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Understanding MSR.3 One Year Later

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A comprehensive look at MSR.3 one year after its inception, including syntax, semantics, logical derivations, and transition details. Explore the significance and applications of this security protocol language.

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Understanding MSR.3 One Year Later

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  1. MSR 3:One Year Later Iliano Cervesatoiliano@itd.nrl.navy.mil ITT Industries, inc @ NRL Washington, DC http://theory.stanford.edu/~iliano Protocol eXchange Seminar, UMBC May 27-28, 2004

  2. A B: {nA, A}kB B A: {nA, nB}kA A B: {nB}kB NSPK in MSR 3 MSR 2 spec. A:princ. { L: princ B:princ.pubK B  nonce  mset. B: princ. kB: pubK B.  nA: nonce. net ({nA, A}kB), L (A, B, kB, nA) B: princ. kB: pubK B. kA: pubK A. kA': prvK kA. nA: nonce. nB: nonce. net ({nA, nB}kA), L (A, B, kB, nA) net ({nB}kB) } Interpretation of L • Rule invocation • Implementation detail • Control flow • Local state of role • Explicit view • Important for DOS MSR 3: One Year Later

  3. A B: {nA, A}kB B A: {nA, nB}kA A B: {nB}kB NSPK in MSR 3 Not an MSR 2 spec. A:princ. B: princ. kB: pubK B.  nA: nonce. net ({nA, A}kB), (kA: pubK A. kA': prvK kA. nB: nonce. net ({nA, nB}kA) net ({nB}kB)) • Succinct • Continuation-passing style • Rule asserts what to do next • Lexical control flow • State is implicit • Abstract MSR 3: One Year Later

  4. A B: {nA, A}kB B A: {nA, nB}kA A B: {nB}kB Parametric strand Alice (A,B,NA,NB) : NA Fresh, pA(A,B) {NA, A}KB {NA, NB}KA {NB}KB Looks Familiar? Process calculus A:princ. B: princ. kB: pubK B. kA: pubK A. kA': prvK kA. nB: nonce. nnA: nonce. net ({nA, A}kB) . net <{nA, nB}kA> . net ({nB}kB) . 0 MSR 3: One Year Later

  5. What is MSR 3? A new language for security protocols • Supports • State transition specs • Conservative over MSR 2 • Process algebraic specs • Rewriting re-interpretation of logic • Rich composable set of connectives • Universal connector Neutral paradigm MSR 3: One Year Later

  6. More than the Sum of its Parts Process- and transition-based specs. in the same language • Choose the paradigm • User’s preference • Highlight characteristics of interest • Support various verification techniques (FW) • Mix and match styles • Within a spec. • Within a protocol • Within a role MSR 3: One Year Later

  7. What is in MSR 3 ? • Security-relevant signature • Network • Encryption, … • Typing infrastructure • Dependent types • Subsorting • Data Access Specification (DAS) • Module system • Equations FromMSR 1 FromMSR 2 w-Multisets MSR 2 Protocols Repr. gap From MSR 2implementation MSR 3: One Year Later

  8. w-Multisets Specification language for concurrent systems • Crossroad of • State transition languages • Petri nets, multiset rewriting, … • Process calculi • CCS, p-calculus, … • (Linear) logic • Benefits • Analysis methods from logic and type theory • Common ground for comparing • Multiset rewriting • Process algebra • Allows multiple styles of specification • Unified approach w-Multisets MSR 2 Protocols Repr. gap MSR 3: One Year Later

  9. Syntax A ::= a atomic object | 1[] empty | A B [A, B] formation | A  B [A  B] rewrite | T no-op | A & B [A || B] choice | x. A instantiation | x. A generation | ! A replication Generalizes FO multiset rewriting (MSR 1-2) x1…xn. a(x)y1…yk. b(x,y) MSR 3: One Year Later

