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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 16:52, 22 November 2018
, 22 November 2018→Stage 2 Server’s Computation
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###The Pauli key encryptions are homomorphically updated according to <math>P_{zx}</math>. | ###The Pauli key encryptions are homomorphically updated according to <math>P_{zx}</math>. | ||
### Three encrypted CNOTs are used to correct <math>C^{zx}</math> as follows under <math>\mathrm{AltHE}</math>. | ### Three encrypted CNOTs are used to correct <math>C^{zx}</math> as follows under <math>\mathrm{AltHE}</math>. | ||
####Server converts <math>\hat{c} = | ####Server converts <math>\hat{c} = \mathrm{HE.Convert(c)}</math>. | ||
####Server generates <math>\sum_{\mu\in\{0,1\},r}\sqrt{D(\mu,r)}|\mu,r\rangle</math> | ####Server generates <math>\sum_{\mu\in\{0,1\},r}\sqrt{D(\mu,r)}|\mu,r\rangle</math> | ||
#### Servers entangles above superposition and <math>\psi</math> with a third register as follows:</br><math>\sum_{a,b,\mu\in\{0,1\},r}\alpha_{ab}\sqrt{D(\mu,r)}|a,b\rangle|\mu,r\rangle|f_a(r)\rangle</math>, such that</br> <math>f_0=\mathrm{AltHE.Enc}_{pk}()</math>;</br><math>f_1(\mu_1,r_1)=f_0 (\mu_0,r_0)\oplus_H \hat{c}=\mathrm{AltHE.Enc}_{pk}(\mu_0,r_0)\oplus_H \mathrm{AltHE.Enc}_{pk}(s)</math> | #### Servers entangles above superposition and <math>\psi</math> with a third register as follows:</br><math>\sum_{a,b,\mu\in\{0,1\},r}\alpha_{ab}\sqrt{D(\mu,r)}|a,b\rangle|\mu,r\rangle|f_a(r)\rangle</math>, such that</br> <math>f_0=\mathrm{AltHE.Enc}_{pk}()</math>;</br><math>f_1(\mu_1,r_1)=f_0 (\mu_0,r_0)\oplus_H \hat{c}=\mathrm{AltHE.Enc}_{pk}(\mu_0,r_0)\oplus_H \mathrm{AltHE.Enc}_{pk}(s)</math> | ||