2018/12/14 by Min Liang, Liang, Min · 1 citation
Computer Science · #Complexity and Algorithms in Graphs #Cryptography and Data Security #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1812.07107
openalex publication_date 2018/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This article defines encrypted gate, which is denoted by EG[U]:|α⟩→((a,b),Enca,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 Enca,b(U|α⟩), and the other party obtains the random bits a,b. Based on EG[Px](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.