Quantum Key Distribution in Multiparty Computation for Data Sorting by Entanglement

Multiparty computation (MPC) and quantum key distribution (QKD) offer new paradigms for secure communication within quantum environments. The paper is the first to introduce the data sorting (Dsorting) framework, using entanglement within multiparty quantum contexts to distribute Dsorting. By combining QKD protocols with MPC methodologies, the system ensures that, together with privacy-preserving Dsorting, secure key exchanges are guaranteed. Grover's search algorithm combined with entanglement-based QKD is used and augmented by qudit quantum states to increase security and robustness against errors. The main parts are phase encoding, quantum error correction (QEC), GHZ state preparation, and multiparty entanglement purification. Grover's oracle and privacy amplification provide quantum security for the Dsorting process, and quantum sorting (Qsort) simulates sorting. Experimental results demonstrate sorting accuracy of up to 98% and effective key distribution rates of up to 92%, even under quantum bit error rate (QBER) conditions. Sorting time scales logarithmically with the size of the datasescales logarithmically with the size of the dataset and party count\(\mathcalligra{n}\); \(\mathcalligra{n}\)-party entanglement forces higher communication complexity compared to the traditional MPC. Such results justify the utility of QKD and entanglement in enabling the secure and fault-tolerant multiparty Dsorting while providing much value for distributed computing and secure communication at a certain computational overhead.