Editing Prepare-and-Send Quantum Fully Homomorphic Encryption
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*Server should be able to store entangled states, perform all Clifford and T gates. | *Server should be able to store entangled states, perform all Clifford and T gates. | ||
[[File:Prepare-and-Send Quantum Fully Homomorphic Encryption.png|center|Prepare-and-Send Quantum Fully Homomorphic Encryption]] | |||
==Properties == | ==Properties == | ||
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* <math>\tilde{x}^{[i]}</math>, resulting ciphertext one gets for an input <math>i^{th}</math> element of array x or <math>i^{th}</math> bit of key x after the Encrypting it with <math>i^{th}</math> of public key string, pk. | * <math>\tilde{x}^{[i]}</math>, resulting ciphertext one gets for an input <math>i^{th}</math> element of array x or <math>i^{th}</math> bit of key x after the Encrypting it with <math>i^{th}</math> of public key string, pk. | ||
== | == Pseudocode== | ||
===Stage 1 Client’s Preparation=== | ===Stage 1 Client’s Preparation=== | ||
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=== Stage 2 Server’s Computation=== | === Stage 2 Server’s Computation=== | ||
'''Circuit | '''Circuit Evaluation (QFHE.Eval())''' | ||
* | *Input: public key tuple ( , Evaluation key tuple, Encrypted Pad key ({a˜[0]...a˜[n], ˜b[i]...˜b[n]}), QOTP Input State (Xa[1]Zb[1] ⊗ ..... ⊗ Xa[n]Zb[n]ρZb[1]Xa[1] ⊗ ..... ⊗ Xa[n]Zb[n]) | ||
* | *Output: 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)=(HE.EvalCevkL(a˜),HE.EvalCevkL(˜b)) | ||
Let the Circuit be denoted by C and the gates be | Let the Circuit be denoted by C and the gates be ci | ||
# For all i, | # For all i, ci gate is applied on qubit m and the mth bits of pad key (˜a[m],˜b[m]) are updated to | ||
## If | (a˜0[m],˜b0[m]) as follows. | ||
### if | ## If ci = {P,H,CNOT}, a Clifford gate then (ciXa[m]Zb[m]ψ = Xa0[m]Zb0[m]ciψ) | ||
### if | ### if ci =H then{missing math} (Hadamard tranforms X gate into Z and Z into X) | ||
### if | ### if ci =P then<br/>{missing math} | ||
## If | ###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]) | ||
### | ## If ci = Tj gate then (TjXa[m]Zb[m]ψ = Pa[m]Xa[m]Zb[m]Tjψ) | ||
### | ### Generate Measurement<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’ | |||
### | ### 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. | ## 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()) |