Leveraging Grover’s Algorithm for Quantum Searchable Encryption in Cloud Infrastructure and its application in AES Resource Estimation

Designing efficient techniques to search over encrypted data space has always been an intriguing security challenge, although many solutions based on classical searching methods have been proposed. Grover’s algorithm, a quantum counterpart of searching algorithms, has proven to provide quadratic speedup over any classical search technique on an unsorted database. However, this algorithm is unable to search over encrypted data space. This study proposed an extension of Grover’s algorithm to enable search over encrypted dataspace, allowing clients with limited-capability quantum resources to delegate complex search operations to an untrusted server. The blindness of data in this protocol is achieved by encrypting qubits using Pauli’s rotation gates that maximally mix the outgoing states. The empirical estimation of the overhead of the computation due to the introduction of this technique has been analyzed. This estimate has been used for comparative analysis, showing the efficiency of the proposed protocol. A practical application of the proposed searchable encryption technique has been utilized to estimate the increase in resources needed to carry out a brute-force attack on AES encryption using secure Grover’s algorithm. Furthermore, an extensive experimental analysis of the effect of noise has been studied using four different noise models: amplitude damping, phase damping, depolarizing noise, and bit-flip noise. The investigation provided useful insight into the behavior of the proposed algorithm under noisy conditions and also estimated the tolerance thresholds of the proposed algorithm under different noise models.