(*
 * Formal definition to verify the Fenrir protocol.
 * to be used with ProVerif
 *
 * This is to verify the correctness of the full 3-RTT handshake.
 * DNSSEC is NOT verified, as it is assumed to be correct.
 *
 * The test *WILL* take a while... proverif says it has inserted more than 18k rules, and has a rule base of almost 12k rules.
 * just leave it to work...
 *)

(*
 * ==============
 * Type definition
 * ==============
 *)


type host.
type sKey.	(* symmetric key *)
type pubKey.	(* public  key for asymmetric key encryption *)
type privKey.	(* private key for asymmetric key encryption *)
type nonce.	(* just a nonce *)

const leak: channel. (* to leak private material *)
const cf_full: channel. (* client-fenrir, full-security handshake  *)
const cf_state: channel. (* client-fenrir, stateful handshake  *)
const cf_dir: channel. (* client-fenrir, directory-synchronized handshake *)
const cs: channel. (* client-service *)
const sf: channel [private]. (* service-fenrir: since it is managed as the client-fenrir channel, this is not checked *)

(* various stuff that should remain private *)
const Auth:      nonce     [private].
const prS:       privKey   [private]. (* service private key *)
const prF:       privKey   [private].
const prF_dir:   privKey   [private].
const OTP:       sKey      [private].
free csKey:      sKey      [private].


free Rekey:    bitstring. (* rekey message *)
type algorithm.
const alg_bad:  algorithm. (* broken key exchange algorithm *)
const alg_good: algorithm. (* good key exchange algorithm *)
const alg_both: algorithm. (* both good and bad algorithms support*)

(*
 * ==============
 * Function definition
 * ==============
 *)

(* any to bitstring conversion *)
fun fromKey(sKey) : bitstring.
reduc forall a : sKey; toKey(fromKey(a)) = a.


(* symmetric key encription *)
fun sEnc(bitstring, sKey): bitstring. (* encrypt with symmetric key *)
reduc forall c: bitstring, k: sKey; sDec(sEnc(c,k),k) = c. (* decrypt with symmetric key *)

(* public key definition *)
fun genPub(privKey): pubKey.	(* public keys are generated from private ones *)
(* public key signing *)
fun sign(bitstring, privKey): bitstring.
reduc forall c: bitstring, k: privKey; ver(c, sign(c, k), genPub(k)) = true. (* verify signature *)

(* some key exchange based on public keys *)
fun exchange(privKey, pubKey) : sKey.
equation forall p1 : privKey, p2 : privKey; exchange(p1, genPub(p2)) = exchange(p2, genPub(p1)).

(* hash used by OTP, sKey based *)
fun hash(sKey) : sKey.

(* xor function *)
fun xor(sKey, sKey) : sKey.
reduc forall a : sKey, b : sKey; unxor(xor(a, b), b) = a.
reduc forall a : sKey, b : sKey; unxor2(xor(a, b), a) = b. (* created for proverif, not used for simplicity *)


(*
 * ==============
 * Events -- used for correlation
 * ==============
 *)
event downgrade().
event acceptedFenrir(sKey).
event clientConnect(sKey, sKey).
event serviceConnect(sKey).



(* NOTE: in multiple places we have an if-else branch over a nonce.
 * and the else branch start with an "if" that is the opposite of the first "if".
 * This "if" after the else seems unnecessary but actually hugely speeds up proverif.
 * reason: proverif does not have to check for all the possible nonces, as it seems
 * it doesn't notice that the nonce can have only few vales, as it actually is an enum *)

(*
 * ==========================================================================
 * Client definition, Full-security handshake with good and broken algorithms
 * ==========================================================================
 *)

let client_full(pubF: pubKey, Auth: nonce, supported: algorithm, OTP: sKey) =
	new cn1: nonce; (* Client Nonce 1 *)
    new prC: privKey; (* ephemeral public key. *)

	(* Note: this nonce is technically useless, but prevents amplification/DoS attack
	 * also: the nonce should include a timer, but proverif doesn't check for DoS,
	 * and doesn't play nicely with timers, so we don't really care...
	 *)
(* start cookie exchange *)
	out (cf_full, (cn1, supported));
	in  (cf_full, (sn1: nonce, selected: algorithm, s1: bitstring, s2: bitstring));
	if ver((sn1, cn1, supported, selected), s1, pubF) = true then
	if ver((sn1, selected), s2, pubF) = true then

(* RTT 1 completed *)

	(* start algorithm agreement *)
	new cn2: nonce;
	(* out: nonces and signature, supported_algorithms *)
	(* bad algorithm somehow exposes authentication data *)
	if selected = alg_bad && (supported = alg_both || supported = alg_bad) then
	(
		event downgrade()
	)
	else
	(
		if selected = alg_good then
		out (cf_full, (sn1, selected, s2, cn2, genPub(prC)));
		(* se1: server encrypt 1: contains supported authentication algorithms
		 * unused here, it's the same mechanism as the "selected" one
		 *)
		in  (cf_full, (ephF: pubKey, se1: bitstring, s3: bitstring));
		if ver((ephF, se1), s3, pubF) = true then
		let (cfKey) = exchange(prC, ephF) in
(* RTT 2 Completed *)
		out (cf_full, (sEnc((Auth, Auth), cfKey)));
		in  (cf_full, (se2: bitstring));
		let (chan: channel, xorKey: bitstring) = sDec(se2, cfKey) in

(* RTT 3 completed, can now connect to service *)

        let cs_Key = sDec(xorKey, hash(OTP)) in
		event clientConnect(cfKey, toKey(cs_Key));
		out (chan, sEnc(fromKey(OTP), toKey(cs_Key)))
	).


