Nuprl Lemma : CRX-authentication-theorem
∀sth:SecurityTheory
(CRX-protocol{i:l}(sth-es(sth)) |= CR-initiator4{i:l}(sth-es(sth)) authenticates 2 messages
∧ CRX-protocol{i:l}(sth-es(sth)) |= CR-responder6{i:l}(sth-es(sth)) authenticates 3 messages )
Proof
Definitions occuring in Statement :
CRX-protocol: CRX-protocol{i:l}(s),
CR-responder6: CR-responder6{i:l}(s),
CR-initiator4: CR-initiator4{i:l}(s),
authentication: prtcl |= bs authenticates n messages ,
sth-es: sth-es(s),
security-theory: SecurityTheory,
all: ∀x:A. B[x],
and: P ∧ Q,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
and: P ∧ Q,
cand: A c∧ B,
member: t ∈ T,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
guard: {T},
ses-axioms: SecurityAxioms,
uimplies: b supposing a,
authentication: prtcl |= bs authenticates n messages ,
ses-disjoint: ActionsDisjoint,
exists: ∃x:A. B[x],
prop: ℙ,
is-basic-seq: thr[A;B] |= bs,
CR-initiator4: CR-initiator4{i:l}(s),
basic-seq-1-5: A ⟶ B: pas[A;B;m;n;x;y;z],
ses-is-protocol-actions: pas(thr),
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
ses-thread: Thread,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
ses-act: Act,
so_apply: x[s],
sq_stable: SqStable(P),
es-locl: (e <loc e'),
es-causl: (e < e'),
squash: ↓T,
sq_type: SQType(T),
subtract: n - m,
le: A ≤ B,
less_than': less_than'(a;b),
less_than: a < b,
true: True,
mk-pa: n(v),
ses-is-protocol-action: pa(e),
select: L[n],
cons: [a / b],
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
ses-V: PropertyV,
es-E-interface: E(X),
Id: Id,
ses-S: PropertyS,
ses-signer: signer(e),
pi2: snd(t),
pi1: fst(t),
CRX-protocol: CRX-protocol{i:l}(s),
ses-protocol1: Protocol1(bss),
ses-action: Action(e),
ses-protocol1-thread: (thr is one of bss at A),
iff: P ⇐⇒ Q,
CR-initiator1: CR-initiator1{i:l}(s),
basic-seq-1-1: A ⟶ B: pas[A; B; m],
ses-thread-member: e ∈ thr,
CR-initiator2: CR-initiator2{i:l}(s),
basic-seq-1-3: A ⟶ B: pas[A; B; m; n; x],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
CR-responder4: CR-responder4{i:l}(s),
ses-NR: PropertyNR,
rev_implies: P ⇐ Q,
ses-thread-loc: loc(thr)= A,
event-has: (e has a),
class-value-has: X(e) has a,
nat: ℕ,
nil: [],
it: ⋅,
ge: i ≥ j ,
matching-conversation: MatchingConversation(n;thr1;thr2),
thread-messages: thread-messages(thr),
firstn: firstn(n;as),
lt_int: i <z j,
send-rcv-match: send-rcv-match(m1;m2),
CR-responder5: CR-responder5{i:l}(s),
CR-responder6: CR-responder6{i:l}(s),
ses-NU: PropertyNU
Latex:
\mforall{}sth:SecurityTheory
(CRX-protocol\{i:l\}(sth-es(sth)) |= CR-initiator4\{i:l\}(sth-es(sth)) authenticates 2 messages
\mwedge{} CRX-protocol\{i:l\}(sth-es(sth)) |= CR-responder6\{i:l\}(sth-es(sth)) authenticates 3 messages )
Date html generated:
2016_05_17-PM-00_51_30
Last ObjectModification:
2016_01_18-PM-07_16_18
Theory : event-logic-applications
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