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dnl // Tamarin uses ' which is an m4 close quote. So use <! !> for quoting instead.
changequote(<!,!>)
changecom(<!@,@!>)
/*
* Protocol: Wireguard protocol
* Modeler: Kevin Milner
* Date: February 2017
* Source: Original
* Status: WIP
*/
theory WireGuard
begin
builtins: hashing, diffie-hellman
functions: aead/4, decrypt/2
equations: decrypt(aead(k,n,p,a),k) = p //Plaintext can be recovered using the key
//Uncomment these to prevent any adversary message modifications
dnl define(In, AuthenticatedMessage($*))
dnl define(Out, AuthenticatedMessage($*))
dnl define(State,F_State($*))
restriction Eq_testing: "All x y #i. Eq(x,y) @ i ==> x = y"
restriction InEq_testing: "All x y #i. InEq(x,y) @ i ==> not(x = y)"
//Pre-established trust relationships
restriction pairings_unique:
"All id1 id2 pka pkb #i #j.
Paired(id1,pka,pkb) @ i & Paired(id2,pka,pkb) @ j
==> #i = #j"
rule KeyGen:
[ Fr(~ltk) ]
--[Key(~ltk)]->
[!AgentKey(~ltk), Out('g'^~ltk)]
rule ExchangePublicKeys:
[ !AgentKey(~ltkA)
, !AgentKey(~ltkB)
, Fr(~inj)
]--[
Paired(~inj, 'g'^~ltkA, 'g'^~ltkB)
, Paired(~inj, 'g'^~ltkB, 'g'^~ltkA)
, InEq($A,$B)
]->
[ State(~inj, ~ltkA, 'g'^~ltkB, ('g'^~ltkA)^~ltkB, '0')
, State(~inj, ~ltkB, 'g'^~ltkA, ('g'^~ltkA)^~ltkB, '0')
]
/* Uncomment to allow long term key compromise
rule CompromiseKey:
[!AgentKey($Agent,ltk)]
--[ Compromise($Agent,ltk) ]->
[Out(ltk)]
*/
// MESSAGE RULES
rule Handshake_InitNoPSK:
let cii = h('nopsk')
hi0 = h(<cii,'id',pkR,'g'^~ekI>) //No PSK means no intermediate hashes necessary here
ki0 = h(<cii,pkR^~ekI,'2'>)
ci0 = h(<cii,pkR^~ekI,'1'>)
altk= aead(ki0,'0','g'^~ltkI,hi0)
hi1 = h(<hi0,altk>)
ki1 = h(<ci0,sisr,'2'>)
ci1 = h(<ci0,sisr,'1'>)
ats = aead(ki1,'0',~ts,hi1)
hi2 = h(<hi1,ats>)
m1 = <'1',~sidI,'g'^~ekI,altk,ats,$mac1,$mac2> in //TODO:Model MACs
[ State(inj,~ltkI,pkR,sisr,anything)
, Fr(~sidI)
, Fr(~ekI)
, Fr(~ts)
]--[
Binding(inj,'g'^~ltkI,pkR)
, HandshakeInit('g'^~ltkI, pkR, hi2)
]->
[ State(inj,~ltkI,pkR,sisr,<'init',~sidI,~ekI,ci1,ki1,hi2>)
, Out(m1)
]
rule Handshake_RespNoPSK:
let cri = h('nopsk')
eisr = pekI^~ltkR
eier = pekI^~ekR
sier = pkI^~ekR
hr0 = h(<cri,'id','g'^~ltkR,pekI>) //No PSK means no intermediate hashes necessary here
kr0 = h(<cri,eisr,'2'>)
cr0 = h(<cri,eisr,'1'>)
altk= aead(kr0,'0',pkI,hr0)
hr1 = h(<hr0,altk>)
kr1 = h(<cr0,sisr,'2'>)
cr1 = h(<cr0,sisr,'1'>)
ats = aead(kr1,'0',ts,hr1)
hr2 = h(<hr1,ats>)
m1 = <'1',sidI,pekI,altk,ats,$mac1,$mac2> //TODO:Model MACs
hr3 = h(<hr2,'g'^~ekR>)
kr2 = h(<cr1,eier,'2'>)
cr2 = h(<cr1,eier,'1'>)
kr3 = h(<cr2,sier,'2'>)
cr3 = h(<cr2,sier,'1'>)
aemp= aead(kr3,'0','0',hr3)
hr4 = h(<hr3,aemp>)
m2 = <'2',sidI,~sidR,'g'^~ekR,aemp,$mac1,$mac2> in
[ State(inj,~ltkR,pkI,sisr,anything)
, Fr(~ekR)
, Fr(~sidR)
, In(m1)
]--[
Binding(inj,pkI,'g'^~ltkR)
, HandshakeResp(pkI,'g'^~ltkR,hr2,hr4)
, RespTransportKeys(pkI,'g'^~ltkR,cr3) //Not actually cr3, but derived from it.
]->
[ State(inj,~ltkR,pkI,sisr,<'resp',cr3>)
, Out(m2)
]
rule Handshake_CompleteNoPSK:
let eier = pekR^~ekI
sier = pekR^~ltkI
hi3 = h(<hi2,pekR>)
ki2 = h(<ci1,eier,'2'>)
ci2 = h(<ci1,eier,'1'>)
ki3 = h(<ci2,sier,'2'>)
ci3 = h(<ci2,sier,'1'>)
aemp= aead(ki3,'0','0',hi3)
hi4 = h(<hi3,aemp>)
m2 = <'2',sidI,sidR,pekR,aemp,$mac1,$mac2> in
[ State(inj,~ltkI,pkR,sisr,<'init',sidI,~ekI,ci1,ki1,hi2>)
, In(m2)
]--[
Binding(inj,'g'^~ltkI,pkR)
, InitTransportKeys('g'^~ltkI,pkR,ci3) //Not actually ci3, but derived from it.
]->
[ State(inj,~ltkI,pkR,sisr,<'init',ci3>)
]
/*/////////////////////////////////////////////////////////////////////////////
TRACE EXISTENCE
Status: All autoprove (~15 minutes, almost entirely on exists_detect)
*/
lemma exists_session: exists-trace
"Ex a b ck #i #j.
InitTransportKeys(a,b,ck) @ i & RespTransportKeys(a,b,ck) @ j & #j < #i"
lemma state_invariant[reuse,use_induction]:
"All inj pka pkb #i.
Binding(inj,pka,pkb) @ i ==> Ex #j. Paired(inj,pka,pkb) @ j & #j < #i"
lemma key_secrecy:
"(All a b ck #i.
InitTransportKeys(a,b,ck) @ i ==> not(Ex #j. K(ck) @ j))
&(All a b ck #i.
RespTransportKeys(a,b,ck) @ i ==> not(Ex #j. K(ck) @ j))"
lemma injective_agreement:
"All a b ck #i #j.
InitTransportKeys(a,b,ck) @ i & RespTransportKeys(a,b,ck) @ j
==> #j < #i & not(Ex #k. RespTransportKeys(a,b,ck) @ k & not(#k = #j))"
end
// vim: ft=spthy
|
