prey to the ‘Rackoff’ attack

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**The ‘Rackoff attack’ (on NSLv2)**

B EKB( A || Na) EKA( Na || Nb || B ) EKB(Nb) EKB(K) K =? Nb ? K if K = Nb O.W. Adv

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Achieving soundness Soundness requires new symbolic definition of secrecy [BPW]: ‘traditional’ secrecy + ‘non-use’ Thm: new definition implies secrecy (in their framework) But: must analyze infinite concurrent sessions and all resulting protocols Here: ‘traditional’ secrecy + symbolic real-or-random Non-interference property; close to ‘strong secrecy’ [B] Thm: new definition equivalent to UC secrecy Demonstrably automatable (Demo 2) Suffices to consider single session! (Infinite concurrency results from joint-state UC theorems) Implies decidability (forthcoming)

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**Decidability (not in paper)**

Traditional secrecy Symbolic real-or-random Unbounded sessions Undecidable [EG, HT, DLMS] [B] Bounded sessions Decidable (NP-complete) [DLMS, RT] EG = Evan & Goldreich HT = Heintze & Tygar DLMS = Durgin, Lincoln, Mitchell, Scedrov RT = Rusinowitch & Turauni

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**Proof overview (soundness)**

Symbolic key-exchange Construct simulator Information-theoretic Must strengthen notion of UC public-key encryption Intermediate step: trace properties (as in [MW,BPW]) Every activity-trace of UC adversary could also be produced by symbolic adversary Rephrase: UC adversary no more powerful than symbolic adversary Single session UC KE (ideal crypto) UC w/ joint state [CR] (Info-theor.) Multi-session UC KE (ideal crypto) UC theorem Multi-session KE (CCA-2 crypto)

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Summary & future work Result: symbolic proofs are computationally sound (UC) For some protocols For strengthened symbolic definition of secrecy With UC theorems, suffices to analyze single session Implies decidability! Additional primitives Have public-key encryption, signatures [P] Would like symmetric encryption, MACs, PRFs… Symbolic representation of other goals Commitment schemes, ZK, MPC…

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Backup slides

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**Traditional secrecy is undecidable for:**

Two challenges Traditional secrecy is undecidable for: Unbounded message sizes [EG, HT] or Unbounded number of concurrent sessions (Decidable when both are bounded) [DLMS] Traditional secrecy is unsound Cannot imply standard security definitions for computational key exchange Example: NSLv2 (Demo) EG = Evan and Goldreich, On the security of ping-pong protocols (1983) HT=Heintze, Tygar, A model for secure protocols and their composition, 1994 (Oakland) DLMS = Durgin, Lincoln, Mitchell, Scedrov, Multiset rewriting and complexity of bounded security protocols (2003)

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**Prior work: BPW New symbolic definition Implies UC key exchange**

Theory Practice Implies UC key exchange (Public-key & symmetric encryption, signatures)

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**Our work New symbolic definition: ‘real-or-random’**

Theory Practice Automated verification! Equiv. to UC key exchange (Public-key encryption [CH], signatures [P]) UC suffices to examine single protocol run + Finite system Decidability? Demo 3: UC security for NSLv1

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**Our work: solving the challenges**

Soundness: requires new symbolic definition of secrecy Ours: purely symbolic expression of ‘real-or-random’ security Result: new symbolic definition equivalent to UC key exchange UC theorems: sufficient to examine single protocol in isolation Thus, bounded numbers of concurrent sessions Automated verification of our new definition is decidable!… Probably

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**Summary Summary: Future work Symbolic key-exchange sound in UC model**

Computational crypto can now harness symbolic tools Now have the best of both worlds: security and automation! Future work

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**Secure key-exchange: UC**

? P P K K A Answer: yes, it matters Negative result [CH]: traditional symbolic secrecy does not imply universally composable key exchange

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**Secure key-exchange: UC**

P ? F S ? P K A Adversary gets key when output by participants Does this matter? (Demo 2)

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**Secure key-exchange [CW]**

P K, K’ P A Adversary interacts with participants Afterward, receives real key, random key Protocol secure if adversary unable to distinguish NSLv1, NSLv2 satisfy symbolic def of secrecy Therefore, NSLv1, NSLv2 meet this definition as well

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**? F P P S A KE Adversary unable to distinguish real/ideal worlds**

Effectively: real or random keys Adversary gets candidate key at end of protocol NSL1, NSL2 secure by this defn.

