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In this paper, new authenticated key agreement (AKA) protocols are proposed to be used by two entities and three entities in order to establish a common session key between these entities. This key is used later to encrypt the data exchanged between the entities to assure confidentiality over public insecure channels. Authenticated key agreement protocols additionally offer authentication; that is, verifying the identities of the entities involved in the protocol. The security properties of thefatcat:vklml7ey7begxg3tft2ay2iigy