* Confidentiality: any independent third party other than the entities involved cannot acquire any valuable advice related to the plaintext of a ciphertext
Evaluate and Decrypt: These are the same as the ones in the , except that the ciphertext
is reduced by modulo 0 after addition and multiplication.
1) What is the number of packets per ciphertext
?: This is evaluated as follows.
that the government has in hand is really a valid
Algorithm 3 takes a ciphertext
[CT.sub.F], a file tag value [Tag.sub.F], a master key [MK.sub.Srv] and the highest challenge [mathematical expression not reproducible] as an input and outputs an expected response set [ResArr.sub.Srv].
The decryption algorithm takes public key PK, ciphertext
C, and user secret key S[K.sub.S] as the input.
Then, the challenger responds the challenge ciphertext
CT = Enc(pk, [m.sub.b]) under a random bit b.
The protocol enables Alice, who is in possession of a ciphertext
c, to finish the protocol with the correct decryption of c.
It needs 9 plaintext and ciphertext
pairs to conduct computation 9 times in Step 3, and the equation system will have a finite set of solutions.
Third, there are pixel substitution and ciphertext
proposed a KP-ABE scheme  which can achieve the revocation of users; however, this scheme is limited to be used if and only if the number of attributes associated with ciphertext
is just half of the whole attributes in the system; therefore, the limit is too high which impedes its actual application.