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**Analysis strategy Dolev-Yao protocol Dolev-Yao key-exchange**

Simple, automated Natural translation for large class of protocols Main result of talk (Need only be done once) Would like Concrete protocol UC key-exchange functionality

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“Simple” protocols Concrete protocols that map naturally to Dolev-Yao framework Two cryptographic operations: Randomness generation Encryption/decryption (This talk: asymmetric encryption) Example: Needham-Schroeder-Lowe {P1, N1}K2 P1 P2 {P2, N1, N2}K1 {N2}K2

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**UC Key-Exchange Functionality**

(P1 P2) (P1 P2) FKE (P1 P2) A P1 Key P1 Key k k {0,1}n Key P2 X (P2 P1) (P2 P1) (P2 P1) P2 Key k Key P2

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**A The Dolev-Yao model P1 P2 M1 M2 Participants, adversary take turns**

Participant turn: M1 A L P1 P2 M2 Local output: Not seen by adversary

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**The Dolev-Yao adversary**

Adversary turn: A Application of deduction P1 P2 Know

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**Dolev-Yao adversary powers**

Already in Know Can add to Know M1, M2 Pair(M1, M2) M1 and M2 M, K Enc(M,K) Enc(M, K), K-1 M Always in Know: Randomness generated by adversary Private keys generated by adversary All public keys

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**The Dolev-Yao adversary**

Know M P1 P2

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**Dolev-Yao key exchange**

Assume that last step of (successful) protocol execution is local output of (Finished Pi Pj K) Key Agreement: If P1 outputs (Finished P1 P2 K) and P2 outputs (Finished P2 P1 K’) then K = K’. Traditional Dolev-Yao secrecy: If Pi outputs (Finished Pi Pj K), then K can never be in adversary’s set Know Not enough!

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**Goal of the environment**

Recall that the environment Z sees outputs of participants Goal: distinguish real protocol from simulation In protocol execution, output of participants (session key) related to protocol messages In ideal world, output independent of simulated protocol If there exists a detectable relationship between session key and protocol messages, environment can distinguish Example: last message of protocol is {“confirm”}K where K is session key Can decrypt with participant output from real protocol Can’t in simulated protocol

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**Real-or-random (1/3) Need: real-or-random property for session keys**

Can think of traditional goal as “computational” Need a stronger “decisional” goal Expressed in Dolev-Yao framework Let be a protocol Let r be , except that when participant outputs (Finished Pi Pj Kr), Kr added to Know Let f be , except that when any participant outputs (Finished Pi Pj Kr), fresh key Kf added to adversary set Know Want: adversary can’t distinguish two protocols

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Real-or-random (2/3) Attempt 1: Let Traces() be traces adversary can induce on . Then: Traces(r) = Traces(f) Problem: Kf not in any traces of r Attempt 2: Traces(r) = Rename(Traces(f), Kf Kr) Problem: Two different traces may “look” the same Example protocol: If participant receives session key, encrypts “yes” under own (secret) key. Otherwise, encrypts “no” instead Traces different, but adversary can’t tell

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**Real-or-random (3/3) Observable part of trace: Abadi-Rogaway pattern**

Undecipherable encryptions replaced by “blob” Example: t = {N1, N2}K1, {N2}K2, K1-1 Pattern(t) = {N1, N2}K1, K2, K1-1 Final condition: Pattern(Traces(r)) = Pattern(Rename(Traces(f), Kf Kr)))

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**Main results Let key-exchange in the Dolev-Yao model be:**

Key agreement Traditional Dolev-Yao secrecy of session key Real-or-random Let be a simple protocol that uses UC asymmetric encryption. Then: DY() satisfies Dolev-Yao key exchange iff UC() securely realizes FKE

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**Future work How to prove Dolev-Yao real-or-random?**

Needed for UC security Not previously considered in the Dolev-Yao literature Can it be automated? Weaker forms of DY real-or-random Similar results for symmetric encryption and signatures

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