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Prepare-and-Send Quantum Fully Homomorphic Encryption: Difference between revisions
Prepare-and-Send Quantum Fully Homomorphic Encryption (edit)
Revision as of 10:40, 11 July 2019
, 11 July 2019→Stage 2 Server’s Computation
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=== Stage 2 Server’s Computation=== | === Stage 2 Server’s Computation=== | ||
'''Circuit's Evaluation (QFHE.Eval())''' | |||
*'''Input:''' public key tuple <math>(pk_i)_{i = 0}^{L}</math>, Evaluation key tuple, Encrypted Pad key (<math>\{\tilde{a}^{[0]}...\tilde{a}^{[n]}</math>, <math>\tilde{b}^{[i]}...\tilde{b}^{[n]}\}</math>), QOTP Input State (<math> X^{a^{[1]}}Z^{b^{[1]}}\otimes.....\otimes X^{a^{[n]}}Z^{b^{[n]}}\rho Z^{b^{[1]}}X^{a^{[1]}}\otimes.....\otimes X^{a^{[n]}}Z^{b^{[n]}}</math>)</br> | *'''Input:''' public key tuple <math>(pk_i)_{i = 0}^{L}</math>, Evaluation key tuple, Encrypted Pad key (<math>\{\tilde{a}^{[0]}...\tilde{a}^{[n]}</math>, <math>\tilde{b}^{[i]}...\tilde{b}^{[n]}\}</math>), QOTP Input State (<math> X^{a^{[1]}}Z^{b^{[1]}}\otimes.....\otimes X^{a^{[n]}}Z^{b^{[n]}}\rho Z^{b^{[1]}}X^{a^{[1]}}\otimes.....\otimes X^{a^{[n]}}Z^{b^{[n]}}</math>)</br> | ||
*'''Output:''' QOTP Circuit Output State (<math> X^{a'^{[1]}}Z^{b'^{[1]}}\otimes.....\otimes X^{a'^{[k]}}Z^{b'^{[k]}}\rho' Z^{b'^{[1]}}X^{a'^{[1]}}\otimes.....\otimes X^{a'^{[k]}}Z^{b'^{[k]}}</math>), Corresponding Encrypted Pad key (<math>\tilde{a'},\tilde{b'}</math>)=(HE.Eval<math>_{evk_L}^\text{C}(\tilde{a}</math>),HE.Eval<math>_{evk_L}^\text{C}(\tilde{b}</math>))</br></br> | *'''Output:''' QOTP Circuit Output State (<math> X^{a'^{[1]}}Z^{b'^{[1]}}\otimes.....\otimes X^{a'^{[k]}}Z^{b'^{[k]}}\rho' Z^{b'^{[1]}}X^{a'^{[1]}}\otimes.....\otimes X^{a'^{[k]}}Z^{b'^{[k]}}</math>), Corresponding Encrypted Pad key (<math>\tilde{a'},\tilde{b'}</math>)=(HE.Eval<math>_{evk_L}^\text{C}(\tilde{a}</math>),HE.Eval<math>_{evk_L}^\text{C}(\tilde{b}</math>))</br></br> | ||