Cryptanalysis and improvement of quantum secure multi-party summation using single photons

<jats:title>Abstract</jats:title>
<jats:p>A previous study [Entropy 25.4 (2023): 590] proposed a quantum secure multi-party summation protocol wherein <jats:italic>n</jats:italic> participants could obtain the modulo-2 summation result using single photons and single-particle operations. Owing to the absence of an entanglement state, this protocol was more practical than other quantum summation protocols that used entanglement properties. Thus, this study investigated the claim that this proposed protocol prevented the participants’ secret inputs from being disclosed. It was found that the previously proposed protocol was vulnerable to a quantum Trojan horse attack owing to the circular qubit transmission mode. Using a security loophole, this study proposed an attack strategy that allowed an outside attacker to steal any participant’s secret input without being detected by a third party and participants. In addition, a simulation experiment was conducted to demonstrate the feasibility of the proposed attack and evaluate the number of quantum Trojan horse probes that the attacker must inject into regular qubit sequences. Finally, a solution was proposed by modifying the protocol to securely prevent quantum Trojan horse attacks.</jats:p>