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naxos.spdl
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naxos.spdl
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/*
* NAXOS AKE (Authenticated Key Exchange) protocol
*
* Modeled by Cas Cremers, 2009
*
* From "Stronger Security of Authenticated Key Exchange" LaMacchia
* Lauter Mityagin 2006
*
* Attacks:
*
* For state-reveal with automatic state inference, we find attacks for
* both the initiator and responder roles.
*/
// Hash functions
hashfunction h1,h2;
// Exponentiation operator modeled using one-way function and helper
// protocols (see below)
hashfunction p;
// Generator
const g;
/*
* Simulate public knowledge of public keys.
*
* The '@' prefix of the protocol name denotes that it is a helper
* protocol, which is used by Scyther for displaying, and such protocols
* are ignored in auto-generation of protocol modifiers.
*/
protocol @publickeys(PK)
{
role PK
{
send_!1(PK,PK, p(g,sk(PK)));
}
}
/*
* Approximation for the equational theory g^ab = g^ba in subterms of
* the Naxos protocol.
*/
protocol @exponentiation(RA,RB,RC)
{
role RA
{
var X,Y, T1,T2: Ticket;
recv_!1(RA,RA, h2(
p(p(g,X),Y),
T1, T2, RA,RB
));
send_!2(RA,RA, h2(
p(p(g,Y),X),
T1, T2, RA,RB
));
}
role RB
{
var X,Y, T1,T2: Ticket;
recv_!3(RB,RB, h2(
T1,
p(p(g,X),Y),
T2, RA,RB
));
send_!4(RB,RB, h2(
T1,
p(p(g,Y),X),
T2, RA,RB
));
}
role RC
{
var X,Y, T1,T2: Ticket;
recv_!5(RC,RC, h2(
T1, T2,
p(p(g,X),Y),
RA,RB
));
send_!6(RC,RC, h2(
T1, T2,
p(p(g,Y),X),
RA,RB
));
}
}
protocol @keysymmetry(R1,R2,R3)
{
role R1
{
var Y,X: Ticket;
var Z1,Z2: Ticket;
recv_!1(R1,R1, h2(
p(p(g,Y),X),
Z1,Z2,
R1,R2));
send_!2(R1,R1, h2(
p(p(g,X),Y),
Z1,Z2,
R1,R2));
}
role R2
{
var Y,X: Ticket;
var Z1,Z2: Ticket;
recv_!4(R2,R2, h2(
Z1,
p(p(g,Y),X),
Z2,
R2,R3));
send_!5(R2,R2, h2(
Z1,
p(p(g,X),Y),
Z2,
R2,R3));
}
role R3
{
var Y,X: Ticket;
var Z1,Z2: Ticket;
recv_!5(R3,R3, h2(
p(p(g,Y),X),
Z1,
Z2,
R3,R1));
send_!6(R3,R3, h2(
p(p(g,X),Y),
Z1,
Z2,
R3,R1));
}
}
// The Naxos protocol description
protocol naxos(I,R)
{
role I
{
fresh eskI: Nonce;
var Y: Ticket;
send_1(I,R, p(g,h1(eskI,sk(I))) );
recv_2(R,I, Y );
claim(I,SKR,h2(
p(Y,sk(I)),
p(p(g,sk(R)),h1(eskI,sk(I))),
p(Y,h1(eskI,sk(I))),
I,R));
}
role R
{
fresh eskR: Nonce;
var X: Ticket;
recv_1(I,R, X );
send_2(R,I, p(g,h1(eskR,sk(R))) );
claim(R,SKR,h2(
p(p(g,sk(I)),h1(eskR,sk(R))),
p(X,sk(R)),
p(X,h1(eskR,sk(R))),
I,R));
}
}