Secure quantum network coding based on quantum homomorphic message authentication

As the principal security threat, pollution attacks also seriously affect the security of quantum network coding, just like they do for the classical network coding. Based on this, we first propose two secure quantum homomorphic message authentication schemes based on quantum circuit, which well resist the pollution attacks launched by outside attackers and the attackers including inside untrusted nodes over the general quantum network. Then, we apply this authentication method into our extended quantum network coding scheme over the multi-unicast network N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {N}$$\end{document}, solving the quantum k-pair problem securely and perfectly. Analysis results show that our proposed quantum network coding scheme has higher security and higher quantum communication rate, compared with the existing secure scheme.