author | paulson |
Fri, 17 Jan 1997 12:49:31 +0100 | |
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child 2532 | cde25bf71cc1 |
permissions | -rw-r--r-- |
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(* Title: HOL/Auth/Recur |
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ID: $Id$ |
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
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Copyright 1996 University of Cambridge |
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Inductive relation "recur" for the Recursive Authentication protocol. |
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*) |
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Recur = Shared + |
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(*Two session keys are distributed to each agent except for the initiator, |
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who receives one. |
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Perhaps the two session keys could be bundled into a single message. |
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*) |
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consts respond :: "event list => (msg*msg*key)set" |
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inductive "respond evs" (*Server's response to the nested message*) |
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intrs |
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(*The message "Agent Server" marks the end of a list.*) |
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One "[| A ~= Server; Key KAB ~: used evs |] |
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==> (Hash[Key(shrK A)] |
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{|Agent A, Agent B, Nonce NA, Agent Server|}, |
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{|Crypt (shrK A) {|Key KAB, Agent B, Nonce NA|}, Agent Server|}, |
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KAB) : respond evs" |
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(*newK2(i,Suc j) is the key for A & B; newK2(i,j) is the key for B & C*) |
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Cons "[| (PA, RA, KAB) : respond evs; |
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Key KBC ~: used evs; Key KBC ~: parts {RA}; |
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PA = Hash[Key(shrK A)] {|Agent A, Agent B, Nonce NA, P|}; |
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B ~= Server |] |
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==> (Hash[Key(shrK B)] {|Agent B, Agent C, Nonce NB, PA|}, |
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{|Crypt (shrK B) {|Key KAB, Agent A, Nonce NB|}, |
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Crypt (shrK B) {|Key KBC, Agent C, Nonce NB|}, |
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RA|}, |
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KBC) |
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: respond evs" |
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(*Induction over "respond" can be difficult due to the complexity of the |
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subgoals. The "responses" relation formalizes the general form of its |
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third component. |
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*) |
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consts responses :: event list => msg set |
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inductive "responses evs" |
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intrs |
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(*Server terminates lists*) |
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Nil "Agent Server : responses evs" |
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Cons "[| RA : responses evs; Key KAB ~: used evs |] |
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==> {|Crypt (shrK B) {|Key KAB, Agent A, Nonce NB|}, |
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RA|} : responses evs" |
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consts recur :: agent set => event list set |
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inductive "recur lost" |
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intrs |
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(*Initial trace is empty*) |
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Nil "[]: recur lost" |
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(*The spy MAY say anything he CAN say. We do not expect him to |
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invent new nonces here, but he can also use NS1. Common to |
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all similar protocols.*) |
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Fake "[| evs: recur lost; B ~= Spy; |
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X: synth (analz (sees lost Spy evs)) |] |
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==> Says Spy B X # evs : recur lost" |
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(*Alice initiates a protocol run. |
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"Agent Server" is just a placeholder, to terminate the nesting.*) |
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RA1 "[| evs: recur lost; A ~= B; A ~= Server; Nonce NA ~: used evs |] |
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==> Says A B |
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(Hash[Key(shrK A)] |
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{|Agent A, Agent B, Nonce NA, Agent Server|}) |
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# evs : recur lost" |
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(*Bob's response to Alice's message. C might be the Server. |
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XA should be the Hash of the remaining components with KA, but |
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Bob cannot check that. |
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P is the previous recur message from Alice's caller. |
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NOTE: existing proofs don't need PA and are complicated by its |
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presence! See parts_Fake_tac.*) |
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RA2 "[| evs: recur lost; B ~= C; B ~= Server; Nonce NB ~: used evs; |
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Says A' B PA : set_of_list evs; |
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PA = {|XA, Agent A, Agent B, Nonce NA, P|} |] |
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==> Says B C (Hash[Key(shrK B)] {|Agent B, Agent C, Nonce NB, PA|}) |
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# evs : recur lost" |
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(*The Server receives and decodes Bob's message. Then he generates |
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a new session key and a response.*) |
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RA3 "[| evs: recur lost; B ~= Server; |
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Says B' Server PB : set_of_list evs; |
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(PB,RB,K) : respond evs |] |
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==> Says Server B RB # evs : recur lost" |
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(*Bob receives the returned message and compares the Nonces with |
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those in the message he previously sent the Server.*) |
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RA4 "[| evs: recur lost; A ~= B; |
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Says C' B {|Crypt (shrK B) {|Key KAB, Agent A, Nonce NB|}, |
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Crypt (shrK B) {|Key KBC, Agent C, Nonce NB|}, RA|} |
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: set_of_list evs; |
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Says B C {|XH, Agent B, Agent C, Nonce NB, |
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XA, Agent A, Agent B, Nonce NA, P|} |
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: set_of_list evs |] |
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==> Says B A RA # evs : recur lost" |
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(**No "oops" message can readily be expressed, since each session key is |
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associated--in two separate messages--with two nonces. |
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***) |
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end |