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In PKC 2010, Herranz et al. proposed the first fully threshold ciphertext policy attribute‐based encryption (CP‐ABE) scheme with constant length ciphertext. However, their scheme is selectively secure with respect to the chosen plaintext attack. They have left three open problems for CP‐ABE with constant ciphertext length, that is, Security against the Chosen Ciphertext Attacks, Security Reduction to a better mathematical problem and to make the scheme Fully Secure. Indeed, in ACISP 2012, Ge et al. proposed the solutions to the first two problems but left their proposed scheme selective secure. This makes their scheme weaker because it is secure only for a particular policy. With an aim to propose a fully secure constant ciphertext length CP‐ABE scheme, in this paper, we discuss our attempts at extending the approach of Lewko et al. (in EUROCRYPT 2010). The scheme that we propose here allows any subset of attributes of the secret key as a part of the ciphertext policy. Copyright © 2013 John Wiley & Sons, Ltd.

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