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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 conv ey or imply MITRE's concurrence with, or support for, the positions, opinions or viewpoints expressed by the author. 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 conv ey or imply MITRE's concurrence with, or support for, the positions, opinions or viewpoints expressed by the author. 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! Needham-Schroeder-Lowe protocol (Prev: A, B get other‟s public encryption keys) A EKB(A || Na) B EKA(Na || Nb || B) K EKB(Nb) K Version 1: K = Na Version 2: K = Nb Which one is secure? 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 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 M1 || M2 M1, M2 M, K EK(M) EK(M), K-1 M „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? What we‟d like Symbolic Symbolic protocol key-exchange Simple, automated Natural translation for „Soundness‟ large Would like class of protocols (need only be done once) Concrete Computational protocol key-exchange 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 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 The „Rackoff attack‟ (on NSLv2) A EKB( A || Na) B EKA( Na || Nb || B ) EKB(Nb) EKB(K) ? K if K = Nb K =? Nb Adv O.W. 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) Decidability (not in paper) Traditional Symbolic secrecy real-or-random Unbounded Undecidable Undecidable sessions [EG, HT, DLMS] [B] Bounded sessions Decidable Decidable (NP-complete) (NP-complete) [DLMS, RT] Proof overview (soundness) Symbolic Construct simulator key-exchange • Information-theoretic • Must strengthen notion of UC public-key Single session UC KE encryption (ideal crypto) UC w/ Intermediate step: trace joint state properties (as in Multi-session UC KE [CR] [MW,BPW]) (ideal crypto) (Info-theor.) • Every activity-trace of UC adversary could also UC be produced by symbolic Multi-session KE adversary theorem • Rephrase: UC adversary (CCA-2 crypto) no more powerful than symbolic adversary 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… Backup slides Two challenges 1. Traditional secrecy is undecidable for: • Unbounded message sizes [EG, HT] or • Unbounded number of concurrent sessions (Decidable when both are bounded) [DLMS] 2. Traditional secrecy is unsound • Cannot imply standard security definitions for computational key exchange • Example: NSLv2 (Demo) Prior work: BPW New symbolic definition Theory Practice Implies UC key exchange (Public-key & symmetric encryption, signatures) Our work New symbolic definition: „real-or-random‟ Theory Practice Equiv. to UC key Automated exchange verification! (Public-key encryption [CH], signatures [P]) UC suffices to examine + Finite system single protocol run Decidability? Demo 3: UC security for NSLv1 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 Summary Summary: • 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 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 Secure key-exchange: UC P F P ? S K K A Adversary gets key when output by participants • Does this matter? (Demo 2) Secure key-exchange [CW] K, K’ P 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 KE P P ? F A S 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. Analysis strategy Dolev-Yao Dolev-Yao protocol key-exchange Simple, automated Natural translation for Main result of talk Would like class of large (Need only be done protocols once) Concrete UC key-exchange protocol functionality “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 {P2, N1, N2}K1 P1 P2 {N2}K2 UC Key-Exchange Functionality (P1 P2) (P1 P2) (P1 P2) P1 Key k Key P1 k {0,1}n X Key P2 A (P2 P1) (P2 P1) (P2 P1) P2 Key k Key P2 FKE The Dolev-Yao model Participants, adversary take turns Participant turn: M1 L A P1 P2 M2 Local output: Not seen by adversary The Dolev-Yao adversary Adversary turn: P1 Know P2 Application of deduction A Dolev-Yao adversary powers Already in Know Can add to Know M1, M2 Pair(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 The Dolev-Yao adversary Know M P1 P2 A Dolev-Yao key exchange Assume that last step of (successful) protocol execution is local output of (Finished Pi Pj K) 1. Key Agreement: If P1 outputs (Finished P1 P2 K) and P2 outputs (Finished P2 P1 K’) then K = K’. 2. Traditional Dolev-Yao secrecy: If Pi outputs (Finished Pi Pj K), then K can never be in adversary‟s set Know Not enough! 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 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 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 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, , K1-1K2 Final condition: Pattern(Traces(r)) = Pattern(Rename(Traces(f), Kf Kr))) 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 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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cryptographic protocols, security protocols, Ran Canetti, key exchange, symbolic analysis, Security Analysis, mutual authentication, R. Canetti, Theory of Cryptography Conference, security proofs

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posted: | 2/18/2010 |

language: | English |

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