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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 12:28, 20 November 2018
, 20 November 2018→Stage 2 Server’s Computation
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#Server creates a superposition state for the encrypted classical message and Pauli one time pads it using encrypted pad key. He applies the circuit on it as follows:</br>Let the Circuit be denoted by C and the gates be <math>c_i</math> | #Server creates a superposition state for the encrypted classical message and Pauli one time pads it using encrypted pad key. He applies the circuit on it as follows:</br>Let the Circuit be denoted by C and the gates be <math>c_i</math> | ||
# For all i, <math>c_i</math> gate is applied on qubit l and the <math>l_{th}</math> bits of pad key <math>(\tilde {a}^{[l]},\tilde{b}^{[l]})</math> are updated to <math>(\tilde {a}'^{[l]},\tilde{b}'^{[l]})</math> as follows. | # For all i, <math>c_i</math> gate is applied on qubit l and the <math>l_{th}</math> bits of pad key <math>(\tilde {a}^{[l]},\tilde{b}^{[l]})</math> are updated to <math>(\tilde {a}'^{[l]},\tilde{b}'^{[l]})</math> as follows. | ||
## If <math>c_i=\{P,H,CNOT\}</math>, a Clifford gate then< | ## If <math>c_i=\{P,H,CNOT\}</math>, a Clifford gate then<!--i-->(<math>c_iX^{a^{[l]}}Z^{b^{[l]}}|\psi\rangle=X^{a'^{[l]}}Z^{b'^{[l]}}c_i|\psi\rangle</math>) | ||
### if <math>c_i=</math>H then <comment/>Hadamard Gate | ### if <math>c_i=</math>H then <comment/>Hadamard Gate | ||
### if ci =P then //Pauli Gate<br/>(a˜[l],˜b[l]) → (a˜[l],a˜[l] ⊕˜b[l]) | ### if ci =P then //Pauli Gate<br/>(a˜[l],˜b[l]) → (a˜[l],a˜[l] ⊕˜b[l]) | ||