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302
proverif/pq/sender-keys-pqxdh.pv
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302
proverif/pq/sender-keys-pqxdh.pv
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(*
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Sender Keys protocol with PQXDH; proving secrecy, authentication, PFS, quantum PFS
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Author: [redacted]
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*)
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free m1: bitstring [private].
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free m2: bitstring [private].
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set selFun = Nounifset.
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set redundancyElim = best.
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set simpEqAll = false.
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set redundantHypElim = true.
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set simplifyProcess = true.
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set stopTerm = false.
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free c: channel.
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free a: channel. (* channel for the attacker *)
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free p: channel [private]. (* For the distribution of public keys with integrity and authenticity - verification happens out of band. This is a standard assumption. *)
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(* Symmetric key encryption *)
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type key.
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fun senc(key, bitstring): bitstring.
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reduc forall m: bitstring, k: key; sdec(k, senc(k,m)) = m.
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(* Asymmetric key encryption *)
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type skey.
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type pkey.
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fun rb(pkey): bitstring.
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fun pk(skey): pkey.
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fun aenc(bitstring, pkey): bitstring.
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reduc forall m: bitstring, sk: skey; adec(aenc(m,pk(sk)),sk) = m.
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(* Digital signatures *)
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fun sign(skey, bitstring): bitstring.
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fun okay():bitstring.
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reduc forall m: bitstring, sk: skey; checksign(pk(sk), m, sign(sk, m)) = okay.
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(* MACs *)
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fun mac(key, bitstring): bitstring.
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reduc forall k: key, m: bitstring; checkmac(k, m, mac(k, m)) = okay.
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(* Diffie-Hellman *)
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(* DH -> Public^Private *)
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fun dh(pkey, skey): key.
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equation forall a: skey, b: skey; dh(pk(a), b) = dh(pk(b), a). (* symmetry of DH *)
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(* KEM encapsulation *)
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type kempriv.
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type kempub.
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fun kempk(kempriv):kempub.
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fun penc(kempub, bitstring):bitstring.
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(* fun pdec(kempriv,bitstring):bitstring. *)
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reduc forall sk: kempriv, m:bitstring; pdec(sk, penc(kempk(sk), m)) = m.
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letfun kempriv2pub(k:kempriv) = kempk(k).
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letfun pqkem_enc(pk:kempub) =
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new ss:bitstring;
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(penc(pk,ss),ss).
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letfun pqkem_dec(sk:kempriv,ct:bitstring) =
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pdec(sk,ct).
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fun qb(kempub): bitstring [data].
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(* the concats *)
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fun concat1(bitstring, pkey, bitstring): bitstring [data].
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fun concat2(key, key, key, key, bitstring): bitstring [data].
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fun concat3(key, key): key [data].
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fun concat4(bitstring, pkey): bitstring [data].
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fun khash(key): key.
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fun hkdf1(bitstring): key [data].
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fun hkdf2_dev1(key): key [data].
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fun hkdf2_dev2(key): key [data].
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letfun hkdf2(k: key) =
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(hkdf2_dev1(k), hkdf2_dev2(k)).
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(* event declarations *)
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event sendOE1(pkey, key, pkey).
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event recvOE1(pkey, key, pkey).
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event sendOE2(pkey, key, pkey).
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event recvOE2(pkey, key, pkey).
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event sendME1(bitstring, key).
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event recvME1(bitstring, key).
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event sendME2(bitstring, key).
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event recvME2(bitstring, key).
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event compromiseSKA(skey).
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event compromiseSKB(skey).
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event breakDH(key, key, key, key).
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event start().
