Table A1 Symbol definition table
From: Quantum identity authentication based on the extension of quantum rotation
Symbol1 | Definition and Description |
|---|---|
\(\mathbb{N}\) | {0,1,2,3,…} |
\(\mathbb{Z}\) | \(\{0,1,2,\dots,n-1\vert n \in \mathbb{N}\}\) |
\(\theta _{n}\) | \(\frac{\pi}{2^{n-1}} n \in \mathbb{N}\) |
\(R(s\theta _{n})\) | A quantum rotation, where \(s\in \mathbb{Z}_{n}\) |
\(R(s_{1}\theta _{n},s_{2}\theta _{n})_{(\Omega )}\) | Ternary quantum rotation occurring in Hilbert space Ω |
\(\vert \xi _{s_{i}}\rangle \) | The quantum rotation results with \(s_{i}\) |
n in protocol | Number of bits of authentication code |
\(k_{\mathrm{ide}}\) | String of authentication code |
\(k_{\mathrm{app}}\) | String of authentication application, \(\vert k_{\mathrm{app}}^{i}\vert \in \mathbb{Z}_{n}\) |
\(k_{\mathrm{ver}}\) | String of authentication verification, \(\vert k_{\mathrm{ver}}^{i}\vert \in \mathbb{Z}_{n}\) |
\(k_{\mathrm{ide}}^{i}\) | The i-th bit of the string, \(k_{\mathrm{ide}}^{i}\in \mathbb{Z}_{n}\) |
l | Auxiliary binary string |
\(l_{i}\) | The i-th bit of the auxiliary string, \(l_{i} \in \{0,1\}\) |
η | Quantum bit efficiency |