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Prepare-and-Send Quantum Fully Homomorphic Encryption (edit)
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The [https://arxiv.org/abs/1603.09717 example protocol] deals deals achieves the functionality of [[Secure Delegated Quantum Computation]] by a method which involves quantum offline and classical offline communication, called Quantum Fully Homomorphic Encryption (QFHE). It allows the Client to encrypt quantum data in such a way that Server can carry out any arbitrary quantum computations on the encrypted data without having to interact with the encrypting party. It hides the output and input of the computation while Server is allowed to choose the unitary operation for required computation. Thus, the circuit is known to the Server while efforts can be made to hide it from the encrypting party i.e. Client. Based on the existence of classical [[Homomorphic Encryption]] (HE) scheme, it comes with properties of correctness, i.e. for any arbitrary circuit if both the parties follow the protocol, the final outcome is deemed to be correct, compactness, i.e. decryption of data should be independent of the size of the quantum circuit used for computation and full homomorphism, i.e. it can perform any quantum computation. QFHE can be used to keep the circuit private to the Server and hidden from the Client unlike UBQC where circuit is private to the Client and hidden from the Server.</br></br> | |||
'''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]] | |||
[[Prepare and Send Verifiable Quantum Fully Homomorphic Encryption | |||
==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 | ||