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let PeerA(SK_A: skey, PK_A: pkey, PK_B: pkey, FSK_A: skey, FPK_A: pkey) =
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new ae1: skey;
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new ae2: skey;
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let gae1 = pk(ae1) in
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let gae2 = pk(ae2) in
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(* generate amaster and enc msg (PHASE 1) *)
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phase 1;
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in(c, (gbssig: bitstring, gbs: pkey, gbo: pkey, gpqbo: kempub, gpqbsig: bitstring));
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if checksign(PK_B, rb(gbs), gbssig) = okay then
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if checksign(PK_B, qb(gpqbo), gpqbsig) = okay then
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let (ct: bitstring, ss: bitstring) = pqkem_enc(gpqbo) in
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let amaster = hkdf1(concat2(dh(gbs, SK_A), dh(PK_B, ae1), dh(gbs, ae1), dh(gbo, ae1), ss)) in
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let (ra1: key, ca1: key) = hkdf2(amaster) in (* derive the root and chain key *)
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let ak1 = khash(ca1) in
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let (ak1_auth: key, ak1_enc: key) = hkdf2(ak1) in
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new mra0: key; (* mra0 := fan out layer ratchet *)
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let x1 = senc(ak1_enc, (FPK_A, mra0)) in
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let x1_mac = mac(ak1_auth, concat1(x1, gae1, ct)) in
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event sendOE1(FPK_A, mra0, gae1);
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out(c, (x1, x1_mac, gae1, ct));
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(* =================== PHASE 3: SENDER KEYS SESSION B -> A =================== *)
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in(c, (x2: bitstring, x2_mac: bitstring, gtb2: pkey));
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let (ca2: key, ra2: key) = hkdf2(concat3(khash(ra1), dh(gtb2, ae1))) in
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let ak2 = khash(ca2) in
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let (ak2_auth: key, ak2_enc: key) = hkdf2(ak2) in
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if checkmac(ak2_auth, concat4(x2, gtb2), x2_mac) = okay then
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let (FPK_B: pkey, mrb0: key) = sdec(ak2_enc, x2) in
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event recvOE2(FPK_B, mrb0, gae2);
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(* =================== PHASE 4: SENDER KEYS MSG A -> B =================== *)
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let mra1 = khash(mra0) in
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let (mak1_auth: key, mak1_enc: key) = hkdf2(mra1) in
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let mx1 = senc(mak1_enc, m1) in
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let mx1_sig = sign(FSK_A, mx1) in
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event sendME1(m1, mra1);
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out(c, (mx1, mx1_sig));
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(* =================== PHASE 5: SENDER KEYS MSG B -> A =================== *)
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in(c, (mx2: bitstring, mx2_sig: bitstring));
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let mrb1 = khash(mrb0) in
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let (mbk1_auth: key, mbk1_enc: key) = hkdf2(mrb1) in
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if checksign(FPK_B, mx2, mx2_sig) = okay then
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let m2 = sdec(mbk1_enc, mx2) in
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event recvME2(m2, mrb1);
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(* =================== PHASE 6: Compromise =================== *)
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phase 5;
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event compromiseSKA(SK_A);
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out(a, SK_A);
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phase 6;
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event breakDH(dh(gbs, SK_A), dh(PK_B, ae1), dh(gbs, ae1), dh(gbo, ae1));
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out(a, (dh(gbs, SK_A), dh(PK_B, ae1), dh(gbs, ae1), dh(gbo, ae1)));
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0.
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let PeerB(SK_B: skey, PK_B: pkey, PK_A: pkey, FSK_B: skey, FPK_B: pkey) =
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new bo: skey;
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new bs: skey;
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new pqbo: kempriv;
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let gbs = pk(bs) in
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let gbo = pk(bo) in
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let gpqbo = kempk(pqbo) in
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let gbssig = sign(SK_B, rb(gbs)) in
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let gpqbsig = sign(SK_B, qb(gpqbo)) in
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out(c, (gbssig, gbs, gbo, gpqbo, gpqbsig));
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phase 1; (* peer B commits first *)
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(* =================== PHASE 2: DERIVE P2P MASTER + SENDER KEYS SESSION A -> B =================== *)
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in(c, (x1: bitstring, x1_mac: bitstring, gae1: pkey, ct: bitstring));
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let ss = pqkem_dec(pqbo, ct) in
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let bmaster = hkdf1(concat2(dh(PK_A, bs), dh(gae1, SK_B), dh(gae1, bs), dh(gae1, bo), ss)) in
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let (rb1: key, cb1: key) = hkdf2(bmaster) in (* derive the root and chain key *)
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let bk1 = khash(cb1) in
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let (bk1_auth: key, bk1_enc: key) = hkdf2(bk1) in
