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Internet Security CSCE 813 Communicating Sequential Processes

Internet Security CSCE 813 Communicating Sequential Processes. Reading. Today: Modelling and analysis of security protocols: Chapter 1 Next Class: Modelling and analysis of security protocols: Chapter 1 and 2. CSP Objectives. Model dynamics Model and analyze concurrency

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Internet Security CSCE 813 Communicating Sequential Processes

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  1. Internet Security CSCE 813Communicating Sequential Processes

  2. Reading • Today: • Modelling and analysis of security protocols: Chapter 1 • Next Class: • Modelling and analysis of security protocols: Chapter 1 and 2 CSCE 813 - Farkas

  3. CSP Objectives • Model dynamics • Model and analyze concurrency • E.g., calculation intensive systems, distributed applications • Support parallelism CSCE 813 - Farkas

  4. CSP • Notation for describing systems of parallel agents that communicate by passing messages between them • Formal study of systems • Concurrency • Security • Mathematical notation for describing interaction • Different components influence each other CSCE 813 - Farkas

  5. CSP Components • Processes • Operators • Communication: visible events:  • Invisible (internal) event:  • CSP: allows to describe the states in which processes might be  allows to work out what actions are immediately possible for the process and what the result states of the actions are CSCE 813 - Farkas

  6. Message Passing • Synchronous: both processes MUST be ready to communicate • Non-buffered sends and receives • Explicit naming of source and destination processes CSCE 813 - Farkas

  7. Messages Send (B, message) Receive (A, message) Process A Process B Input command: <source-process> ?<target value> e.g., keyboard?m Output command: <destination process>!<target value> e.g., screen?average CSCE 813 - Farkas

  8. Communication • Process P executes and input command specifying process Q as its source AND • Process Q executes an output command specifying process P as its destination AND • The target variable in the input statement matches the value in the output statement CSCE 813 - Farkas

  9. Program Equivalence • Two programs P1 and P2 are equivalent if they produce patterns of visible actions that cannot be distinguished by an observer. • Only the communications of a program matters! CSCE 813 - Farkas

  10. Communication • Prefix: given a process P and a communication a in , a→ P is a program that • Performs a then • Behaves as P • Given in, out in  what is • in → out → P • Process Stop: no visible or non-visible action • Given a in  what is a → Stop CSCE 813 - Farkas

  11. Build Processes • Consider: Given a,b,c in  • Proc = a → b → c → Stop • Proc: finite succession of choices before stopping • Proc’s environment might choose not to accepted any of a,b,c, so it might get stuck before Stop CSCE 813 - Farkas

  12. Build Processes • Recursion: processes “go on forever” • Looping back to a state they have been before • Alt = to → fro → Alt • Dalt = to → fro → to → fro → Dalt • Malt1 = to → Malt2 • Malt2 = fro → Malt1 • Nalt = to → fro → Dalt • 1, 2, 5, and (3,4) are equivalent programs CSCE 813 - Farkas

  13. Prefix • Offering a single action • Offering of choice: any set of visible actions • If A  , ?x : A → P(x) represent all the actions in A • x is the parameter of P -- parameters can beused in events or manipulated • When a  A is chosen, it behaves like P(a) • Example: always prepared to offer any event from A  • RUNA = ?x : A → RUNA CSCE 813 - Farkas

  14. Compound events • Coding Machine example • CM1(s) = ?x : L  {off} → CM1’ (s,x) • CM1’(s,off) = Stop • CM1’(s,x) = crypt(s,x) → CM1(newstate(s,x)) (x  L) • Action: channel name followed by zero or more data components • Coding Machine example without off • CM2(s) = in?x → out!crypt(s,x) → CM2(newstate(s,x)) CSCE 813 - Farkas

  15. Choice Operators • Deterministic finite state machine over finite  • e.g., Pi = ? X : Ai→ Pi’(x) • Choice operator:  • Gives the option between the actions of two processes then • Behaves like the one chosen CSCE 813 - Farkas

  16. Choice Operator • Example Choice • if A = B  C then ?x : A → P(x) = (?x : B → P(x))  (?x : C → P(x) ) • Stop and equivalence • if A = A  Ø then ?x : A → P(x) = (?x : A → P(x))  Stop that is P  P  Stop • If B= Ø then ?x : B → P(x)  Stop CSCE 813 - Farkas

  17. Choice Operator • Revisit: if A = B  C then ?x : A → P(x) = (?x : B → P(x))  (?x : C → P(x) ) • If B and C are disjoint: together they give all the choices in A • What happens if B and C overlap? • Given processes P and Q, what does P Q mean? • Choosing an action x  B  C what is the result of (?x : B → P(x))  (?x : C → Q(x) ) • CSP allows the implementor to make a choice between the two sides • After action x, the process may behave as P(x) or Q(x), the environment has no control over it. CSCE 813 - Farkas

  18. Non-determinism • Program acts nondeterministically if it is unpredictable • The program is allowed to make internal decision that affect how it behaves as viewed from the outside • Implementation is allowed to choose • E.g., (a → a → Stop)  (a → b → Stop) CSCE 813 - Farkas

  19. Non-Deterministic Choice • P Q • behaves like P or like Q • User has no control over which • Can be implemented using two internal actions • Implementer is not required to implement this way (can choose either P or Q or (P or Q)) • Useful for model degree of unpredictability, like communication medium that transmits data correctly or loose it. CSCE 813 - Farkas

  20. Non-Deterministic Choice • P Q and P  Qhave identical traces: sequences of visible communications • In most circumstances it cannot be told whether a non-deterministic choice was made by observing the process. • What is the difference between (a → P) Stop and (a → P)Stop ? CSCE 813 - Farkas

  21. Parallel Operators • Put sequential processes parallel • System state: state of each component • Number of possible states increases exponentially with the size of the network • How to put processes together for parallel network? • How to check whether such a network satisfies a specification? CSCE 813 - Farkas

  22. Parallel Combination • Just an other process to which any of the previous operators can be applied. • Each parallel process is equivalent to a sequential one (with infeasibly large number of states) • CSP processes influence each other by affecting what communications they can perform. CSCE 813 - Farkas

  23. Parallel Combination • Synchronize all visible actions • P || Q can perform a   only when P and Q can • (?x : A → P(x)) || (?x : B → Q(x)) = ?x : A B→ (P(x) || Q(x)) CSCE 813 - Farkas

  24. Parallel Combinations • Interfaces parallel operator: P ||X Q • Synchronize all events in X • Example: • P = ?x : A → P’(x) • Q = ?x : B → Q’(x) • P ||X Q = ?x : X  A  B → (P’(x) || Q’(x))  ?x : A \ X → (P’(x) ||X Q)  ?x : B \ X → (P||X Q’(x)) CSCE 813 - Farkas

  25. Alphabet Controlled • P X ||Y Q • Each process is given control of a particular set of events • No process is ever permitted to communicate outside of its own alphabet • Interface between two processes: intersection of their alphabet CSCE 813 - Farkas

  26. CSP Operators • Stop process does nothing • a → P event prefix • ?x:A → P event prefix choice • P  Q choice between two processes • P  Q nondeterministic choice • P || Q lockstep parallel • P ||X Q interface parallel • P X ||Y Q synchronizing parallel CSCE 813 - Farkas

  27. Next Class: CSP CH 1 finishModeling security protocols in CSP CSCE 813 - Farkas

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