(*
 * ===========================================================================
 * Fenrir definition, full security handshake, with good and broken algorithms
 * ===========================================================================
 *)

let fenrir_full(privF: privKey, Auth: nonce, supported: algorithm) =
	(* Nonce exchange *)
	in (cf_full, (fin1: nonce, client_alg: algorithm));
	new s_nonce: nonce;
	(* triggers "event downgrade()" in the client, no need to go further *)
		(* bad only if both support bad *)
	if client_alg = alg_bad && (supported = alg_bad || supported = alg_both) then
	(
		out (cf_full, (s_nonce, alg_bad, sign((s_nonce, fin1, client_alg, alg_bad), privF),
										 sign((s_nonce, alg_bad), privF)))
	)
	else
	(
		if client_alg = alg_good || client_alg = alg_both then
		out (cf_full, (s_nonce, alg_good, sign((s_nonce, fin1, client_alg, alg_good), privF),
										 sign((s_nonce, alg_good), privF)));
(* RTT 1 finished *)
		in (cf_full, (=s_nonce, =alg_good, signed: bitstring, fin2: nonce, pubC: pubKey));
		if ver((s_nonce, alg_good), signed, genPub(privF)) = true then
		new prF2: privKey;
		let (cfKey) = exchange(prF2, pubC) in
		out (cf_full, (genPub(prF2), sEnc((supported, supported), cfKey), sign((genPub(prF2), sEnc((s_nonce, s_nonce), cfKey)), privF)));
(* RTT 2 finished, now we have a state *)
		in (cf_full, (ce1: bitstring));
		let (data: nonce, data2: nonce) = sDec(ce1, cfKey) in
		if data = Auth && data2 = Auth then

        new user_info : nonce;
        out (sf, user_info);
        in  (sf, key : sKey);
		event acceptedFenrir(cfKey);
        out (cf_full, (sEnc((cs, key), cfKey)))
(* RT3 finished *)
	).

(*
 * ==================================
 * Service definition, common for all
 * ==================================
 *)

let service(OTP : sKey) =
    (* sf channel is secret, thus trusted. do not encrypt to reduce
     * proverif running time *)
    in (sf, rnd : nonce); (* user info. useless in our model *)
    (* this should be cskey XOR hash(OTP), but proverif can't handle XOR.
     * so we treat it as encryption, as it has the same properties in our case *)
    out (sf, sEnc(fromKey(csKey), hash(OTP)));
	in (cs, enc2 : bitstring);
	let is_OTP : bitstring = sDec(enc2, csKey) in
    if OTP = toKey(is_OTP) then
	event serviceConnect(csKey).

(*
 * ======================================================================
 * Client Definition, Stateful handshake, with good and broken algorithms
 * ======================================================================
 *)

let client_state (pubF: pubKey, Auth: nonce, supported: algorithm, OTP: sKey) =
    new cn1: nonce; (* Client Nonce 1 *)
    new prC: privKey; (* ephemeral key *)

    (* Note: this nonce is technically useless, but prevents amplification/DoS attack
     * also: the nonce should include a timer, but proverif doesn't check for DoS,
     * and doesn't play nicely with timers, so we don't really care...
     *)
(* start cookie exchange *)
    out (cf_state, (cn1, supported));
    in  (cf_state, (alg: algorithm, ephF: pubKey, s1: bitstring));
    if ver((cn1, supported, alg, ephF), s1, pubF) = true then

(* RTT 1 completed *)

    if alg = alg_bad then
    (
        if supported = alg_bad || supported = alg_both then
        (* bad algorithm exposes authentication data *)
        event downgrade()
    )
    else
    (
        if alg = alg_good then
        if supported = alg_good || supported = alg_both then

        let (cfKey) = exchange(prC, ephF) in
        out (cf_state, (genPub(prC), sEnc((Auth,Auth), cfKey)));
        in  (cf_state, enc: bitstring);
    
(* RTT 2 completed, can now connect to service *)

		let (chan: channel, xorKey: bitstring) = sDec(enc, cfKey) in
        let cs_Key = sDec(xorKey, hash(OTP)) in
		event clientConnect(cfKey, toKey(cs_Key));
		out (chan, sEnc(fromKey(OTP), toKey(cs_Key)))
    ).

