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In this work, we consider the problem of key cloning in attribute-based encryption schemes. We introduce a new type of attribute-based encryption scheme, called token-based attribute-based encryption (tk-ABE) that provides strong deterrence for key cloning, in the sense that delegation of keys reveals some personal information about the user. It also has the feature that a misbehaving user can be easily revoked. We formalise the security requirements for such a scheme in terms of indistinguishability of the ciphertexts and two new security requirements which we call uncloneability and privacy-preserving. We construct a privacy-preserving uncloneable token-based attribute-based encryption scheme based on Cheung and Newport's ciphertext-policy attribute-based encryption scheme and prove the scheme satisfies the above three security requirements. We also introduce the notion of non-interactive uncloneable attribute-based encryption in order to remove the online token server in the tk-ABE. We then construct such a new scheme with provable security. It should be pointed out that, although our non-interactive scheme is token-free, the scheme does not have the capability to easily revoke users from the scheme. Hence, both types of schemes have their own merits of existence.