Prepare-and-Send Quantum Fully Homomorphic Encryption: Difference between revisions

# 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: <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: <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: <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: <math> (T_jX^{a^{[m]}}Z^{b^{[m]}}\psi=P^{a^{[m]}}X^{a^{[m]}}Z^{b^{[m]}}T_j\psi)</math>

##'''Generate Measurement''' M<math>\leftarrow</math> QFHE.GenMeasurement(<math>\tilde {a}^{[m]},\Gamma_{pk_{j+1}}(sk_j),evk_j)</math>

##'''Gadget Correction'''<math>(X^{a'^{[m]}}Z^{b'^{[m]}}T_j)\psi\leftarrow</math> QFHE.Measurement(M, <math>P^{a^{[m]}}X^{a^{[m]}}Z^{b^{[m]}}T_j\psi)</math>;