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The Formal Method CAPSL

The Formal Method CAPSL. Kyle Taylor Zhenxiao Yang. {A, N a } PB. A B: {A, N a } PB B A: {N a , N b } PA A B: {N b } PB. {N a , N b } PA. A. B. {N b } PB. CAPSL. Common Authentication Protocol Specification Language Message list protocol description. Overview.

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The Formal Method CAPSL

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  1. The Formal Method CAPSL Kyle Taylor Zhenxiao Yang

  2. {A, Na}PB • A B: {A, Na}PB • B A: {Na, Nb}PA • A B: {Nb}PB {Na, Nb}PA A B {Nb}PB CAPSL • Common Authentication Protocol Specification Language • Message list protocol description

  3. Overview

  4. CAPSL Notation • Declarations • Imports • Types • Variables • Functions • Constants • Modules • Typespec • Protocol • Environment

  5. Typespec TYPESPEC PPK; IMPORTS SPKE; TYPES PKUser : Principal Functions pk(PKUser): Pkey; sk(PKUser): Pkey, PRIVATE; VARIABLES A: PKUser; X: Field; Axioms ped(sk(A), ped(pk(A), X)) = X; ped(pk(A), ped(sk(A), X)) = X; INVERT ped(pk(A), X): X | sk(A); INVERT ped(sk(A), X): X | pk(A); • Introduce New Types • Define Functions for a Type • Extend Existing Types • Syntax • Declarations • Axioms

  6. Protocol • The Message List • Syntax • Declaration • Assumptions • Messages • Goals PROTOCOL Simple; VARIABLES A, B: Principal; K: Skey, FRESH, CRYPTO; F: Field; ASSUMPTIONS HOLDS A: B; MESSAGES A -> B: {A,K}pk(B); GOALS SECRET K;

  7. Protocol Declaration and Assumptions • Declaration • Denotes • Allows a variable to be defined as the value of an expression • Assumptions • Boolean-valued terms or equalities • BELIEVES • Used to indicate a initial belief • HOLDS • Used to indicate knowledge of another entity • KNOWS • Belief plus truth Example: BELIEVES A : BELIEVES B : HOLDS A : K

  8. Protocol Messages • Message Format • id. sender -> receiver : field, …; • Concatenation of Fields • {,} denotes associative concatenation • [,] denotes non-associative concatenation • Encryption • Built in functions ped(), pk(), se(), sd() • {A, K}pk(B) == ped(pk(B), {A, K}) • {X}K == se(K, X) and {X}’K == sd(K, X)

  9. Protocol Messages Continued • Arithmetic • Allows +, -, *, /, and ^ with built in type Skey • %-operator • Distinguishes between the senders and the receivers view of a message • {A%B, C%D} • Sender constructs {A, C} • Receiver constructs {B, D}

  10. Protocol Messages Continued • Actions • Assignment or comparison test • Assume and Prove • Assumptions and Goals that are associated with intermediate states rather than initial and final states • Phrases • Phrase = message + actions before and after it • “/” used to separate receiver actions from sender actions • A -> B: X; • X < Y;/ • A -> C: Z;

  11. Protocol Messages Continued • Subprotocols • A protocol may invoke a different protocol using the INCLUDE P; • No statements may follow and INCLUDE • Conditional Selection • IF A=B THEN INCLUDE P2; • ELSE INCLUDE P3; ENDIF;

  12. Protocol Goals • States security objectives • SECRET V : P1, … • Variable V is a secret shared only by P1, … • PRECEDES A : B | V1, V2 • If B reaches its final state, it agrees with A on V1, V2 • AGREE A, B : V1, … | W1, … • If A and B agree on W1 then they must agree on V1

