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Classical Fully Homomorphic Encryption for Quantum Circuits: Difference between revisions
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Classical Fully Homomorphic Encryption for Quantum Circuits (edit)
Revision as of 13:33, 20 November 2018
, 20 November 2018→Stage 2 Server’s Computation
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### Three encrypted CNOTs are used to correct <math>C^{ab}</math> as follows. | ### Three encrypted CNOTs are used to correct <math>C^{ab}</math> as follows. | ||
####The server applies encrypted CNOT operation to the two qubit state <math>Z^zX^x|\psi\rangle</math> using the secret text <math>\hat{c} = </math>HE.Convert<math>(c)</math>. | ####The server applies encrypted CNOT operation to the two qubit state <math>Z^zX^x|\psi\rangle</math> using the secret text <math>\hat{c} = </math>HE.Convert<math>(c)</math>. | ||
####Server generates following superposition sampled over random distribution D for the TCF function pairs (<math>f_0=</math>AltHE.Enc<math>_{pk}(),f_1</math>) based on the condition</br> <math>f_0\oplus_H f_1=\hat{c} | ####Server generates following superposition sampled over random distribution D for the TCF function pairs (<math>f_0=</math>AltHE.Enc<math>_{pk}(),f_1</math>) based on the condition</br> <math>f_0\oplus_H f_1=\hat{c}\sum_{\mu\in\{0,1\},r} \sqrt{D(\mu,r)}|\mu,r\rangle</math> | ||
#### Servers generates three register for quantum input, function input, function output and entangles them as follows:</br><math> | #### Servers generates three register for quantum input, function input, function output and entangles them as follows:</br><math>\sum_{a,b,\mu\in\{0,1\},r}\alpha_{ab}\sqrt{D(\mu,r)}|a\rangle|b\rangle|\mu,r\rangle|f_a(r)\rangle</math> | ||
####Server measures the last register to get a secret text <math>y = </math>AltHE.Enc<math>_{pk}(\mu_0,r_0)</math>, where <math>\mu_0\oplus\mu_1=s</math>. | ####Server measures the last register to get a secret text <math>y = </math>AltHE.Enc<math>_{pk}(\mu_0,r_0)</math>, where <math>\mu_0\oplus\mu_1=s</math>. | ||
####Server performs Hadamard on second register and measures it to get a string d such that first register of input quantum state is reduced to: the following ideal state:</br><math>(Z^{d\cdot ((\mu_0,r_0)\oplus (\mu_1,r_1))}\otimes X^{\mu_0})\textrm{CNOT}_{1,2}^s|\psi\rangle</math> </br>where <math>\text{AltHE.Enc}_{pk}(\mu_0;r_0) = \text{AltHE.Enc}_{pk}(\mu_1;r_1) \oplus_H \hat{c}</math> and <math>\oplus_H</math> is the homomorphic XOR operation. | ####Server performs Hadamard on second register and measures it to get a string d such that first register of input quantum state is reduced to: the following ideal state:</br><math>(Z^{d\cdot ((\mu_0,r_0)\oplus (\mu_1,r_1))}\otimes X^{\mu_0})\textrm{CNOT}_{1,2}^s|\psi\rangle</math> </br>where <math>\text{AltHE.Enc}_{pk}(\mu_0;r_0) = \text{AltHE.Enc}_{pk}(\mu_1;r_1) \oplus_H \hat{c}</math> and <math>\oplus_H</math> is the homomorphic XOR operation. | ||