Anonymous multi-attribute encryption with range query and conditional decryption

We introduce the concept of Anonymous Multi-Attribute Encryption with Range Query and Con-ditional Decryption (AMERQCD). In AMERQCD, a plaintext is encrypted under a point in multi-
dimensional space. To a computationally bounded adversary, the ciphertext hides both the plaintext
and the point under which it is encrypted. In a range query, a master key owner releases the decryp-
tion key for an arbitrary hyper-rectangle in space, thus allowing decryption of ciphertexts previ-
ously encrypted under any point within the hyper-rectangle. However, a computationally bounded
adversary cannot learn any information on ciphertexts outside the range covered by the decryption
key (except the fact that they do not lie within this range). We give an efficient construction based
on the Decision Bilinear Diffie-Hellman (D-BDH) and Decision Linear (D-Linear) assumption.