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

Prepare-and-Send Quantum Fully Homomorphic Encryption (edit)

Revision as of 21:56, 18 September 2018

32 bytes added , 18 September 2018

→‎Stage 2 Server’s Computation

Shraddha

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 ###	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 =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] ⊕ a˜[n],˜b[n])
 ##	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/>
-  QFHE.Recpkk+1(a˜[m],˜b[m]).<br/>
 ##Server updates the recrypted key using x,z and x’,z’.
 ## Server sends the updated encryption and QOTP output state to Client.
- '''Stage 3 Client’s Correction'''
+===Stage 3 Client’s Correction===
-. Decryption (QFHE.Dec())
+ '''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)
-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
-	skL	pkL
+#	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
-[i]	0[i]
+#	Client repeats this for all single qubits and hence gets the quantum state ρ0, final outcome of the computation.
-(b)	Client uses pad key and operates Xa	Zb	on single qubits i separately just like encryption.
-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
-(c)	Client repeats this for all single qubits and hence gets the quantum state ρ0, final outcome of the computation.
 == 	References ==