Quantum homomorphic encryption scheme based on elliptic curve cryptography

As an important component of the quantum encryption algorithm family, quantum homomorphic encryption performs evaluation calculations on ciphertext quantum states without decryption, and the calculated results are the same as those obtained by directly calculating plaintext quantum states. In the evaluation process, when using T-gate as the evaluation operator, an error of S-gate will be generated. In the current scheme, the complexity of the method to eliminate this error is too high. Therefore, in this paper, elliptic curve cryptography(ECC) and quantum encoding methods are integrated into the quantum homomorphic encryption scheme, enhancing the security of evaluation parameters during transmission. At the same time, a method is proposed to eliminate S-gate errors by constructing an Gamma u\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Gamma _u$$\end{document}-operator. Compared to other similar QHE encryption schemes, the proposed scheme has higher security and reduces the complexity of eliminating S-gate errors. Finally, the security of each process in the algorithm was analyzed, and the feasibility and correctness of the algorithm were verified through simulation experiments.