Recommandé
Recommandé
Contenu connexe
Similaire à Logic for security
Similaire à Logic for security (20)
Dernier
Dernier (20)
Logic for security
- 1. . . . . . . Introduction Approaches Applications Specialized Logic Logic for Computer Security Jack Yao HKUST rainoftime@gmail.com December 20, 2015 Jack Yao Logic4Sec
- 2. . . . . . . Introduction Approaches Applications Specialized Logic Overview 1 Introduction 2 Approaches Model checking Inductive Proof Type theory SAT and SMT 3 Applications Security Protocols OS Security Software Model Checking 4 Specialized Logic Model Logic and its variants Linear Logic Bunched logic Others Jack Yao Logic4Sec
- 3. . . . . . . Introduction Approaches Applications Specialized Logic Areas of Applications Computer Security Multilevel Operating System Access Control Policies Network Security Public-Key Infrastructure and Trust Management Cryptographic Authentication Protocols Other areas: databases, firewalls, routers, intrusion detection Jack Yao Logic4Sec
- 4. . . . . . . Introduction Approaches Applications Specialized Logic Contribution of Logic Undecidability or complexity Results Safety problem for discretionary access control Cryptographic protocol analysis Theorem Proving Environments Verifying correctness of formal OS specifications Inductive proofs of cryptographic protocols Logic Programming Prolog programs for cryptographic protocol analysis, etc Model Checking Cryptographic protocol analysis More and more work on software model checking Specialized Logics Linear Logic, Separation Logic, Affine Logic, etc Jack Yao Logic4Sec
- 5. . . . . . . Introduction Approaches Applications Specialized Logic Roles of Logic Model theory Study semantic What does the the assertion language mean? Proof theory Formally proving security properties Automatic or Interactive? Recursion(Computability) theory Is it possible to verify something? If yes, what’s the price? Specialized logic Jack Yao Logic4Sec
- 6. . . . . . . Introduction Approaches Applications Specialized Logic Proof Systems Goals: formally prove properties Axioms Formulas predefined in the certain logic Or simple formulas proved by hand and used as axioms. Inference rules Proof steps Theorem Formula obtained from axioms by application of inference rules Techniques Hilbert-frege style(e.g, originally, Hoare logic used this) Gentzen’s Natural deduction and sequent calculi Nested sequent, labeled sequent, display calculi, etc. Jack Yao Logic4Sec
- 7. . . . . . . Introduction Approaches Applications Specialized Logic Other tools for modeling and proving Tree Automata, Graph Automata.. Graph based IR and program analysis Pushdown system(PDS), WSTS(e.g, petri net) Term rewriting system Algebra and calculus(CSP, CCS, pi calculus..) ... Jack Yao Logic4Sec
- 8. . . . . . . Introduction Approaches Applications Specialized Logic Model checking Inductive Proof Type theory SAT and SMT Model checking Developed independently by Clarke and Emerson and by Queille and Sifakis in early 80s Originally, temporal logic model checking(specifications are written in propositional temporal logic) Verification procedure is an intelligent exhaustive search of the state space of the design Jack Yao Logic4Sec
- 9. . . . . . . Introduction Approaches Applications Specialized Logic Model checking Inductive Proof Type theory SAT and SMT Advantages and Disadvantage Advantages: No proofs!!(Algorithmic rather than Deductive) Diagnostic counterexamples Allow partial specification Flow and path sensitive, but fast(compared to theorem proving) Disadvantages: State explosion!! Development: symbolic MC, bounded MC(usually with SAT solver), CEGAR.. Jack Yao Logic4Sec
- 10. . . . . . . Introduction Approaches Applications Specialized Logic Model checking Inductive Proof Type theory SAT and SMT Model checking Tools State-space search for reachability of insecure states History: back to 1984, Interrogator program in Prolog General-purpose model-checkers Search automatically given initial conditions, bounds Roscoe and Lowe, FDR(model-checker for CSP), 1995 Clarke et al, SMV, 1998 Jack Yao Logic4Sec
