Privacy-Preserving Computational Geometry (PPCG) is a special Secure Multi-party Computation, which is a hot research in information security. This paper presented a special PPCG problem of secure two-party computing the quadratic function's extreme minimal value on a secret interval. Based on Paillier's additive homomorphic and secure comparison protocol, a novel protocol for this problem is proposed. Furthermore, its correctness, security and efficiency are analyzed. The analysis results show that the proposed protocol is much more efficient than current protocol, which can be applied in some military and commercial fields.
Privacy-Preserving Computational Geometry (PPCG) is a special Secure Multi-party Computation, which is a hot research in information security. This paper presented a special PPCG problem of secure two-party computing the quadratic function's extreme minimal value on a secret interval. Based on Paillier's additive homomorphic and secure comparison protocol, a novel protocol for this problem is proposed. Furthermore, its correctness, security and efficiency are analyzed. The analysis results show that the proposed protocol is much more efficient than current protocol, which can be applied in some military and commercial fields.
Secure multi-party computation (SMC) is a research hotspot in cryptography in recent years, and is also a key technology for information security protection. The interval secure multi-party computation problems have important theoretical significance in cryptography. Previous studies rarely involve secret interval, that is, interval is generated by two-party or multi-party, and any one knows nothing about the interval information. The secret interval problems have important practical significance in real life. This paper mainly studies the privacy-preserving determination of secret interval and threshold. Firstly, for the secret interval is generated by two-party, based on Paillier’s homomorphic encryption, this paper proposes a protocol. Secondly, for the secret interval is generated by multi-party, this paper proposes an optimization protocol that uses the coding principle combined with Lifted ElGamal homomorphic encryption. Thirdly, this paper proves the protocols can resist collusion attacks, and proves they are safe by using the simulation paradigm. Finally, many practical application problems can be solved by using the protocols proposed in this paper.
Convex hull computation is a fundamental problem in secure multi-party computational geometry (SMCG), classified under secure multi-party computation (SMC) for finding the convex hull of a set of points. Existing quantum solutions largely depend on quantum homomorphic encryption (QHE), which introduces significant computational overhead due to frequent key updates by a trusted third party (TTP). Furthermore, most current protocols lack a mechanism for input commitment, making them vulnerable to post-computation input tampering or denial by the TTP. To overcome these limitations, we propose an efficient convex hull protocol that utilizes quantum secret commitment (QSC) as a more secure alternative to QHE. Our protocol enables a designated party (the committer) to securely commit to input values in a manner that guarantees both binding (no post-hoc alteration) and hiding (input secrecy). We introduce a novel value comparison protocol within an Ideal Quantum K-Party model, ensuring privacy-preserving convex hull computation without reliance on QHE. Rigorous security analysis demonstrates significant improvements in computational efficiency and resilience against quantum adversaries. Our protocol represents a pivotal advancement for quantum-secure multi-party computations and lays the groundwork for scalable, future-proof privacy-preserving geometry in quantum computing contexts.
At present, research on secure multi-party computation is of great interest in modern cryptography. It should be acknowledged that if any function can be computed securely, then it results in a very powerful tool. In fact, all natural protocols are, or can be rephrased to be, special cases of the multi-party computation problems. Design and analysis of the special multi-party computation protocols is meaningful and has attracted much interest in this field. Based on the combination of a public-key cryptosystem of the homomorphic encryption and on the theoretic construction relying on the F-hiding assumption, a protocol for comparing information of equality is proposed. The protocol needs only a single round of interaction and ensures fairness, efficiency and security. The protocol is fair, which means that one party knows the sound result of the comparison if and only if the other one knows the result. The protocol is efficient with the help of an oblivious third party for calculating. However, the third party cannot learn any information about the participant抯 private inputs and even about the comparison result, and cannot collude with any participant. The protocol is secure for the two participants, that is, any information about their secret input will not leak except the final computation result. A precise proof of security of the protocol is presented. Applications of this protocol may include private bidding and auctions, secret ballot elections, commercial business, identification in a number of scenarios and so on. It is believed that the protocol may be of practical significance for electronic transaction.
Abstract Secure multi-party computational geometry is a branch of secure multi-party computation, which is applied in many important fields. But up to now, the research on how to solve this problem with quantum methods has just started. Therefore, we study the design of quantum secure multi-party computational geometry (QSMCG) protocols in this paper. As the foundation, we extend the two-party summation and multiplication protocols proposed by Sutradhar and Om to multi-party protocols. Then we propose three new QSMCG protocols. Our proposed quantum secure two-party distance computation protocol has improvement in efficiency and accuracy. And the proposed quantum secure multi-party polytope volume computation protocol as well as the quantum secure circle–circle intersection area computation protocol are designed for the first time. Moreover, these protocols are designed to use multi-third parties, which solves the problem of intermediate value leakage in computation. The correctness, security and performance of all these protocols are analyzed.
The emergence of cloud computing provides a new computing paradigm for users -- massive and complex computing tasks can be outsourced to cloud servers. However, the privacy issues also follow. Fully homomorphic encryption shows great potential in privacy-preserving computation, yet it is not ready for practice. At present, secure multiparty computation (MPC) remains mainly approach to deal with sensitive data. In this paper, following the secret sharing based MPC paradigm, we propose a secure 2-party computation scheme, in which cloud servers can securely evaluate functions with high efficiency. We first propose the multiplicative secret sharing (MSS) based on typical additive secret sharing (ASS). Then, we design protocols to switch shared secret between MSS and ASS, based on which a series of protocols for comparison and nearly all of the elementary functions are proposed. We prove that all the proposed protocols are Universally Composable secure in the honest-but-curious model. Finally, we will show the remarkable progress of our protocols on both communication efficiency and functionality completeness.
Secure multi-party computation with its applications is an important direction in current cryptography research field. The research focuses on how to accomplish the secure cooperative computation among multi-party without the participation of the third party. The two-party bargaining protocol, based on homomorphic public key cryptosystem, was an example of secure multi-party computation's applications. One participant can make a bargain with the other by implementing the protocol. During the implementation of protocol, the privacy of input and the correctness of output could be preserved. The protocol can be implemented without the participation of the third party and its security was based on additive homomorphic public key cryptosystem.