(*
 * ===========================================================================
 * Fenrir definition, stateful handshake, with good and broken algorithms
 * ===========================================================================
 *)

let fenrir_state (privF: privKey, Auth: nonce, supported: algorithm) =
    (* Nonce exchange *)
    new prF2 : privKey;
    new s_nonce: nonce;
    in (cf_state, (fin1: nonce, client_alg: algorithm));
    if client_alg = alg_bad && (supported = alg_bad || supported = alg_both) then
    (
        out(cf_state, (alg_bad, genPub(prF2), sign((fin1, client_alg, alg_bad, genPub(prF2)), privF)))
    )
    else
    (
        if (client_alg = alg_good || client_alg = alg_both) && (supported = alg_good || supported = alg_both) then
        out(cf_state, (alg_good, genPub(prF2), sign((fin1, client_alg, alg_good, genPub(prF2)), privF)));
(* RTT 1 finished *)
        in (cf_state, (pubC: pubKey, enc: bitstring));
        let (cfKey) = exchange(prF2, pubC) in
        let (data: nonce, data2: nonce) = sDec(enc, cfKey) in
        if data = Auth && data2 = Auth then
        new user_info : nonce;
        out (sf, (user_info));
        in (sf, key : sKey);
        event acceptedFenrir(cfKey);
        out (cf_state, sEnc((cs, key), cfKey))
(* RTT 2 finished *)    
    ).


(*
 * ===========================================================================
 * Client definition, directory synchronized handshake
 * ===========================================================================
 *)
let client_dir (pubF: pubKey, Auth: nonce, OTP: sKey) =
    new prC : privKey;
    new cn : nonce;
    let (cfKey) = exchange(prC, pubF) in
    out (cf_dir, (genPub(prC), sEnc((Auth,cn), cfKey)));
    in  (cf_dir, enc: bitstring);
(* RTT 1 finished, now connect to service *)
    let (=cn, chan: channel, xorKey: bitstring) = sDec(enc, cfKey) in
    let cs_Key = sDec(xorKey, hash(OTP)) in
    event clientConnect(cfKey, toKey(cs_Key));
    out (chan, sEnc(fromKey(OTP), toKey(cs_Key))).
(*
 * ===========================================================================
 * Fenrir definition, directory synchronized handshake
 * ===========================================================================
 *)

let fenrir_dir (privF: privKey, Auth: nonce) =
    in (cf_dir, (pubC: pubKey, enc: bitstring));
    let (cfKey) = exchange(privF, pubC) in
    let (=Auth, cn: nonce) = sDec (enc, cfKey) in

    new user_info : nonce;
    out (sf, user_info);
    in (sf, key : sKey);
    event acceptedFenrir(cfKey);
    out (cf_dir, sEnc((cn, cs, key), cfKey)).






(*
 * ==============
 * Event correlation:
 * ==============

query k1 : sKey, k2 : sKey; event(serviceConnect(k2)) ==> event(clientConnect(k1, k2)) ==> event(clientConnect(k1, k2)) ==> event(acceptedFenrir(k1)).
 *)

(*
 * ==============
 * What should be secret?
 * ==============
 *)

query event(downgrade()).
query attacker(Auth).	(* client auth data.  *)
query attacker(OTP).	(* client-service OTP data. *)

(*
 * ==============
 * Run the verification
 * ==============
 *)


process
	let pbF     = genPub(prF)     in
	let pbF_dir = genPub(prF_dir) in
    ((!service(OTP)) 
		| (!client_full (pbF, Auth, alg_both, OTP)) | (!client_full (pbF, Auth, alg_good, OTP))
		| (!fenrir_full (prF, Auth, alg_both)) | (!fenrir_full (prF, Auth, alg_good))
        | (!client_state(pbF, Auth, alg_both, OTP)) | (!client_state(pbF, Auth, alg_good, OTP))
        | (!fenrir_state(prF, Auth, alg_both)) | (!fenrir_state(prF, Auth, alg_good))
        | (!client_dir  (pbF_dir, Auth, OTP)) | (!fenrir_dir  (prF, Auth))
		| phase 1; out(leak, prF)
(* PFS: leaking of the long-term secret will NOT affect previous communications *)
	(* Now do everything again, WITHOUT leaking. Everything must be done again since
	 * we leaked the previous private key. If we didn't do everything again we could not prove
	 * that the interaction of the handshakes is secure.
	 * This is because the 1-RTT handshake does NOT have long-term secret
	 *)
(*
        ; (!service(OTP))
        | (!client_full (pbF_dir, Auth, alg_both, OTP)) | (!client_full (pbF_dir, Auth, alg_good, OTP))
        | (!fenrir_full (prF_dir, Auth, alg_both)) | (!fenrir_full (prF_dir, Auth, alg_good))
        | (!client_state(pbF_dir, Auth, alg_both, OTP)) | (!client_state(pbF_dir, Auth, alg_good, OTP))
        | (!fenrir_state(prF_dir, Auth, alg_both)) | (!fenrir_state(prF_dir, Auth, alg_good))
        | (!client_dir  (pbF_dir, Auth, OTP)) | (!fenrir_dir  (prF, Auth))
*)
	)