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if checkmac(bk1_auth, concat1(x1, gae1, ct), x1_mac) = okay then
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let (mra0: key, FPK_A: pkey) = sdec(bk1_enc, x1) in
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event recvOE1(FPK_A, mra0, gae1);
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(* =================== PHASE 3: SENDER KEYS SESH B -> A =================== *)
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new tb2: skey;
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let gtb2 = pk(tb2) in
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let (rb2: key, cb2: key) = hkdf2(concat3(khash(rb1), dh(gae1, tb2))) in
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let bk2 = khash(cb2) in
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let (bk2_auth: key, bk2_enc: key) = hkdf2(bk2) in
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new mrb0: key; (* mrb0 := sender keys ratchet *)
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let x2 = senc(bk2_enc, (FPK_B, mrb0)) in
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let x2_mac = mac(bk2_auth, concat4(x2, gtb2)) in
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event sendOE2(FPK_B, mrb0, gae1);
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out(c, (x2, x2_mac, gtb2));
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(* =================== PHASE 4: SENDER KEYS MSG A -> B =================== *)
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in(c, (mx1: bitstring, mx1_sig: bitstring));
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let mra1 = khash(mra0) in
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let (mak1_auth: key, mak1_enc: key) = hkdf2(mra1) in
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if checksign(FPK_A, mx1, mx1_sig) = okay then
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let m1 = sdec(mak1_enc, mx1) in
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event recvME1(m1, mra1);
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(* =================== PHASE 5: SENDER KEYS MSG B -> A =================== *)
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let mrb1 = khash(mrb0) in
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let (mbk1_auth: key, mbk1_enc: key) = hkdf2(mrb1) in
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let mx2 = senc(mbk1_enc, m2) in
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let mx2_sig = sign(FSK_B, mx2) in
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event sendME2(m2, mrb1);
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out(c, (mx2, mx2_sig));
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(* =================== PHASE 6: Compromise =================== *)
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phase 5;
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event compromiseSKB(SK_B);
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out(a, SK_B);
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0.
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query event(start()).
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(* forward secrecy *)
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query sk1: skey, sk2: skey; (event(compromiseSKA(sk1)) && event(compromiseSKB(sk2)) && attacker(m1)) ==> false.
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(* secrecy *)
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query attacker(m1).
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query attacker(m2).
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(* forward pq secrecy *)
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query k1: key, k2: key, k3: key, k4: key; (event(breakDH(k1, k2, k3, k4)) && attacker(m1)) ==> false.
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(* auth *)
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query k1: pkey, rk: key, k2: pkey; inj-event(recvOE1(k1, rk, k2)) ==> inj-event(sendOE1(k1, rk, k2)).
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query k1: pkey, rk: key, k2: pkey; inj-event(recvOE2(k1, rk, k2)) ==> inj-event(sendOE2(k1, rk, k2)).
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query m: bitstring, rk: key; inj-event(recvME1(m, rk)) ==> inj-event(sendME1(m, rk)).
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query m: bitstring, rk: key; inj-event(recvME2(m, rk)) ==> inj-event(sendME2(m, rk)).
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(* reachability *)
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query k1: pkey, rk: key, k2: pkey; event(sendOE1(k1,rk,k2)).
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query k1: pkey, rk: key, k2: pkey; event(recvOE1(k1,rk,k2)).
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query k1: pkey, rk: key, k2: pkey; event(sendOE2(k1,rk,k2)).
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query k1: pkey, rk: key, k2: pkey; event(recvOE2(k1,rk,k2)).
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query m: bitstring, rk: key; event(sendME1(m, rk)).
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query m: bitstring, rk: key; event(recvME1(m, rk)).
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query m: bitstring, rk: key; event(sendME2(m, rk)).
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query m: bitstring, rk: key; event(recvME2(m, rk)).
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process
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new SK_A: skey; let PK_A = pk(SK_A) in
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new SK_B: skey; let PK_B = pk(SK_B) in
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new FSK_A: skey; let FPK_A = pk(FSK_A) in
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new FSK_B: skey; let FPK_B = pk(FSK_B) in
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out(a, PK_A);
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out(a, PK_B);
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(*
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out(a, FPK_A);
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out(a, FPK_B);
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*)
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event start();
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( (PeerA(SK_A, PK_A, PK_B, FSK_A, FPK_A)) |
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(PeerB(SK_B, PK_B, PK_A, FSK_B, FPK_B)))
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