Confidential Message Authentication via Quantum Teleportation

Table 1: \varepsilon_1 = \varepsilon_2 = 10^{-9}. The data are plotted for F^2 ranging from 0.80 to 1.00 in increments of 0.01. The dependence of the required number of comparisons n and decision thresholds (T_1, T_2) on the square of the quantum teleportation fidelity, F^2. In the ideal case where a=F^2=1, our calculations yield n=36 and T_1=T_2=35; specifically, the messages are considered identical if and only if all 36 comparisons are consistent. Table 2~5: a=0.88 (0.8、0.9、0.999) and \varepsilon_1 = 10^{-9}. The data points are plotted at integer intervals of -\log_{10}(\varepsilon_2). Table 6~7: a=0.85 and \varepsilon_2 = 10^{-6} (\varepsilon_2 = 10^{-9}). The data points are plotted at integer intervals of -\log_{10}(\varepsilon_1). Table 8~9: a=0.8 and \varepsilon_2 = 10^{-6} (\varepsilon_2 = 10^{-9}). The data points are plotted at integer intervals of -\log_{10}(\varepsilon_1). Table 10: For the case of distinct messages, we specifically consider scenarios where the discrepancy occurs in the first bit, the last bit, or at two arbitrary positions.The simulation reveals that when the messages differ, the number of consistent outcomes across the 194 encoded bit comparisons is primarily distributed between 84 and 110. This range falls below the threshold T_2, allowing for the correct identification of the messages as distinct. Conversely, when the messages are identical, the number of consistent matches centers around 170, which exceeds the threshold T_1, thereby enabling the correct verification of message identity.表1：ε₁=ε₂=10⁻⁹。数据以量子隐形传态保真度（quantum teleportation fidelity）平方F²从0.80到1.00、步长0.01进行绘图，展示了所需比较次数n与判决阈值（decision thresholds）(T₁, T₂)随F²的变化关系。在a=F²=1的理想场景中，我们的计算结果为n=36且T₁=T₂=35；具体而言，当且仅当全部36次比较结果均一致时，才判定两条消息完全相同。 表2~表5：a=0.88（0.8、0.9、0.999）且ε₁=10⁻⁹，数据点以-log₁₀(ε₂)的整数间隔进行绘图。 表6~表7：a=0.85且ε₂=10⁻⁶（ε₂=10⁻⁹），数据点以-log₁₀(ε₁)的整数间隔进行绘图。 表8~表9：a=0.8且ε₂=10⁻⁶（ε₂=10⁻⁹），数据点以-log₁₀(ε₁)的整数间隔进行绘图。 表10：针对消息存在差异的场景，我们特别考虑了差异出现在首比特、末比特，或任意两个位置的情况。仿真结果显示，当消息不同时，194次编码比特比较的一致结果数量主要分布于84至110之间，该区间低于阈值T₂，可正确识别两条消息为不同；反之，当消息完全相同时，一致匹配的数量集中在170左右，该数值高于阈值T₁，从而能够正确验证消息的一致性。