Password-Only Authenticated Three-Party Key Exchange Proven Secure against Insider Dictionary Attacks

Box 2

The Exp₃ Modification

When asks an Execute or Send query, the simulator answers it exactly as in experiment Exp₂,

except that it modifies the way of generating the public Diffie-Hellman values (denoted as and

in the protocol) as follows:

 (i) The simulator chooses two random and computes and .

 (ii) For each instance , the simulator chooses a random , computes

   and uses as the public Diffie-Hellman value (i.e., as or ) of .