- 11. . . . . . . Introduction Approaches Applications Specialized Logic Model checking Inductive Proof Type theory SAT and SMT Software model checking Tools for verifying source code combine many techniques Program analysis techniques such as slicing, range analysis Abstraction: e.g, abstract interpretation Model checking, SAT and SMT solving... Refinement from counter-examples(CEGAR) New challenges for MC(beyond finite-state reachability analysis) Recursion gives pushdown control: pushdown system, higher order MC.. Pointers, dynamic objects, inheritence... A very active and emerging area Abstraction-based tools: SLAM, BLAST Direct state encoding: CBMC, CheckFence Jack Yao Logic4Sec
- 12. . . . . . . Introduction Approaches Applications Specialized Logic Model checking Inductive Proof Type theory SAT and SMT Inductive Proofs Application of general-purpose specification and verification tools Influential Examples: L.Paulson, ”The inductive approach to verifying cryptographic protocols”, J. Comp. Sec.98(used Isabelle) L.Beringer et al, ”Verified Correctness and Security of OpenSSL HMAC”, Usenix Sec.15 Tools: Coq, Isabelle, PVS, Automath, Agda... Jack Yao Logic4Sec
- 13. . . . . . . Introduction Approaches Applications Specialized Logic Model checking Inductive Proof Type theory SAT and SMT Types and security We want to check specification vs. the code; Types can be specification. Type system is Part of nearly all mainstream languages Usually flow-insensitive, thus efficient Relation with proof theory(for some functional language and theorem provers) C-H isomorphism: proposition as type, and proving as type checking Essentially, it is a natural deduction style proof. Jack Yao Logic4Sec
- 14. . . . . . . Introduction Approaches Applications Specialized Logic Model checking Inductive Proof Type theory SAT and SMT Substructural type Borrow the ideas from substructural logic Affine logic, linear logic, relevant logic... Key insights: Restrict the use of resource: number, ordering, etc. Examples: Linear Type system. Affine Type, Turner et al. Hoare Type, David Walker and G.Morrisett Jack Yao Logic4Sec
- 15. . . . . . . Introduction Approaches Applications Specialized Logic Model checking Inductive Proof Type theory SAT and SMT Flow sensitive type Extending standard type systems with flow-sensitive type qualifiers. Used to ”encode” flow information J.Foster, Flow-Sensitive Type Qualifiers, PLDI 02 S.Hunt, On Flow-Sensitive Security Types, POPL 06 ... Jack Yao Logic4Sec
- 16. . . . . . . Introduction Approaches Applications Specialized Logic Model checking Inductive Proof Type theory SAT and SMT Dependent type Foundations for many theorem provers, and integrated into general programming lang Theorem proving: Coq, Agda, F star,... General programming lang: Lightweight support in Haskell, and full in Idris.. Some variants: Refinement type Studied intensively in recent years. And usually implemented with SMT solver. Jack Yao Logic4Sec
- 17. . . . . . . Introduction Approaches Applications Specialized Logic Model checking Inductive Proof Type theory SAT and SMT The Story of SAT Propositional Satisfiability: Given a formula over Boolean variables, is there an assignment of 0 or 1s to vars which makes the formula true? Canonical NP-hard problem (Cook 1971) Enormous progress in tools that can solve instances with 1000s of variables and millions of clauses Jack Yao Logic4Sec
- 18. . . . . . . Introduction Approaches Applications Specialized Logic Security Protocols OS Security Software Model Checking Security Protocol Applications military communications, business communications, electronic commerce, privacy Examples Kerberos: MIT protocol for unitary login to network services SSL (Secure Socket Layer, used in Web browsers) IPSec: standard suite of Internet protocols due to the IETF SET (Secure Electronic Transaction) protocol PGP (Pretty Good Privacy) Verification of security protocols has been and is still a very active research area Jack Yao Logic4Sec
- 19. . . . . . . Introduction Approaches Applications Specialized Logic Security Protocols OS Security Software Model Checking Solutions to undecidability Abstraction Tree automata(TA4SP) Horn clauses(ProVerif) User help Logics(BAN, PCL,...) Even use iteractive proving Decidable subclass Jack Yao Logic4Sec
- 20. . . . . . . Introduction Approaches Applications Specialized Logic Security Protocols OS Security Software Model Checking File systems File systems are complex and have bugs Research on finding bugs: Crash injection(e.g, EXPLODE, OSDI 06) Symbolic execution(e.g., EXE, Okaland 06) ... Elimination of bugs by proving: BilbyFS, Keller 14 UBIFS, Ernst et al. 13 FSCQ(with Hoare Crash Logic),SOSP 15 Jack Yao Logic4Sec
