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Prepare-and-Send Quantum Fully Homomorphic Encryption (edit)
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'''Tags:''' [[:Category: Two Party Protocols|Two Party]],[[:Category:Universal Task|Universal Task]], [[:Category: Quantum Functionality|Quantum Functionality]], [[Secure Delegated Quantum Computation|Secure Delegated Quantum Computation]], Quantum Offline Communication, Classical Offline Communication, [[Supplementary Information#Entanglement|Entanglement]], [[Quantum Gadgets]], [[Prepare and Send Verifiable Quantum Fully Homomorphic Encryption]], [[Classical Fully Homomorphic Encryption for Quantum Circuits]]. | '''Tags:''' [[:Category: Two Party Protocols|Two Party]],[[:Category:Universal Task|Universal Task]], [[:Category: Quantum Functionality|Quantum Functionality]], [[Secure Delegated Quantum Computation|Secure Delegated Quantum Computation]], Quantum Offline Communication, Classical Offline Communication, [[Supplementary Information#Entanglement|Entanglement]], [[Quantum Gadgets]], [[Prepare and Send Verifiable Quantum Fully Homomorphic Encryption]], [[Classical Fully Homomorphic Encryption for Quantum Circuits]]. | ||
[[Category:Two Party Protocols]][[Category: Universal Task]][[Category:Quantum Functionality]] | [[Category:Two Party Protocols]][[Category: Universal Task]][[Category:Quantum Functionality]] | ||
==Assumptions== | |||
* This protocol is secure against malicious adversary setting | |||
* One cannot decrypt the ciphertext without performing the Evaluation step | |||
* A one time quantum channel from Client to Server | |||
* A one time quantum channel from Server to Client | |||
* The circuit has polynomial number of T-Gates. | |||
==Outline== | ==Outline== | ||
Homomorphic Encryption [[Supplementary Information#Homomorphic schemes|(HE)]] schemes can be divided into four stages: Key Generation generates keys for encryption, decryption and evaluation of the circuit, Encryption encodes the input into a ciphertext using encryption key, Homomorphic Evauation performs operations (imlpements the circuit) on the encrypted input using evaluation key and Decryption transforms result of the ciphertext to actual outcome of the circuit using decryption key. This protocol requires Client to prepare and send the quantum states to Server, hence the name, ''Prepare and Send QFHE''. A QFHE scheme is fundamentally different from classical FHE in the aspect that evaluation key is allowed to be a quantum state in former case. Also, in the last step decryption for FHE is carried out subsystem by subsystem. This cannot be correct for QFHE as quantum states can be entangled, hence decryption should be carried out on the system as a whole. The QFHE version of encryption is based on quantum one time pad [[Supplementary Information#Quantum One Time Pad|(QOTP)]] i.e. randomly applying a Pauli Gate (X, Y, Z, I) in order to hide the input. A Fully Homomorphic Encryption can implement Universal Gates (a set of gates which can implement any quantum circuit). Most of the gates in this set work well with QOTP while for T gates one needs an additional gadget, in order to implement any arbitrary circuit and make the scheme Fully Homomorphic. This adds an additional step called ”Gadget Construction” during Key Generation Stage in this protocol | Homomorphic Encryption [[Supplementary Information#Homomorphic schemes|(HE)]] schemes can be divided into four stages: Key Generation generates keys for encryption, decryption and evaluation of the circuit, Encryption encodes the input into a ciphertext using encryption key, Homomorphic Evauation performs operations (imlpements the circuit) on the encrypted input using evaluation key and Decryption transforms result of the ciphertext to actual outcome of the circuit using decryption key. This protocol requires Client to prepare and send the quantum states to Server, hence the name, ''Prepare and Send QFHE''. A QFHE scheme is fundamentally different from classical FHE in the aspect that evaluation key is allowed to be a quantum state in former case. Also, in the last step decryption for FHE is carried out subsystem by subsystem. This cannot be correct for QFHE as quantum states can be entangled, hence decryption should be carried out on the system as a whole. The QFHE version of encryption is based on quantum one time pad [[Supplementary Information#Quantum One Time Pad|(QOTP)]] i.e. randomly applying a Pauli Gate (X, Y, Z, I) in order to hide the input. A Fully Homomorphic Encryption can implement Universal Gates (a set of gates which can implement any quantum circuit). Most of the gates in this set work well with QOTP while for T gates one needs an additional gadget, in order to implement any arbitrary circuit and make the scheme Fully Homomorphic. This adds an additional step called ”Gadget Construction” during Key Generation Stage in this protocol | ||