Teleportation-based quantum homomorphic encryption scheme with quasi-compactness and perfect security
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This article defines encrypted gate, which is denoted by EG[U]:|α〉→((a,b),Enc_a,b(U|α〉)). We present a gate-teleportation-based two-party computation scheme for EG[U], where one party gives arbitrary quantum state |α〉 as input and obtains the encrypted U-computing result Enc_a,b(U|α〉), and the other party obtains the random bits a,b. Based on EG[P^x](x∈{0,1}), we propose a method to remove the P-error generated in the homomorphic evaluation of T/T^†-gate. Using this method, we design two non-interactive and perfectly secure QHE schemes named GT and VGT. Both of them are F-homomorphic and quasi-compact (the decryption complexity depends on the T/T^†-gate complexity). Assume F-homomorphism, non-interaction and perfect security are necessary property, the quasi-compactness is proved to be bounded by O(M), where M is the total number of T/T^†-gates in the evaluated circuit. VGT is proved to be optimal and has M-quasi-compactness. According to our QHE schemes, the decryption would be inefficient if the evaluated circuit contains exponential number of T/T^†-gates. Thus our schemes are suitable for homomorphic evaluation of any quantum circuit with low T/T^†-gate complexity, such as any polynomial-size quantum circuit or any quantum circuit with polynomial number of T/T^†-gates.
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