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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 10:14, 11 July 2019
, 11 July 2019→Stage 2 Server’s Computation
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# For all i, <math>c_i</math> gate is applied on qubit m and the <math>m_{th}</math> bits of pad key <math>(\tilde {a}^{[m]},\tilde{b}^{[m]})</math> are updated to <math>(\tilde {a}'^{[m]},\tilde{b}'^{[m]})</math> as follows. | # For all i, <math>c_i</math> gate is applied on qubit m and the <math>m_{th}</math> bits of pad key <math>(\tilde {a}^{[m]},\tilde{b}^{[m]})</math> are updated to <math>(\tilde {a}'^{[m]},\tilde{b}'^{[m]})</math> as follows. | ||
# If <math>c_i=\{P,H,CNOT\}</math>, a Clifford gate then: <math>c_iX^{a^{[m]}}Z^{b^{[m]}}\psi=X^{a'^{[m]}}Z^{b'^{[m]}}c_i\psi</math>) | # If <math>c_i=\{P,H,CNOT\}</math>, a Clifford gate then: <math>c_iX^{a^{[m]}}Z^{b^{[m]}}\psi=X^{a'^{[m]}}Z^{b'^{[m]}}c_i\psi</math>) | ||
## if <math>c_i=</math>H then //Hadamard Gate: <math>(\tilde {a}^{[m]},\tilde{b}^{[m]})\rightarrow (\tilde{b}^{[m]},\tilde{a}^{[m]})</math> (Hadamard tranforms X gate into Z and Z into X) | ## if <math>c_i=</math>H then //Hadamard Gate: | ||
<math>(\tilde {a}^{[m]},\tilde{b}^{[m]})\rightarrow (\tilde{b}^{[m]},\tilde{a}^{[m]})</math> (Hadamard tranforms X gate into Z and Z into X) | |||
## if <math>c_i=</math>P then: //Pauli Gate | |||
<math>(\tilde {a}^{[m]},\tilde{b}^{[m]})\rightarrow (\tilde{a}^{[m]},\tilde{a}^{[m]}\oplus\tilde{b}^{[m]})</math> | |||
## if <math>c_i=</math>CNOT with m as target bit and n as control bit then: (CNOT) | |||
<math>(\tilde {a}^{[m]},\tilde{b}^{[m]};\tilde {a}^{[n]},\tilde{b}^{[n]})\rightarrow (\tilde {a}^{[m]},\tilde{b}^{[m]}\oplus \tilde {b}^{[n]};\tilde{a}^{[m]}\oplus \tilde {a}^{[n]},\tilde{b}^{[n]})</math> | |||
# If <math>c_i=T_j</math> gate then: //T Gate | |||
<math> (T_jX^{a^{[m]}}Z^{b^{[m]}}\psi=P^{a^{[m]}}X^{a^{[m]}}Z^{b^{[m]}}T_j\psi)</math> | |||
* '''Generate Measurement''' | |||
\item[] M$\leftarrow$ QFHE.GenMeasurement($\tilde {a}^{[m]},\Gamma_{pk_{j+1}}(sk_j),evk_j)$ | \item[] M$\leftarrow$ QFHE.GenMeasurement($\tilde {a}^{[m]},\Gamma_{pk_{j+1}}(sk_j),evk_j)$ | ||
\item \textbf{Gadget Correction} | \item \textbf{Gadget Correction} | ||