author | paulson |
Thu, 19 Dec 1996 11:58:39 +0100 | |
changeset 2451 | ce85a2aafc7a |
parent 2449 | d30ad12b1397 |
child 2481 | ee461c8bc9c3 |
permissions | -rw-r--r-- |
2449 | 1 |
(* 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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syntax |
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newK2 :: "nat*nat => key" |
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translations |
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"newK2 x" == "newK(nPair x)" |
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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 :: "nat => (nat*msg*msg)set" |
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inductive "respond i" (*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; |
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MA = {|Agent A, Agent B, Nonce NA, Agent Server|} |] |
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==> (j, {|Hash{|Key(shrK A), MA|}, MA|}, |
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{|Agent A, |
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Crypt (shrK A) {|Key(newK2(i,j)), Agent B, Nonce NA|}, |
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Agent Server|}) |
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: respond i" |
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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 "[| (Suc j, PA, RA) : respond i; |
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B ~= Server; |
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MB = {|Agent B, Agent C, Nonce NB, PA|}; |
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PA = {|Hash{|Key(shrK A), MA|}, MA|}; |
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MA = {|Agent A, Agent B, Nonce NA, P|} |] |
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==> (j, {|Hash{|Key(shrK B), MB|}, MB|}, |
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{|Agent B, |
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Crypt (shrK B) {|Key(newK2(i,Suc j)), Agent A, Nonce NB|}, |
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Agent B, |
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Crypt (shrK B) {|Key(newK2(i,j)), Agent C, Nonce NB|}, |
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RA|}) |
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: respond i" |
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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 :: nat => msg set |
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inductive "responses i" |
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intrs |
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(*Server terminates lists*) |
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Nil "Agent Server : responses i" |
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Cons "RA : responses i |
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==> {|Agent B, |
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Crypt (shrK B) {|Key(newK2(i,k)), Agent A, Nonce NB|}, |
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RA|} : responses i" |
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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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2451
ce85a2aafc7a
Extensive tidying and simplification, largely stemming from
paulson
parents:
2449
diff
changeset
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RA1 "[| evs: recur lost; A ~= B; A ~= Server; |
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MA = {|Agent A, Agent B, Nonce(newN(length evs)), Agent Server|}|] |
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==> Says A B {|Hash{|Key(shrK A),MA|}, MA|} # 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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2451
ce85a2aafc7a
Extensive tidying and simplification, largely stemming from
paulson
parents:
2449
diff
changeset
|
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RA2 "[| evs: recur lost; B ~= C; B ~= Server; |
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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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MB = {|Agent B, Agent C, Nonce (newN(length evs)), PA|} |] |
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==> Says B C {|Hash{|Key(shrK B),MB|}, MB|} # 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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2451
ce85a2aafc7a
Extensive tidying and simplification, largely stemming from
paulson
parents:
2449
diff
changeset
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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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(0,PB,RB) : respond (length 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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2451
ce85a2aafc7a
Extensive tidying and simplification, largely stemming from
paulson
parents:
2449
diff
changeset
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RA4 "[| evs: recur lost; A ~= B; |
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Says C' B {|Agent B, |
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Crypt (shrK B) {|Key KAB, Agent A, Nonce NB|}, |
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Agent B, |
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Crypt (shrK B) {|Key KAC, 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 |