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International Conference on Computer Information Science and Application Technology (CISAT)

Improvement and extension of secure vector dominance protocol

Zhengtao Jiang, Ting Yu, Huiqiang Li, Ye Chen

Published Oct 20, 2022• 0 citations
Publisher

Abstract

The millionaire’s problem is the origin of secure multi-party computation. This problem has always been the focus of scholars' research, and it is also the design basis and important part of other secure multi-party computation protocols. An in-depth study of the millionaires’ problem is of great significance to promote the further development of secure multi-party computation. Based on millionaires’ problem and secure vector dominance protocol, we propose an improved protocol and an extended protocol. The improved protocol solves the problem of coarse granularity when comparing elements in the original protocol, and can realize that two parties can compare the relationships of greater than, equal to or less than between their elements by executing the protocol once. The improved protocol and the extended protocol are further applied to solve the problem of finding the cardinality of the intersection of the two-party sets in two cases. In addition, based on the integer division problem, we give a method to privately evaluate the greatest common factor of two integers.

DOI
10.1117/12.2656663

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The millionaire’s problem is the origin of secure multi-party computation. This problem has always been the focus of scholars' research, and it is also the design basis and important part of other secure multi-party computation protocols. An in-depth study of the millionaires’ problem is of great significance to promote the further development of secure multi-party computation. Based on millionaires’ problem and secure vector dominance protocol, we propose an improved protocol and an extended protocol. The improved protocol solves the problem of coarse granularity when comparing elements in the original protocol, and can realize that two parties can compare the relationships of greater than, equal to or less than between their elements by executing the protocol once. The improved protocol and the extended protocol are further applied to solve the problem of finding the cardinality of the intersection of the two-party sets in two cases. In addition, based on the integer division problem, we give a method to privately evaluate the greatest common factor of two integers.
Secure multi-party computation is a hot research topic in cryptography in recent years, and has become an important research direction in cryptography. This paper studies the millionaires’ problem in secure multi-party computation, and its essence is a comparison issue about the size of two encrypted data. Yao offered a solution to the millionaires’ problem, but his protocol can’t accurately compare two numbers. We improved Yao’s protocol and proposed two generic protocols to solve the millionaires’ problem. Our first protocol has one more round of communication between participants than Yao’s, but our protocol can accurately compare the size of two numbers. The second protocol improved the first protocol, and only one round of communication is needed to get accurate comparison results. Finally, we realized the second protocol based on RSA encryption algorithm, and analyze the security under the semi-honest model.
The millionaires’ problem is the basis of secure multiparty computation and has many applications. Using a vectorization method and the Paillier encryption scheme, we first propose a secure two-party solution to the millionaires’ problem, which can determine x=y, x<y , or x>y in one execution. Subsequently, using the vectorization and secret splitting methods, we propose an information-theoretically secure protocol to solve the multiparty millionaires’ problem (a.k.a. secure sorting problem), and this protocol can resist collusion attacks. We analyze the accuracy and security of our protocols in the semihonest model and compare the computational and communication complexities between the proposed protocols and the existing ones.
Secure multiparty computation (SMC) is a research focusing in the international cryptographic community. The protocols used to address the millionaires' problem are the basic building blocks of most SMC protocols and their efficiency dominates that of many other SMC protocols. To the best of our knowledge, almost all protocols used to address the millionaires' problem are based on integers, which means that their applications are limited. In this study, we propose precise and efficient protocols for rational numbers based on additively homomorphic encryptions. One of our protocols is inspired by computational geometry and it reduces the millionaires problem to computing the area of a triangle formed by three private points. This approach can determine whether the relationship between two private inputs is greater than, equal to or less than, and it has a much lower computational complexity compared with existing methods. We proved that these protocols are secure using simulation paradigm. Our approaches can be used in many SMC protocols that involve rational numbers and integers, and they can also be used directly to solve some secure multiparty computational geometry problem in rational number field.
As the basic problem that introduces the idea of secure multi-party computation (SMC), millionaires’ problem (MP) is one of the research highlights in the field of SMC. However, most of current protocols for MP are only secure in semi-honest model, which using public key cryptography schemes, and there are few secure schemes in malicious model exist security defects. Therefore, this paper analyzes the Li et al.’s protocol for MP that secure in malicious model. Firstly, we point out several behaviours that can be successfully implemented in Li et al.’s protocol. Secondly, by using the zero-knowledge proof (ZKP) for the equality of discrete logarithm (DL), cut-and-choose method etc. We propose the improved protocol and show how to detect malicious behaviours. Finally, we analyze the correctness and security against malicious behaviours of the improved protocol.
Private integer comparison has been an essential computation function for many applications, including online auction, credential identification, data mining, and joint bidding. In the setting of two-party computation, two parties with private inputs (x and y) want to jointly compare them without revealing the value of those inputs to others (also known as the Millionaires’ problem) while the output should ensure correctness and preserve data privacy. The private inputs only can be revealed if they are equal, i.e., x = y. Many related works have been proposed to solve the integer comparison problem in various settings, focusing on different properties such as round and computation complexity. Most solutions decompose integers into bitwise representation and then securely evaluate the function in a Boolean circuit on encrypted bits. However, this type of solution is costly (especially for large integers) as each bit requires encryption and decryption. In this paper, we transform the private integer comparison into a block comparison problem. In particular, we employ a block vectorization mechanism to encode the private inputs into blocks. We show the security of our two-party protocol in the semi-honest model. Also, we implement the protocol to demonstrate its efficiency using block vectorization mechanism and homomorphic encryption. The experimental result proves that our proposed solution achieves high efficiency, particularly for large integer comparisons.
Secure multi-party computation is a focus of international cryptography in recent years. Protocols for Yao's millionaires' problem have become an important building block of many secure multi-party computation protocols. Their efficiency are crucial to the efficiency of many secure multi-party computation protocols. Unfortunately, known protocols for Yao's millionaries' problem have high computational complexity or communication complexity. In this study, based on the 1-out of-m oblivious transfer and set-inclusion problem, we propose a new protocol to solve this problem. This new protocol is very efficient in terms of both computational and communication complexities. Its privacy-preserving property is also proved by simulation patadigm which is generally accepted in the study of secure multi-party computation. We also compare the information leakage of our new protocol and the known protocols.