  10. State and Transitions • States S ; G ; D S ; D • S is a list • G and D arecommutative monoids • Transitions S; G; D S’; G’; D’ S; G; D*S’; D’ • * for reflexive and transitive closure • Constructor: “,” • Empty: “” - logic- system w- rewriting - processes- security MSR 3: One Year Later

  11. Transition Semantics S ; G ; (D, A, A  B) S ; G ; (D, B) T (no rule) & S ; G ; (D, A1& A2) S ; G ; (D, Ai) S ; G ; (D, x. A) S ; G ; (D, [t/x]A) if S |- t S ; G ; (D, x. A) (S, x) ; G ; (D, A) ! S ; G ; (D, !A)S ; (G, A) ; D S ; (G, A) ; D S ; (G, A) ; (D, A) S ;G;D*S ;D S ;G;D*S’’;D’’ if S ;G;D S’;G’;D’ andS’;G’;D’ *S’’;D’’ MSR 3: One Year Later

  12. Linear Logic • Formulas A, B ::= a | 1 | A B | A  B | ! A | T | A & B | x. A | x. A • LV sequents G ; D -->S C • Constructor: “,” • Empty: “” - logic- system w- rewriting - processes- security Unrestrictedcontext Goalformula Linearcontext Signature MSR 3: One Year Later

  13. Logical Derivations G’’’; C -->S’’’C • Proof of C from D and G • Emphasis on C • C is input • Finite • Closed • Rules shown • Major premise • Preserves C • Minor premise • Starts subderivation G’’; D’’ -->S’’CG’; D’ -->S’C - logic- system w- rewriting - processes- security G; D -->SC MSR 3: One Year Later

  14. A Rewriting Re-Interpretation • Transition • From conclusion • To major premise • Emphasis on G, Dand S • C is output, at best • Does not change • Possibly infinite • Open • Minor premise • Auxiliary rewrite chain • Finite • Topped with axiom G’’’; C -->S’’’C G’’; D’’ -->S’’CG’; D’ -->S’C - logic- system w- rewriting - processes- security G; D -->SC MSR 3: One Year Later

  15. S; G; (D, x. A) S; G; (D, [t/x]A) if S |- t S |- t G; D,[t/x]A -->SC G; D,x.A -->SC Interpreting Unary Rules S; G; (D, !A)S; (G, A); D G; D, A, B -->SC G; D, AB -->SC S; G; (D, AB) S; G; (D, A, B) G; D, A -->S,xC G; D, $x.A -->SC - logic- system w- rewriting - processes- security S; G; (D, x. A) (S, x); G; (D, A) G, A; D -->SC G; D, !A -->SC … … MSR 3: One Year Later

  16. Minor premise Auxiliary rewrite chain Top of tree Focus shifts to RHS Axiom rule Observation Binary Rules and Axiom G’; A -->S’A G; D’ -->SAG; D, B -->SC G; D, D’, AB -->SC - logic- system w- rewriting - processes- security MSR 3: One Year Later

  17. G,G’; A’ -->S,S’A’ Observations G; D -->SS’.A’ • Observation states S ; D • In D, we identify • , with  •  with 1 Categorical semantics • Identified with x1. … xn.D • For S = x1, …, xn De Bruijn’s telescopes • Observation transitions S; G; D*S’; D’ A D = D - logic- system w- rewriting - processes- security S; D = S.D MSR 3: One Year Later

  18. G; D’ -->SAG; D, B -->SC G; D, D’, AB -->SC G; D’ -->SA G; D, A-->SC G; D, D’ -->S C Interpreting Binary Rules G; A -->SA S; G; (D, D’, A  B) S; G; (D, B)if S; G; D’* S; A S; G; D*S; D S; G; D*S’’; D’’if S; G; D S’; G’; D’and S’; G’; D’* S’’; D’’ - logic- system w- rewriting - processes- security S;G;D,D’ S;G; (A, D)if S;G;D’*S; A … … MSR 3: One Year Later

