Towards Efficient Privacy-Preserving Multi-Party Multi-Data Sorting

In recent years， secure multi-party computation has received extensive attention in academia and industry. Secure multi-party computation allows multiple participants with private inputs to jointly compute a multi-input function without revealing any information about the private inputs of each participant，which makes the data available but invisible. As a fundamental problem in secure multi-party computation， privacy-preserving sorting allows multiple participants to compute the joint sorting result of multiple datasets without disclosing the privacy of the datasets and the sorting result，which has a wide range of application needs and values，such as product pricing， auctions， interest recommendations. Most of the existing privacy-preserving sorting protocols only support two participants，and cannot meet the joint sorting requirements of multiple participants in practical scenarios. The existing multi-party multi-data sorting protocols have the problems of high communication overhead，high computational complexity. As a result，they all suffer low overall efficiency. At the same time， the existing privacy-preserving sorting protocols do not consider the malicious security model of exhaustive attacks by malicious participants， and only realize security under the semi-honest adversary model， thus providing insufficient security protection against the more realistic malicious adversary model. In this paper，we propose an efficient privacy-preserving multi-party multi-data sorting protocol to overcome the above problems. Through this protocol，multiple participants can collectively compute the sorting results of their data in a privacy-preserving way with only O（1） rounds of interaction. Specifically， this paper designs a polynomial-based encoding method that encodes a participant′s dataset as a polynomial. In such a polynomial，the exponent and coefficient represent the data and the number of the data，respectively. Therefore，the sorting of multiple participant datasets can be realized by polynomial addition. For the above polynomial-based encoding algorithms，this paper also proposes polynomial encryption， aggregate polynomial generation， and decryption polynomial generation algorithms to realize the privacy protection of the encoded polynomials of each dataset based on the guarantee of computational correctness. The above algorithms can ensure the security of the encoded polynomials at the cost of low computational and communication overheads. Finally， each participant obtains the sorting result in a privacy-preserving way by means of communication-efficient oblivious transfer. In this paper，we consider a more realistic security model，provide for the first time the definition of malicious security under the non-colluding participant exhaustive attack， and define ideal functionalities of privacy-preserving sorting in different security models. The security analysis shows that the proposed protocol not only achieves semi-honest security， but also achieves malicious security against the exhaustive attack of non-colluding malicious users. In addition， a large number of experiments show that the proposed protocol is very efficient in both communication and computation. For example，when the number of participants is 15，each participant holds 20 000 data，and the upper bound of data is 500 000， our protocol’s communication and computation overheads are 898. 44 MB and 69. 76 s， which are only 12. 08% and 76. 85% of that of the LDYW protocol. Compared with the AHM+ scheme，our protocol’s computational efficiency is improved by about 20 times with only 4 times increase in the communication overhead. © 2024 Science Press. All rights reserved.