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A convertible authenticated encryption (CAE) scheme is a technique which allows the signer to generate a valid authenticated ciphertext on the chosen message so that only the designated recipient can recover and verify the message. In case of a dispute, the recipient has the ability to convert the authenticated ciphertext into ordinary signature that can be verified by anyone. In this paper, we elaborate on the merits of CAE and secret sharing schemes to propose two new (t,n) threshold authenticated encryption schemes for hierarchical structures. Our proposed schemes not only allow i-th level participants to support the (i+1)-th level participants to generate the authenticated encryption messages, but also allow the participants of i-th or higher levels to cooperatively generate the valid ones. Any authenticated ciphertext for a message is addressed to a specified group of signers in such a way that the ability to generate the ciphertext is regulated by the adopted (t,n) threshold schemes. Furthermore, the proposed schemes achieve the security requirements of an authenticated encryption scheme. [ABSTRACT FROM AUTHOR]