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An enhanced authentication key exchange protocol was proposed to exchange multiple session keys between two participants at a time. This paper shows that this enhanced protocol is insecure under the known session key attack, known long-term private key attack, signature forgery attack, and replay attack. This paper also proposes an enhanced and secure key agreement protocol for exchanging multiple session keys in one run of the protocol. The protocol is secure against the attacks mentioned above. Besides, a formal proof is given to guarantee the security of the proposed protocol under other potential attacks.
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