# Lowe's fixed version of Needham Schroeder Public Key
#
# Modelled after the description in the SPORE library
# http://www.lsv.ens-cachan.fr/spore/nspkLowe.html
#
#
# Note:
# The modelling in SPORE includes a server to distribute the public keys
# of the agents, this is not necessary and it allows for attacks against
# synchronisation and agreement, because the keys that the server sends
# out can be replayed.

secret pk: Function; # For some reason SPORE models it such that the agents
                     # do not know the public keys of the other agents
secret sk: Function;
inversekeys(pk,sk);

protocol needhamschroederpk-Lowe(I,R,S)
{
    role I
    {
        const Ni: Nonce;
        var Nr: Nonce;

        send_1(I,S, (I,R));
        read_2(S,I, {pk(R), R}sk(S));
        send_3(I,R,{Ni,I}pk(R));
        read_6(R,I, {Ni,Nr,R}pk(I));
        send_7(I,R, {Nr}pk(R));
        claim_I1(I,Secret,Ni);
        claim_I2(I,Secret,Nr);
        claim_I3(I,Nisynch);
    }    
    
    role R
    {
        const Nr: Nonce;
        var Ni: Nonce;
        
        read_3(I,R,{Ni,I}pk(R));
        send_4(R,S,(R,I));
        read_5(S,R,{pk(I),I}sk(S));
        send_6(R,I,{Ni,Nr,R}pk(I));
        read_7(I,R,{Nr}pk(R));
        claim_R1(R,Secret,Nr);
        claim_R2(R,Secret,Ni);
        claim_R3(R,Nisynch);
    }

    role S
    {
        read_1(I,S,(I,R));
        send_2(S,I,{pk(R),R}sk(S));
        read_4(R,S,(R,I));
        send_5(S,R,{pk(I),I}sk(S));
    }
}

const Alice,Bob,Simon,Eve: Agent;

untrusted Eve;
const ne: Nonce;
compromised sk(Eve);
compromised pk(Eve);
compromised pk(Simon); # Needed because of the way SPORE models nsl