(* Bellovin, Merritt, Oakland 92, section 2.1
   Version in which A and B talk to anybody *)

free c.

(* Symmetric cryptography
   One does not know whether decryption succeeds or not
   For use with weak secrets *)

fun enc/2.
fun dec/2.
equation dec(enc(x,y),y) = x.
equation enc(dec(x,y),y) = x.

(* Symmetric cryptography
   One knows whether decryption succeeds or not *)

fun senc/2.
reduc sdec(senc(x,y),y) = x.

(* Public key cryptography *)

fun penc/2.
fun pk/1.
reduc pdec(penc(x,pk(y)),y) = x.

(* Host name *)

fun host/2.

free hostA, hostB.
private free P.

let processA =
	new sEA;
	let EA = pk(sEA) in
	out(c, (hostA, enc(EA, P)));
	in(c,m2);
	let R = pdec(dec(m2,P),EA) in
	new challengeA;
	out(c, senc((challengeA), R));
	in(c, m4);
	let (=challengeA, challengeB) = sdec(m4, R) in
	out(c, senc((challengeB), R)).


let processB =
	in(c, (=hostX, m));
	let EA = dec(m, P) in
	new R;
	out(c, enc(penc(R, EA), P));
	in(c,m3);
	let (challengeA) = sdec(m3, R) in
	new challengeB;
	out(c, senc((challengeA, challengeB), R));
	in(c, m5);
	if sdec(m5, R) = (challengeB) then
	0.

let processAtalkingX =
        in(c, (PA,PB));
        let hostX = host(PA,PB) in
        let P = PA in
        processA.

let processBtalkingX =
        in(c, (PA,PB));
        let hostX = host(PA,PB) in
        let P = PB in
        processB.

process 
	(!let hostX = hostB in processA) |
	(!let hostX = hostA in processB) |
	(!processAtalkingX) |
	(!processBtalkingX) |
	(phase 1;
	new w;
	out(c, choice[w,P]))
