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Prepare-and-Send Quantum Fully Homomorphic Encryption (edit)
Revision as of 08:09, 11 July 2019
, 11 July 2019→Pseudocode
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* ''Circuit Privacy.'' This protocol is not circuit private as it does not guarantee that the client cannot gain information about the circuit evaluated i.e. the circuit is not private to one party and unknown to another. It can make the circuit private to the evaluator (Server) and hidden from the Client apart from the necessary leakage the output states gives if one uses circuit private HE for the protocol. | * ''Circuit Privacy.'' This protocol is not circuit private as it does not guarantee that the client cannot gain information about the circuit evaluated i.e. the circuit is not private to one party and unknown to another. It can make the circuit private to the evaluator (Server) and hidden from the Client apart from the necessary leakage the output states gives if one uses circuit private HE for the protocol. | ||
• ''Full Homomorphism.'' This scheme is fully homomorphic for circuits with polynomial sized T gates | • ''Full Homomorphism.'' This scheme is fully homomorphic for circuits with polynomial sized T gates | ||
== Notation == | |||
* <math>\mathrm{k}</math>, security parameter | |||
* <math>\mathrm{L}</math>, number of T gates in the evaluation circuit | |||
* <math>\mathrm{n}</math>, dimension of input qubit | |||
* <math>\mathrm{{pk_i,sk_i,evk_i}}</math>, <math>\mathrm{i_{th}}</math> homomorphic key set generated from HE.KeyGen(). Public key for encryption, secret key for decryption, evaluation function key, respectively for given k, the security parameter. | |||
* <math>\Gamma_{pk_{i+1}}(\mathrm{sk_i})</math>, Gadget using <math>\mathrm{i_th}</math> secret key (<math>sk_i</math>) and encrypted by <math>\mathrm{(i + 1)_{th}}</math> public key (<math>\mathrm{pk_{i+1}}</math>) | |||
* <math>\sigma</math>, single qubit state | |||
* <math>\rho=|\psi\rangle\langle\psi|</math>, here <math>\rho</math> is the density matrix of quantum state <math>|\psi\rangle</math> | |||
* <math>\rho</math>, n-qubit input state, where n is determined by the Client | |||
* <math>\rho</math>(HE.Encpk(a)), a is encrypted with public key pk and is represented by density matrix ρ | |||
* p, location of inverse phase gate | |||
* x,z measurement outcome sets of Client for her Bell Pair measurements. | |||
* x’,z’ measurement outcome sets of Server for his Gadget measurement. | |||
* x˜[i], resulting ciphertext one gets for an input ith element of array x or ith bit of key x after the Encrypting it with ith of public key string, pk. | |||
== Pseudocode== | == Pseudocode== | ||
===Stage 1 Client’s Preparation=== | ===Stage 1 Client’s Preparation=== | ||