Two multi-party private comparison protocols based on GHZ state without pre-shared key

Abstract In this paper, we propose two multi-party quantum private comparison protocols based on the properties of the d -dimensional GHZ state. Protocol 1 is designed to compare the equality of multiple participants’ secrets with the help of a semi-honest third party TP. The semi-honest TP will follow the protocol honestly, but he may attempt to learn additional information from the protocol execution. In this protocol, multiple participants encode their secret information into the corresponding particles in turn through unitary operations, thereby achieving the comparison of the equality of their multiple secrets in a single execution. This protocol has a wide range of applications. For example, by combining the basic model framework of this protocol with the Chinese Remainder Theorem, we propose Protocol 2. In this protocol, multiple participants compare the size relationships of their multiple secrets with the help of a semi-honest third party TP. Therefore, based on the same basic model framework, the two protocols proposed in this paper can be applied respectively to the comparison of the equality and the size relationships of multiple participants’ secrets. Importantly, the two protocols do not require pre-shared keys. Security analysis shows that the proposed protocols can resist various attacks, including entangle-measure attack, intercept-resend attack, third party attacks, and participant attacks.