  13. Environment ENVIORNMENT Test IMPORTS NSPK; CONSTANTS Alice, Bob: PKUser; Mallory: PKUser, EXPOSED; AGENT A1 HOLDS A = Alice; B = Bob; AGENT B1 HOLDS B = Bob; EXPOSED {Bob}sk(Alice); END; • Used for setup • Syntax • Declaration • Agent • Define Roles • Exposed • Defines initial knowledge of an attacker • Axioms • Defines assumptions about constants • Order • Species series parrallel sequencing of agents

  14. Needham-Schroeder Public Key Handshake PROTOCOL NSPK; Variables A, B: PKUser; Na, Nb: Nonce, CRYPTO; ASSUMPTIONS HOLDS A: B; MESSAGES A-> B: {A, Na}pk(B); B-> A: {Na, Nb}pk(A); A-> B: {Nb}pk(B); GOALS SECRET Na; SECRET Nb; PRECEDES A: B | Na; PRECEDES B: A | Nb; END; ENVIORNMENT Test IMPORTS NSPK; CONSTANTS Alice, Bob: PKUser; Mallory: PKUser, EXPOSED; AGENT A1 HOLDS A = Alice; B = Bob; AGENT B1 HOLDS B = Bob; EXPOSED {Bob}sk(Alice); END;

  15. CIL • CAPSL Intermediate Language • Two purposes • Defines CAPSL Semantics • Interface to tool support • Uses Multiset Term Rewriting Rules

  16. CIL Design • General and Expressive enough to represent a wide range of protocols • At a low enough level to be useful to verification and model checking tools • Represents state-transitions in a pattern-matching style, with symbolic terms to represent encryption and other computations

  17. Rewrite Rules Rewrite Rules 0 + x -> x s(x) + y -> s(x +y) 0 * x -> 0 s(x) * y -> y + (x * y) fact(0) -> s(0) fact(s(x)) -> s(x) * fact(x) gcd(0, x) -> x gcd(x, x+y) -> gcd(x, y) Examples s(s(s(0))) = 3 Fact(s(s(0)))) ->s(s(0)) * fact(s(0)) ->s(s(0)) * s(0) * fact(0) ->s(s(0)) * s(0) * s(0) ->s(s(0)) * s(0) + (0 * s(0)) ->s(s(0)) * s(0) + 0 ->s(s(0)) * s(0) ->s(s(0)) + (0 * s(s(0))) ->s(s(0)) + 0 ->s(s(0) = 2 s(0) + (0 * s(0)) ->s(0) + 0 ->s(0) = 1 gcd(s(s(s(s(0)))), s(s(0))) ->gcd(s(s(0)), s(s(0))) ->gcd(0, s(s(0))) ->s(s(0)) = 2

  18. Multi-Set Rewrite • F1, …, Fk ($ X1, …, Xm) G1, …, Gn • " i,j Fi and Gj are facts • Existentially quantified variables are instantiated with fresh (unused) constants • A rule is eligible to fire when the facts on the left side can be matched with facts in the multiset • When a rule fires, facts on the left side of the rule are removed from the multiset and facts on the right side of the rule are inserted into the multiset after being instantiated according to the substitution required by the pattern match.

  19. MSR Example • Rule that defines two new agents • A0(A, B),B0(B) • The message “A  B: A, {N}sk(A) results in at least two rules • A0(A,B)  ($N)A1(A,B,N), M(A, B, { A, {N}sk(A)} • B0(B), M(X, B, { A, {N}sk(A)})  B1(B, A, N)

  20. Translation Output • Slot Table • Maps each protocol variable to an argument position in the state predicate of each role • Symbol Table • Contains all identifiers declared in all the specification modules • Axioms • Single list generated form Typespec and Environment • Localized Assumptions and Goals • Axioms localized to a particular state • Protocol Rewrite Rules • MSR rules • Environment Information • CIL AST representation of an Environment

