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Prepare-and-Send Quantum Fully Homomorphic Encryption: Difference between revisions
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Prepare-and-Send Quantum Fully Homomorphic Encryption (edit)
Revision as of 08:01, 11 July 2019
, 11 July 2019→Outline
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*'''Circuit Evaluation''' This step operates the circuit on the encrypted input state and updates the encrypted classical information using the evaluation key. As stated earlier, any circuit can be implemented using a set of Universal Gates. This set consists of Clifford Gates and T gates. | *'''Circuit Evaluation''' This step operates the circuit on the encrypted input state and updates the encrypted classical information using the evaluation key. As stated earlier, any circuit can be implemented using a set of Universal Gates. This set consists of Clifford Gates and T gates. | ||
The Clifford group gates may affect a single qubit or multiple qubits but they follow a simple set of rules for updation of the encrypted classical information (pad key), given in the pseudocode. The server operates the circuit and with each gate in the circuit, it updates the encrypted classical description.<br/> | The Clifford group gates may affect a single qubit or multiple qubits but they follow a simple set of rules for updation of the encrypted classical information (pad key), given in the pseudocode. The server operates the circuit and with each gate in the circuit, it updates the encrypted classical description.<br/> | ||
On the other hand, T gates affect only single qubits but one needs to make use of the gadgets constructed during key generation. The issue with T gates is that it adds an additional Phase gate (P) depending on the classical random bit used for QOTP in the previous step. As P gates do not commute like Pauli-X and Pauli-Z, so they need to be corrected before applying the next gate by the Server. This would reveal the pad key used for QOTP to the Server. Hence, to avoid this, the Client constructed gadgets, which apply an Inverse Phase operator or Identity on a qubit after every T-Gate, depending on the encrypted bit without leaking any information about the pad key. Thus, after applying a T gate on a qubit, P error is removed using a gadget as follows. | On the other hand, T gates affect only single qubits but one needs to make use of the gadgets constructed during key generation. The issue with T gates is that it adds an additional [[Glosssary#Unitary Operations|Phase gate (P)]] depending on the classical random bit used for QOTP in the previous step. As P gates do not commute like Pauli-X and Pauli-Z, so they need to be corrected before applying the next gate by the Server. This would reveal the pad key used for QOTP to the Server. Hence, to avoid this, the Client constructed gadgets, which apply an Inverse Phase operator or Identity on a qubit after every T-Gate, depending on the encrypted bit without leaking any information about the pad key. Thus, after applying a T gate on a qubit, P error is removed using a gadget as follows. | ||
Out of 2m EPR pairs, some qubits are measured pairwise including the input qubit with/without error and excluding one qubit entangled with one of the measured qubits. Input qubit is thus, transferred to this last unmeasured qubit, according to one-bit teleportation. Following are the steps to get the correct output qubit.<br/> | Out of 2m EPR pairs, some qubits are measured pairwise including the input qubit with/without error and excluding one qubit entangled with one of the measured qubits. Input qubit is thus, transferred to this last unmeasured qubit, according to one-bit teleportation. Following are the steps to get the correct output qubit.<br/> | ||
*'''Generate Measurement (QFHE.GenMeasurement())''' The encrypted one pad key bit which determines phase gate error and the classical information of the gadget is used to determine a measurement order. Private key tells which qubits are entangled, thus, using the location of inverse phase gates, the qubits needed to be measured are decided. If one-pad key bit indicates a phase error then the measurement order of qubits includes an EPR pair with a phase gate else not. | *'''Generate Measurement (QFHE.GenMeasurement())''' The encrypted one pad key bit which determines phase gate error and the classical information of the gadget is used to determine a measurement order. Private key tells which qubits are entangled, thus, using the location of inverse phase gates, the qubits needed to be measured are decided. If one-pad key bit indicates a phase error then the measurement order of qubits includes an EPR pair with a phase gate else not. | ||