Constant ciphertext length in multi-authority Ciphertext Policy Attribute Based Encryption

In Ciphertext Policy Attribute Based Encryption (CP-ABE)a previously defined association between the attributes of a user and the ciphertext associated with these attributes is exploited to determine the secret key of the user. However, for a user with multiple attributes, the length of the key depends on the number of attributes. The existing methods that use reasonably computable decryption policies produce the ciphertext of size at least linearly varying with the number of attributes. In this paper, we propose two schemes. One scheme is of variable length based on Bethencourt et al. construction. In second scheme, the ciphertext remains constant in length, irrespective of the number of attributes. It works for a threshold case: the number of attributes in a policy must be a subset of attributes in a secret key. The security of scheme is based on Decisional Bilinear Diffie-Hellman (DBDH) problem.