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Prepare-and-Send Verifiable Quantum Fully Homomorphic Encryption: Difference between revisions
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Prepare-and-Send Verifiable Quantum Fully Homomorphic Encryption (edit)
Revision as of 13:45, 26 May 2019
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* <math>\rho_{evk} \xleftarrow[]{} (keys, \mu^{P}_0, ..., \mu^{P}_p, \mu^{T}_0, ..., \mu^{T}_t, \mu^{H}_0, ..., \mu^{H}_h, \Gamma_1, ..., \Gamma_t)</math> | * <math>\rho_{evk} \xleftarrow[]{} (keys, \mu^{P}_0, ..., \mu^{P}_p, \mu^{T}_0, ..., \mu^{T}_t, \mu^{H}_0, ..., \mu^{H}_h, \Gamma_1, ..., \Gamma_t)</math> | ||
* return <math>(sk, \rho_{evk})</math> | * return <math>(sk, \rho_{evk})</math> | ||
</br> | </br> | ||
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* <math>\tilde{\sigma} \xleftarrow[]{} \Sigma_{x, z \in \{0,1\}^{3m}} </math> (TC.Enc<math>((\pi, x, z), \sigma) \otimes</math> MAC.Sign<math>_k(HE.Enc_{pk}(x,z)))</math> | * <math>\tilde{\sigma} \xleftarrow[]{} \Sigma_{x, z \in \{0,1\}^{3m}} </math> (TC.Enc<math>((\pi, x, z), \sigma) \otimes</math> MAC.Sign<math>_k(HE.Enc_{pk}(x,z)))</math> | ||
* return <math>\tilde{\sigma}</math> | * return <math>\tilde{\sigma}</math> | ||
</br> | </br> | ||
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</br> | </br> | ||
'''Function | '''Function 5''': TrapTP.EvalX(<math>\tilde{\sigma}, \tilde{x}, \tilde{\pi}, pk, evk</math>) | ||
* <math>(\tilde{x}, log_1) \xleftarrow[]{}</math> HE.Eval<math>_{evk}^{unpermute}(\tilde{\pi}, \tilde{x})</math> | * <math>(\tilde{x}, log_1) \xleftarrow[]{}</math> HE.Eval<math>_{evk}^{unpermute}(\tilde{\pi}, \tilde{x})</math> | ||
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* <math>(\tilde{x}, log_3) \xleftarrow[]{}</math> HE.Eval<math>^{permute}_{evk}(\tilde{\pi}, \tilde{x})</math> | * <math>(\tilde{x}, log_3) \xleftarrow[]{}</math> HE.Eval<math>^{permute}_{evk}(\tilde{\pi}, \tilde{x})</math> | ||
* return (<math>\tilde{\sigma}, \tilde{x}, log_1, log_2, log_3</math>) | * return (<math>\tilde{\sigma}, \tilde{x}, log_1, log_2, log_3</math>) | ||
</br> | |||
'''Function 6''': TrapTP.EvalCondX($\tilde{b}, \tilde{\sigma}, \tilde{x}, \tilde{z}, \tilde{\pi}, pk, evk$) | |||
* <math>(\tilde{x}, log_1) \xleftarrow[]{}</math> HE.Eval<math>_{evk}^{unpermute}(\tilde{\pi}, \tilde{x})</math> | |||
* <math>\tilde{s} \xleftarrow[]{}</math> HE.Eval<math>^{y\xrightarrow[]{} y^m0^{2m}}_{evk}(\tilde{b})</math> | |||
* <math>(\tilde{x}, log_2) \xleftarrow[]{}</math> HE.Eval<math>_{evk}^{\otimes}(\tilde{x}, \tilde{s})</math> | |||
* <math>(\tilde{x}, log_3) \xleftarrow[]{}</math> HE.Eval<math>^{permute}_{evk}(\tilde{\pi}, \tilde{x})</math> | |||
* return (<math>\tilde{\sigma}, \tilde{x}, \tilde{z}, log_1, log_2, log_3</math>) | |||
</br> | |||
'''Function 7''': TrapTP.EvalCNOT(<math>\tilde{\sigma}_1, \tilde{\sigma}_2, \tilde{x}_1, \tilde{x}_2, \tilde{z}_1, \tilde{z}_2, \tilde{\pi}, pk, evk</math>) | |||
* <math>(\tilde{\sigma}_1, \tilde{\sigma}_2) \xleftarrow[]{}</math> apply <math>CNOT</math> on all physical qubit pairs of <math>\tilde{\sigma}_1, \tilde{\sigma}_2</math> | |||
* <math>(\tilde{x}_1, \tilde{x}_2, \tilde{z}_1, \tilde{z}_2, log_1) \xleftarrow[]{}</math> HE.Eval<math>^{CNOT-key-update}_{evk}(\tilde{x}_1, \tilde{x}_2, \tilde{z}_1, \tilde{z}_2)</math> | |||
* return <math>(\tilde{\sigma}_1, \tilde{\sigma}_2, \tilde{x}_1, \tilde{x}_2, \tilde{z}_1, \tilde{z}_2, log_1, log_2)</math> | |||
</br> | |||
'''Function 8''': TrapTP.EvalT(<math>\tilde{\sigma}, \tilde{x}, \tilde{z}, \tilde{\pi}, \mu_i^{T},\Gamma_i, pk_{i-1}, evk_{i-1}</math>) | |||
* <math>(\tilde{\sigma}_1, \tilde{\sigma}_2, \tilde{x}_1, \tilde{z}_1, \tilde{x}_2, \tilde{z}_1, log_1) \xleftarrow[]{}</math> Trap.TP.EvalCNOT(<math>(\mu^T_i, \tilde{\sigma}, \tilde{x}, \tilde{z}, \tilde{\pi}, pk_{i-1}, evk_{i-1} </math>) | |||
* <math>(\tilde{b}, log_2) \xleftarrow[]{}</math> TrapTP.EvalMeasure(<math>\tilde{\sigma}_2, \tilde{x}_2, \tilde{z}_2, \tilde{\pi}, pk_{i-1}, evk_{i-1}</math> | |||
* <math>log_3 \xleftarrow[]{}</math> recrypt all classically encrypted information (except <math>\tilde{b}</math>) from key set <math>i-1</math> into key set <math>i</math>. | |||
* <math>(\tilde{\sigma}, log_4) \xleftarrow[]{}</math> TrapTP.EvalCondP<math>(\tilde{b}, \tilde{\sigma}_1, \tilde{x}_1, \tilde{z}_1, \Gamma_i, \tilde{\pi}, pk_i, evk_i)</math> | |||
* return <math>(\tilde{\sigma}, log_!, log_2, log_3, log_4)</math> | |||
\end{enumerate} | |||
==Further Information== | ==Further Information== | ||
<div style='text-align: right;'>''*contributed by Rhea Parekh''</div> | <div style='text-align: right;'>''*contributed by Rhea Parekh''</div> | ||