# High-Dimensional and Multi-Intensity One-Photon-Interference Quantum Secure Direct Communication
## 3 Security Analysis
Instead, they send phase-encoded weak coherent pulses to a central untrusted relay Charlie, where information is distilled from phase correlations through single-photon interference. If [PERSON] intercepts the photons, she inevitably collapses their quantum states, disrupting the interference and introducing detectable errors in the QBER. Furthermore, intercepting a single path is ineffective since complete information is only reconstructed through interference at the relay. Second, our frame-by-frame encoding scheme (detailed in Appendix A) prevents meaningful data extraction, as each frame carriesnot only its own ciphertext but also secure keys for subsequent frames. Even in the worst case scenario, where [PERSON] controls both channels and conducts the interference by herself, our encoding strategy not only ensures that this behavior will be immediately perceived by [PERSON] and [PERSON] but also prevents her from obtaining the original secret information, leaving her with only pieces of codewords. Moreover, since this pre-encoding occurs before the secret information is modulated onto quantum states, the scheme effectively leverages the one-time-pad property, significantly reducing the risk of information leakage. Third, INCUM technology further strengthens the protocol's security by adding another protective layer of masking with locally generated random numbers. This technique restricts [PERSON]'s effective reception rate to [PERSON]'s level, making it even more difficult for her to reconstruct the original information. Together, these mechanisms grant our protocol resistance to intercept-resend attacks. Another related threat is the PNS attack, where [PERSON] exploits the multi-photon pulses in a practical weak coherent source by splitting off a photon while allowing the remaining photons to reach the legitimate recipient, gaining information without being detected. Our protocol resists this attack through a multi-intensity mode, which functions similarly to the decoy-state method [7; 8; 9]. Since [PERSON] cannot tell whether a pulse is in encoding mode or multi-intensity mode before her measurement, she cannot selectively attack multi-photon pulses without introducing detectable anomalies. By comparing channel parameters of different light intensities that have different mean photon numbers, [PERSON] and [PERSON] can identify the inconsistencies caused by eavesdropping attempts. As a result, the additional pulses with randomized light intensities and phases protect the multi-photon components of WCS-based encoding schemes, noticeably enhancing their secrecy capacity and ensuring security in the face of PNS attacks. While quantum communication protocols are theoretically secure under ideal conditions, the measurement devices used in practical systems retain certain loopholes. Imperfections in detectors can be utilized to bypass security guarantees, such as the bright illumination attack [52] and the dead time attack [53]. Our protocol inherits the MDI nature of MDI-QSDC by shifting measurements to an untrusted third party [PERSON] and relying solely on his results. Because [PERSON] and [PERSON] do not directly receive photons or perform measurements, any inherent imperfections in their detectors do not expose them to vulnerabilities such as side-channel attacks. The security of this protocol relies on quantum interference rather than [PERSON]'s honesty. Even if his detectors are fully controlled by [PERSON] and are maliciously manipulated, [PERSON] has no chance learning any useful information as it is only derived from post-processed correlations between [PERSON] and [PERSON], as long as they strictly follow the correct procedures. In addition, as mentioned earlier, parameters such as error rates are carefully monitored, and any unexpected deviations are identified instantly.