Secure Client- Server Delegated Computation

Functionality Description

Delegated Computation is the task of assigning computation on hidden data to a powerful untrusted party (a device) by a weak (in terms of computational powers) party/parties while maintaining privacy of hidden data from the powerful party. Protocols under this functionality are commonly called Client-Server protocols. Delegated Quantum Computation (DQC) protocols involve partially or fully classical Client/clients delegating a quantum computation to fully powerful single/multiple quantum Server/Servers. All DQC protocols involve three main stages, Preparation Stage, Computation Stage and Output Correction Stage. The roles of Client(s) and Server in the different stages may differ according to the type of communication used see Protocols list.

Tags:Two Party,Multi Party, Quantum Functionality,Quantum Enhanced Classical Functionality,Universal Task

This functionality has been further divided into protocols on the basis of type of communication, number of clients (two party/multi party) and type of delegated tasks (classical/quantum).

Protocols for Delegated Quantum Computation

Classical Online Communication-Quantum Offline Communication (Client-Server)

It involves a partially quantum Client who can prepare and send quantum states use quantum offline communication to send input to the Server, in the preparation Stage and to receive outputs from the Server, during output correction. Client and Server then use classical online communication to exchange classical messages during computation phase. Universal Blind Quantum Computation (UBQC) falls under this category, where Client hides his input, output and computation from the Server using MBQC. If the task performed by Server can be verified by the Client, it is Verifiable Universal Blind Quantum Computation (VUBQC). Classes of protocols under this category are:

• Prepare and Send UBQC
• Prepare and Send VUBQC.

Classical Online Communication-Quantum Online Communication (Client-Server)

It involves a partially quantum Client who can measure quantum states use quantum and classical communication throughout the protocol. Client performs the hidden MBQC on states prepared by Server using her measurement device in the computation Stage. She then corrects her classical outcomes in Correction Stage. Classes of protocols under this category are:

• Measurement Only UBQC
• Measurement Only VUBQC

Classical Online Communication-No Quantum Communication (Client-Server)

It involves a fully classical Client with no quantum power exchanging classical messages with the server throughout. This can be done using protocols for generating secret random qubits, under the functionality, Secret Random Qubit Generator (SQRG). One could append SQRG with UBQC to eliminate quantum communication. A verification protocol using SQRG is still an open question. Class of protocols for SQRG:

• Pseudo-Secret Random Qubit Generator (PSRQG).

Classical Offline Communication-Quantum Offline Communication (Client-Server)

It involves a partially classical Client who can generate entanglement, use both classical and quantum communication with the Server during the preparation stage and output correction. There is no communication between the two parties during computation stage. Quantum Fully Homomorphic Encryption (QFHE) falls under this category, where Client hides her input states with the help of classical Homomorphic Encryption. In addition to this she also prepares some quantum gadgets (using entanglement) which she sends with the encrypted state to Server, in the prepapration stage. Server uses the quantum gadgets for computation on the encrypted state. Such gadgets require steps which cannot be realized by classical HE scheme. Later Client decrypts/deciphers the outcome sent by Server to get the correct result, in the correction Stage. If the task performed by the Server can be verified by the Client, the protocol is called, Verifiable Quantum Fully Homomorphic Encryption (VQFHE). Classes of protocols under this category are:

• Prepare and Send QFHE
• Prepare and Send VQFHE

Classical Offline Communication-No Quantum Communication (Client-Server)

It involves a fully classical Client assign quantum computation to a Server on her classical input/output using only classical communication during the preparation stage and output correction. There is no communication between the two parties during computation stage. It uses only classical Homomorphic Encryption and no quantum gadgets to realize a quantum function/computation. Quantum offline communication would be needed in case of quantum input/output. A verification scheme for such protocols is still an open question. Class of protocols under this category are:

• Quantum Capable Classical Fully Homomorphic Encryption (FHE) for Quantum Circuits

Protocols for Delegated Classical Computation

Secure Client-Server Delegated Classical Computation

Task	No. of Parties	Type of Communication	Protocols
Delegated Quantum Computation	Two/Three (Single Client-Single Server/Single Client-Entangled Servers)	Classical Online Communication-Quantum Offline Communication	Prepare and Send UBQC, Prepare and Send VUBQC.
		Classical Online Communication-Quantum Online Communication	Measurement Only UBQC, Measurement Only VUBQC
		Classical Online Communication-No Quantum Communication	Pseudo-Secret Random Qubit Generator (PSRQG)
		Classical Offline Communication-Quantum Offline Communication	Prepare and Send QFHE, Prepare and Send VQFHE
		Classical Offline Communication-No Quantum Communication	Quantum Capable Classical Fully Homomorphic Encryption (FHE) for Quantum Circuits
	Multi Party (Multiple Clients-Single Server)		Secure Multiparty Delegated Quantum Computation *contributed by Shraddha Singh