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In a cipher text-policy ABE (CP-ABE) scheme, an encrypt or can express any access policy, stating what kind of receivers will be able to decrypt the message in the encryption algorithm. In most CP-ABE schemes, the size of cipher texts is not constant, which depends linearly on the number of attributes involved in the policy for that cipher text. The only constant size CP-ABE scheme is selective secure without random oracles. In this paper, we construct a constant size CP-ABE scheme which achieves full security without random oracles. The scheme admits threshold decryption policies based on an identity-based encryption scheme.