- 21. . . . . . . Introduction Approaches Applications Specialized Logic Security Protocols OS Security Software Model Checking Software model checking Active area of research Examples of tools: Bandera[Dwyer]: Java to SPIN/SMV/* using user-guided abstraction mapping and slicing/abstract interpretation SLAM[Tom Ball]: C to ”Boolean programs”, automatic abstraction refinement using predicate abstraction JavaPathFinder: Java model-checking using special JVM and model-checker... SAGE: random testing. Challenges: Language features: function pointers, higher order function... Scalability: modular, incremental, parallel? Jack Yao Logic4Sec
- 22. . . . . . . Introduction Approaches Applications Specialized Logic Security Protocols OS Security Software Model Checking Two main approaches in Software MC Systematic software testing Idea: control the execution of concurrent processes by intercepting systems calls related to communication, and automatically drive the entire system through many scenarios Flexible and scalable approach (code independent) Counterexamples arise from code execution (sound) Provide complete state-space coverage up to some depth only (incomplete) Static analysis for automatic model extraction Idea: parse code to generate an abstract model which is then analyzed by model-checker; abstraction may/must be guided by the user Coverage can be exhaustive (can be complete) Abstraction may cause spurious counterexamples(unsound) Jack Yao Logic4Sec
- 23. . . . . . . Introduction Approaches Applications Specialized Logic Security Protocols OS Security Software Model Checking Software MC and logic Key insights: Let A be an abstract domain for static analysis. The elements of A act both as computational values and as logic assertions! Data flow analysis, predicate abstraction, and CEGAR-based model checking all exploit this coincidence! Unify different approaches: deductive proving, SAT/SMT, abstract interpretation, model checking... Symbolic abstract interpretation, Thakur and Reps Abstract interpretation as automatic deduction..(working on it..) Jack Yao Logic4Sec
- 24. . . . . . . Introduction Approaches Applications Specialized Logic Model Logic and its variants Linear Logic Bunched logic Others Temporal Logic Recall model checking section.. Jack Yao Logic4Sec
- 25. . . . . . . Introduction Approaches Applications Specialized Logic Model Logic and its variants Linear Logic Bunched logic Others Belief Logics: BAN Logic The BAN (Burrows, Abadi, and Needham)logic Modal logic of belief plus specialized predicates and inference rules Protocol messages are idealized into logical statements Jack Yao Logic4Sec
- 26. . . . . . . Introduction Approaches Applications Specialized Logic Model Logic and its variants Linear Logic Bunched logic Others Linear Logic J.-Y. Girard, ”Linear logic”, Theoretical Comp. Sci, 1987 Used to model state-transition systems, inspire other logic Great impact on logic(proof theory) and cs(verification) community. Application to security Model-checking with linear-logic symbolic search tool LLF, LICS 96 A Linear Logic for Authorization and Knowledge, ESORICS 06 ... Jack Yao Logic4Sec
- 27. . . . . . . Introduction Approaches Applications Specialized Logic Model Logic and its variants Linear Logic Bunched logic Others Bunched logic By Ohearn and Pym, and has many variants(BI, CBI, BBI..etc) Bunched logics extend classical or intuitionistic logic with various ”linear” or multiplicative connectives(borrow from linear logic) Formulas can be understood as sets of ”worlds” (often ”resources”) in an underlying model Boolean BI(BBI) is the foundation of Separation Logic! Jack Yao Logic4Sec
- 28. . . . . . . Introduction Approaches Applications Specialized Logic Model Logic and its variants Linear Logic Bunched logic Others Affine Logic Jack Yao Logic4Sec
- 29. . . . . . . Introduction Approaches Applications Specialized Logic Model Logic and its variants Linear Logic Bunched logic Others Region Logic Jack Yao Logic4Sec
- 30. . . . . . . Introduction Approaches Applications Specialized Logic Model Logic and its variants Linear Logic Bunched logic Others The End Jack Yao Logic4Sec
- 31. . . . . . . Introduction Approaches Applications Specialized Logic Model Logic and its variants Linear Logic Bunched logic Others Reference Jonathan Millen Rajeev Alur Bruno Blanchet Jack Yao Logic4Sec