By Newman, Moskowitz, Chang, Brahmadesam

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Matem` atica Aplicada IV, Universitat Polit`ecnica de Catalunya, C. fr Abstract. Attribute-based cryptography has emerged in the last years as a promising primitive for digital security. For instance, it provides good solutions to the problem of anonymous access control. In a ciphertextpolicy attribute-based encryption scheme, the secret keys of the users depend on their attributes. When encrypting a message, the sender chooses which subset of attributes must be held by a receiver in order to be able to decrypt.

Our new scheme achieves security against selective chosen plaintext attacks (sCPA), in the standard model, under the assumption that the augmented multisequence of exponents decisional Diffie-Hellman (aMSE-DDH) problem is hard to solve. This is essentially the same level of security that was proved for the scheme in [DP08]. Using well-known techniques, it is possible to obtain security against chosen ciphertext attacks (CCA), in the random oracle model. Organization of the paper. We define the syntactics of attribute-based encryption and the required security properties in Section 2, where we also describe the aMSE-DDH problem, on which the security of our scheme will be based.

The key extraction algorithm Ext is an interaction between a user and the master entity. The user proves to the master entity that he enjoys a subset A ⊂ P of attributes. After verifying that this is actually the case, the master entity uses his master secret key msk to generate a secret key skA (which depends on the subset A of attributes), and gives it to the user. Ext(params, A, msk). – The encryption algorithm Enc takes a subset of attributes S ⊂ P, a threshold t such that 1 ≤ t ≤ |S|, and a message M as inputs.

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