A quantum secure multi-party summation protocol based on one-direction quantum walks on a circle

This paper presents a novel quantum secure multi-party summation protocol based on one-direction quantum walks on a circle (ODQWC), which allows the summation computation of different integer sequences from “n” secret holders. Crucially, it ensures that this process does not infringe on the privacy of these secret holders by delivering quantum walk states in a circular pattern. Our proposed protocol employs two-particle product states rather than quantum entangled states as the initial quantum resource and eliminates the need for different secret holders to perform quantum entanglement swapping operations. Instead, it emphasizes imposing one-direction evolution operators on quantum walk states. Additionally, our protocol requires single-particle measurements. Security analysis validates that our proposed protocol can effectively counter external attacks and those initiated by participants. Under specific conditions, our proposed protocol can be adapted into a quantum secure multi-party bit summation protocol based on ODQWC.