IEEE International Conference on Internet of Things (iThings) and IEEE Green Computing and Communications (GreenCom) and IEEE Cyber, Physical and Social Computing (CPSCom) and IEEE Smart Data (SmartData)
A Secure Comparison Protocol in the Malicious Model
Secure comparison is an important problem in the field of secure computing. A classic example is the Millionaires' problem, which is securely compares the wealth of two millionaires without revealing their wealth. However most traditional secure comparison protocol requires autonomous computation among the participants. It is necessary to ensure that the model of the participants is a semi-honest model, otherwise the protocol will not be able to execute correctly. In this paper, we introduce a semi-honest judge to improve the Damgård-Geisler-KrØigaard(DGK) comparison protocol by using techniques such as zero-knowledge proof and homomorphic encryption. The improved protocol is not only applicable to the malicious participant model, but also the introduced judge would not get any information of data. At last, the security analysis shows that the proposed scheme in this paper can guarantee the data fairness of the comparison protocol while ensuring the privacy security of the participants.
Secure comparison is an important problem in the field of secure computing. A classic example is the Millionaires' problem, which is securely compares the wealth of two millionaires without revealing their wealth. However most traditional secure comparison protocol requires autonomous computation among the participants. It is necessary to ensure that the model of the participants is a semi-honest model, otherwise the protocol will not be able to execute correctly. In this paper, we introduce a semi-honest judge to improve the Damgård-Geisler-KrØigaard(DGK) comparison protocol by using techniques such as zero-knowledge proof and homomorphic encryption. The improved protocol is not only applicable to the malicious participant model, but also the introduced judge would not get any information of data. At last, the security analysis shows that the proposed scheme in this paper can guarantee the data fairness of the comparison protocol while ensuring the privacy security of the participants.
When processing signals in the encrypted domain, homomorphic encryption can be used to enable linear operations on encrypted data. Comparison of encrypted data however requires an additional protocol between the parties and will be relatively expensive. A well-known and frequently used comparison protocol is by Damgard, Geisler and Kroigaard. We present two ways of improving this comparison protocol. Firstly, we reduce the computational effort of one party by roughly 50%. Secondly, we show how to achieve perfect security towards the other party without additional costs, whereas the original version with encrypted inputs only achieved statistical security. An additional advantage is that larger inputs are allowed.
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.
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.
Secure multi-party computation is a hotspot in the cryptography field, and it is also a significant means to realize privacy computation. The Millionaires’ problem is the most fundamental problem among them, which is the basic module of secure multi-party computation protocols. Although there are many solutions to this problem, there are few anti-malicious adversarial protocols besides protocols based on Yao’s garbled circuit. Only a few solutions have low efficiency, and there is no protocol for rational numbers comparison under the malicious model, which restricts the solution of many secure multi-party computation problems. In this paper, the possible malicious behaviors are analyzed in the existing Millionaires’ problem protocols. These behaviors are discovered and taken precautions against through the triangle area formula, zero-knowledge proof, and cut-and-choose method, so the protocol of comparing confidentially rational numbers is proposed under the malicious model. And this paper adopts the real/ideal model paradigm to prove the security of the malicious model protocol. Efficiency analysis indicates that the proposed protocol is more effective than existing protocols. The protocol of rational numbers comparison under the malicious model is more suitable for the practical applications of secure multi-party computation, which has important theoretical and practical significance.
Due to high complexity, comparison protocols with secret inputs have been a bottleneck in the design of privacy-preserving cryptographic protocols. Different solutions based on homomorphic encryption, garbled circuits and secret sharing techniques have been proposed over the last few years, each claiming high efficiency. Unfortunately, a fair comparison of existing protocols in terms of run-time, bandwidth requirement and round complexity has been lacking so far. In this paper, we analyze the state-of-the-art comparison protocols for a two-party setting in the semi-honest security protocol. We analyze their performances in three stages, namely initialization, pre-processing and online computation, by implementing them on a single platform. The results of our experiments provide a clear insight for the research community into the advantages and disadvantages of the various techniques .
Abstract Secure multi-party computation(SMPC) is an important research area in cryptography with many application scenarios, but there are still many problems to be solved. Aiming at security and fairness issues in SMPC, we consider that semi-honest participants are able to execute the protocol according to the specification, but there would be some additional malicious operations such as collusion and refuse to exchange information in the process of information interaction, which leads to deviations in the security and fairness of the protocol. To solve the above problems, we combine information entropy and mutual information to propose an n-round information exchange protocol, in which each participant broadcasts a relevant information value in each round without revealing additional information. The uncertainty of the correct result value is fuzzed by the interactive information in each round, and each participant cannot determine the correct result value until the end of the protocol, which effectively prevents malicious behavior and ensures the correct execution of the protocol. Security analysis and fairness analysis show that under the semi-honest model, our protocol guarantees the security and relative fairness of the output obtained by the participants after completing the protocol.