  19. Formal Correspondence • Soundness If S ; G ; D* S,S’; D’then G ; D -->SS’. D’ • Completeness? • No! We have only crippled right rules  ;  ; a  b, b  c*  ; a  c - logic- system w- rewriting - processes- security MSR 3: One Year Later

  20. System w • With cut, rule for  can be simplified to S; G; (D, A, A  B) S; G; (D, B) • Cut elimination holds = in-lining of auxiliary rewrite chains • But … • Careful with extra signature symbols • Careful with extra persistent objects • No rule for  needs a premise •  does not depend on * - logic- system w- rewriting - processes- security MSR 3: One Year Later

  21. Multiset Rewriting • Multiset: set with repetitions allowed a ::=  | a, a • Commutative monoid • Multiset rewriting (a.k.a. Petri nets) • Rewriting within the monoid • Fundamental model of distributed computing • Alternative: Process Algebras • Basis for security protocol spec. languages • MSR family • … several others • Many extensions, more or less ad hoc - logic- system w- rewriting - processes- security MSR 3: One Year Later

  22. Atomic terms Principals A Keys K Nonces N Other Raw data , timestamp, … Constructors Encryption {_}_ Pairing (_, _) Other Signature, hash, MAC, … The Atomic Objects of MSR 3 w-Multisets MSR 2 Protocols Repr. gap Predicates • Network net • Memory MA • Intruder I • … Fully definable MSR 3: One Year Later

  23. Types Fully definable • Powerful abstraction mechanism • At various user-definable level • Finely tagged messages • Untyped: msg only • Simplify specification and reasoning • Automated type checking • Simple types • A : princ • n: nonce • m: msg, … • Dependent types • k : shKAB • K : pubKA • K’ : privKK, … w-Multisets MSR 2 Protocols Repr. gap MSR 3: One Year Later

  24. Subsorting • Allows atomic terms in messages • Definable • Non-transmittable terms • Sub-hierarchies • Discriminant for type-flaw attacks t <: t’ w-Multisets MSR 2 Protocols Repr. gap MSR 3: One Year Later

  25. Data Access Specification • Prevent illegitimate use of information • Protocol specification divided in roles • Owner = principal executing the role • A signing/encrypting with B’s key • A accessing B’s private data, … • Simple static check • Central meta-theoretic notion • Detailed specification of Dolev-Yao access model • Gives meaning to Dolev-Yao intruder • Current effort towards integration in type system • Definable • Possibility of going beyond Dolev-Yao model w-Multisets MSR 2 Protocols Repr. gap MSR 3: One Year Later

  26. Modules and Equations • Modules • Bundle declarations with simple import/export interface • Keep specifications tidy • Reusable • Equations (For free from underlying Maude engine) • Specify useful algebraic properties • Associativity of pairs • Allow to go beyond free-algebra model • Dec(k, Enc(k, M)) = M w-Multisets MSR 2 Protocols Repr. gap MSR 3: One Year Later

  27. State-Based vs. Process-Based • State-based languages • Multiset Rewriting • NRL Prot. Analyzer, CAPSL/CIL, Paulson’s approach, … • Statetransitionsemantics • Process-based languages • Process Algebra • Strand spaces, spi-calculus, … • Independentcommunicatingthreads w-Multisets MSR 2 Protocols Repr. gap MSR 3: One Year Later

  28. PB State vs.processdistance PB SB SB Otherdistance MSR 3 MSR 3 Bridges the Gap • Difficult to go from one to the other • Different paradigms w-Multisets MSR 2 Protocols Repr. gap State  Process translation done once and for all in MSR 3 MSR 3: One Year Later

  29. Summary • MSR 3.0 • Language for security protocol specification • Succinct representations • Simpl specifications • Economy of reasoning • Bridge between • State-based representation • Process-based representation • w-multisets • Logical foundation of multiset rewriting • Relationship with process algebras • Unified logical view • Better understanding of where we are • Hint about where to go next MSR 3: One Year Later

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