  21. Translation Stages • Parsing • Checks syntax and produces a parse tree • Type Checking • Confirms consistency of type and signature declarations • Syntax Transformations • Syntactical sugar is removed • Rule Generation • Creation of rewrite rules from messages and actions • Local Assertions • Transformation of Assertions from interleaved to Associated • Optimization • Reduces the number or rules and the number of states per role by 50%

  22. CAPSL Example AP1.0

  23. CAPSL Example AP1.0 (cont’d) PROTOCOL AP10; VARIABLES A, B: Principal; ASSUMPTIONS HOLDS A:B; MESSAGES A -> B: A; END;

  24. CAPSL Example AP2.0

  25. CAPSL Example AP2.0 (cont’d) PROTOCOL AP20; VARIABLES A, B: Principal; IP: Field; ASSUMPTIONS HOLDS A: B, IP; MESSAGES A -> B: {A,IP}; END;

  26. CAPSL Example AP3.0

  27. CAPSL Example AP3.0 (cont’d) PROTOCOL AP30; VARIABLES A, B: Principal; C: Field; P: Field, CRYPTO; ASSUMPTIONS HOLDS A: B, P; HOLDS B: C; MESSAGES A -> B: {A, P}; B -> A: C; END;

  28. CAPSL Example AP4.0

  29. CAPSL Example AP4.0 (cont’d) PROTOCOL AP40; VARIABLES A, B: Principal; R: Nonce; K: Skey; S: Field; ASSUMPTIONS HOLDS A: B, K; HOLDS B: K, S; MESSAGES A -> B: A; B -> A: R; A -> B: {R}K; B -> A: S; END;

  30. CAPSL Example AP5.0

  31. CAPSL Example AP5.0 (cont’d) PROTOCOL AP50; VARIABLES A, B: PKUser; R: Nonce; C, S: Field; ASSUMPTIONS HOLDS A: B; HOLDS B: S, C; MESSAGES A -> B: A; B -> A: R; A -> B: {R}sk(A); B -> A: S; A -> B: pk(A); B -> A: C; END;

  32. CAPSL Example AP5.0 (cont’d)

  33. CAPSL Example AP5.0 (cont’d)

  34. Tools Support • Translators • Connectors • Maude, PVS, NRL, etc.

  35. Translator • CAPSL Parser and Type Checker • Checks syntax and type consistency • Rule Generator • Uses maude to generate CIL rewrite rules • CIL Optimizer • Optimizes CIL while preserving behavior

  36. Connectors • Objective • A bridge between CIL and various analyzer tools • Example Connectors • cil2pvs • cil2maude

  37. Maude • Rewriting Logic Interpreter • Contains an LTL Model Checker • Reflective Computation Through Meta-Level Modules

  38. Conclusion and Discussions • Good Idea • Unambiguous because of CIL • Simple to describe protocols • Inflexible in that it only specifies protocols • The power of this language is in the tool support • Insightful in the abstraction of the tool support • More Connectors Needed • Better documentation of Tool Support • MuCAPSL

  39. References • CAPSL Homepage: http://www.csl.sri.com/users/millen/capsl/ • G. Denker and J. Millen. CAPSL intermediate language. In N. Heintze and E. Clarke, editor, Workshop on Formal Methods and Security Protocols (FMSP99), Trento, Italy, 1999. URL: http://www.csl.sri.com/~denker/pub_99.html • G. Denker, J. Millen, and H. Ruess. The CAPSL integrated protocol environment. Technical Report SRI-CSL-2000-02, Oct. 2000. URL: http://www.csl.sri.com/papers/sri-csl-2000-02/

  40. References • Grit Denker. Design of a CIL connector to maude. In 2000 Workshop on Formal Methods and Computer Security, Chicago, USA, July 2000. URL: http://www.csl.sri.com/papers/den00 • Narciso Mart-Oliet and Jos Meseguer. Rewriting logic: Roadmap and bibliography. Theoretical Computer Science, 285(2):121-154, Aug. 2002. URL: http://citeseer.nj.nec.com/486097.html

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