Classical Fully Homomorphic Encryption for Quantum Circuits: Difference between revisions

Classical Fully Homomorphic Encryption for Quantum Circuits (edit)

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 ### 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>.
-####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>
+####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 <math>f_0\oplus_H f_1=\hat{c}</math></br><math>\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>\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>.