Table 4 System Parameters and Definitions for the authentication process of CSP

C_m

Check the message used by TPA to examine the correctness of contents stored on a cluster

Db_i

Blocks of data sent in check-message

(F_m, F_t)

Fake check message and fake tag generated by CSP if not provided the required service to CU

(γ^Φ, β).

Prediction of the malicious attacker against protected data (queries and answers)

γ^Φ

Protected data comprising of query and answers

Z _j

The malicious insider entry

Z_j ∉ T_I

Unsuccessful attempt

Z _j  ∈ T _I

Successful attempt

Δq_a = f_a(q_a)

Response from TPA for malicious insider to authenticate itself

β = f_a(q_a)

Successful prediction of malicious insider

s_f

The features of each service assigned to CU

\( \varpi \)←ℕ

Generation of random number by TSP

ρ*

Representing the combination of sampled blocks

ℝ_g

Random generator of TSP

∄ ℝ_m

Impersonated message created by the server

'O

Output for check-message

ℵ _t

Data tag generated by TPA to validate the CSPs provided services to CU

Determining the CSPs illegitimate action

\( \frac{\mathrm{s}\left(\mathrm{z}\right)}{\mathrm{t}\left(\mathrm{z}\right)} \)

Derivative of two quotients

∀ ∂

TPA chooses a random value for checking the CSPs provided service

ℓ

Set of the features