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.