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The area of password-based authenticated key establishment protocols has been the subject of a vast amount of work in the last few years due to its practical aspects. Despite the attention given to it, most Password-Authenticated Key Establishment (PAKE) schemes in the literature consider authentication between a client and a sever. Although some of them are extended to a three-party PAKE protocol, in which a trusted server exists to mediate between two clients to allow mutual authentication, they are less considered in a cross-realm setting like in kerberos system.
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