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Prepare-and-Send Quantum Fully Homomorphic Encryption: Difference between revisions
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Prepare-and-Send Quantum Fully Homomorphic Encryption (edit)
Revision as of 21:56, 18 September 2018
, 18 September 2018→Stage 2 Server’s Computation
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### if ci =H then{missing math} (Hadamard tranforms X gate into Z and Z into X) | ### if ci =H then{missing math} (Hadamard tranforms X gate into Z and Z into X) | ||
### if ci =P then<br/>{missing math} | ### if ci =P then<br/>{missing math} | ||
###if ci =CNOT with m as target bit and n as control bit then (CNOT)<br/> | ###if ci =CNOT with m as target bit and n as control bit then (CNOT)<br/>(a˜[m],˜b[m];˜a[n],˜b[n]) → (a˜[m],˜b[m] ⊕˜b[n];˜a[m] ⊕a˜[n],˜b[n]) | ||
(a˜[m],˜b[m];˜a[n],˜b[n]) → (a˜[m],˜b[m] ⊕˜b[n];˜a[m] | |||
## If ci = Tj gate then (TjXa[m]Zb[m]ψ = Pa[m]Xa[m]Zb[m]Tjψ) | ## If ci = Tj gate then (TjXa[m]Zb[m]ψ = Pa[m]Xa[m]Zb[m]Tjψ) | ||
### Generate Measurement<br/> | ### Generate Measurement<br/>M← QFHE.GenMeasurement(˜a[m],Γpkj+1(skj),evkj)<br/> | ||
M← QFHE.GenMeasurement(˜a[m],Γpkj+1(skj),evkj)<br/> | ### Gadget Correction<br/>(Xa0[m]Zb0[m]Tj)ψ ← QFHE.Measurement(M, Pa[m]Xa[m]Zb[m]Tjψ);<br/> Server gets measurement outcome x’,z’ | ||
### Gadget Correction<br/> | ### Recryption Server recrypts one-pad key using pkk+1<br/>QFHE.Recpkk+1(a˜[m],˜b[m]).<br/> | ||
(Xa0[m]Zb0[m]Tj)ψ ← QFHE.Measurement(M, Pa[m]Xa[m]Zb[m]Tjψ);<br/> | |||
Server gets measurement outcome x’,z’ | |||
### Recryption Server recrypts one-pad key using pkk+1<br/> | |||
##Server updates the recrypted key using x,z and x’,z’. | ##Server updates the recrypted key using x,z and x’,z’. | ||
## Server sends the updated encryption and QOTP output state to Client. | ## Server sends the updated encryption and QOTP output state to Client. | ||
===Stage 3 Client’s Correction=== | |||
'''Decryption (QFHE.Dec()) | |||
Input: QOTP Circuit Output State (Xa0[1]Zb0[1] ⊗ ..... ⊗ Xa0[k]Zb0[k]ρ0Zb0[1]Xa0[1] ⊗ ..... | *Input: QOTP Circuit Output State (Xa0[1]Zb0[1] ⊗ ..... ⊗ Xa0[k]Zb0[k]ρ0Zb0[1]Xa0[1] ⊗ ..... ⊗Xa0[k]Zb0[k]), Corresponding Encrypted Pad key (a˜0,b˜0) | ||
*Output: Final outcome of the computation CρC† = ρ0 (a) Client uses skL to restore the pad key from sent encryption. (a0[i],b0[i])=(HE.Dec [i](a0[i]),HE.Dec [i](b0[i])) | |||
Output: Final outcome of the computation CρC† = ρ0 (a) Client uses skL to restore the pad key from sent encryption. (a0[i],b0[i])=(HE.Dec [i](a0[i]),HE.Dec [i](b0[i])) | # Client uses skL to restore the pad key from sen encryption | ||
# Client uses pad key and operates Xa Zb on single qubits i separately just like encryption.<br/>Let single qubit representation of the output state be Xa0[i]Zb0[i]σ0Zb0[i]Xa0[i], then operation of Pauli X,Z gates as above yields σ0 | |||
# Client repeats this for all single qubits and hence gets the quantum state ρ0, final outcome of the computation. | |||
Let single qubit representation of the output state be Xa0[i]Zb0[i]σ0Zb0[i]Xa0[i], then operation of Pauli X,Z gates as above yields σ0 | |||
== References == | == References == | ||