A novel quantum security multi-party extremum protocol in a d-dimensional quantum system

Secure multi-party extremum computation (SMEC) is a specific application scenario of secure multi-party computation, which allows multiple participants to compute the extremum of data without disclosing private information. The extremum includes maximum, minimum, sum of extremums, and difference of extremums. SMEC has wide applications in financial transactions, market analysis, sports events, healthcare, etc. Current protocol research mainly exists in the classical domain and cannot withstand quantum computing attacks. To address this issue, we propose a novel QSME protocol based on a d-dimensional quantum system, capable of computing the maximum and minimum values among multi-party data under unconditional security, and can compute the sum and difference of extremums without disclosing the maximum and minimum values, to adapt to complex application scenarios. The article proposes a coding method for a d-dimensional quantum system to further enhance security, provides correctness analysis, security analysis, robustness analysis, and comparative analysis, and proposes an experimental method for a d-dimensional quantum system to verify the effectiveness of the protocol, demonstrating strong practicality.