01-01-2020
Teleportation-based quantum homomorphic encryption scheme with quasi-compactness and perfect security
Published in: Quantum Information Processing | Issue 1/2020
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Abstract
GT
and VGT
. Both of them are \({\mathcal {F}}\)-homomorphic and quasi-compact (the decryption complexity depends on the \(T/T^\dagger \)-gate complexity). Assume \({\mathcal {F}}\)-homomorphism, non-interaction and perfect security are necessary properties, the quasi-compactness is proved to be bounded by \(\varOmega (M)\), where M is the total number of \(T/T^\dagger \)-gates in the evaluated circuit. We prove VGT
is M-quasi-compact and reaches the optimal bound. According to our QHE schemes, the decryption would be inefficient when the evaluated circuit contains exponential number of \(T/T^\dagger \)-gates. Thus, our schemes are suitable for homomorphic evaluation of any quantum circuit with low \(T/T^\dagger \)-gate complexity, such as any polynomial-size quantum circuit or any quantum circuit with polynomial number of \(T/T^\dagger \)-gates.