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.
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.
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.
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.
Secure multiparty computation is valuable for studying data privacy protection issues due to its decentralization, input privacy, fairness, etc. One of the most fundamental problems is to confidentially compute the maximum and the minimum of multiple data. In this paper, an efficient secure multipart computation scheme that can compute the maximum and the minimum simultaneously without a trusted third party was proposed to address the problems of existing secure multi-party computation protocols, such as inability of computing the maximum and the minimum at one time, low efficiency, and security risks caused by unique designated decryption key holder. In the scheme, an encoding method that can simultaneously compute the maximum and the minimum was first provided, whose basic idea was to give a complete set of ordinal numbers with potential l (l ≥ the number of participants n), and each participant encodes its data into an array with length l where the location of the data in the complete set was coded as a random number and the other positions were coded as 1. The positions of the leftmost and rightmost non-1 values in the product array were the positions of the maximum and minimum in the whole set. Based on the proposed encoding method, the ElGamal homomorphic encryption algorithm was used to guarantee the confidentiality of all participants’ data, and the maximum threshold decryption was used to make each participant hold part of the decryption key, which avoids the security threats caused by centralized decryption of calculation result by designated key holder. The proposed scheme was proven to be resistant to collusive attacks by any participant under a semi-honest model based on an ideal-realistic simulation paradigm. Finally, the efficiency analysis and performance comparison with related maximum (minimum) computing schemes were given, which showed that the proposed protocol has advantages over existing schemes in terms of computational complexity and communication complexity under the premise of higher security.
Secure multi-party computation (SMC) allows multiple parties to jointly and securely compute a function while preserving the privacy of the involved parties. In this regard, homomorphic cryptosystems allow users to perform addition or multiplication operations on encrypted values without having to decrypt the input values. In this paper, we propose both a cryptographic and a non-cryptographic privacy-preserving protocols that allow one party to collaboratively compute a private polynomial function with at least two other parties using semantically secure cryptosystems. In this respect, the function to be evaluated is kept private to the party in question. In addition, we assume that there is no fully trusted party and that all parties are semi-honest. Moreover, we assume that there is no collusion between the different parties. We present the two protocols in question and report on the underlying performance through the presentation of our implementation results. The proposed protocols are relevant in many applications such as evidence sharing in multi-party forensic investigations, situation awareness through the secure sharing in distributed monitoring of plan execution, etc.
Aiming at the problems of large ciphertext size and low efficiency in the current secure multi-party computation (SMC) protocol based on fully homomorphic encryption (FHE), the paper proves that the fully homomorphic encryption scheme that supports multi-bit encryption proposed by Chen Li et al. satisfies the key homomorphism. Based on this scheme and threshold decryption, a three-round, interactive, leveled, secure multi-party computation protocol under the Common Random String (CRS) model is designed. The protocol is proved to be safe under the semi-honest model and the semi-malicious model. From the non-interactive zero-knowledge proof, it can be concluded that the protocol is also safe under the malicious model. Its security can be attributed to the Decisional Learning With Errors (DLWE) and a variant of this problem (some-are-errorless LWE). Compared with the existing secure multi-party computation protocol based on fully homomorphic encryption under the CRS model, the ciphertext size of this protocol is smaller, the efficiency is higher, the storage overhead is smaller, and the overall performance is better than the existing protocol.
As a fundamental part of cryptography, secure multiparty computation (SMC) is a building block of various cryptographic protocols, and it is also a hot topic in the international cryptographic community.In recent years, many SMC problems, such as secret information comparison, secret set problems and secure multiparty computational geometry, have been widely studied.As many practical problems need to be described by rational numbers, it is both theoretically and practically important to study the SMC problems in the rational number field.However, most of the existing researches focus on integers and the studied data are mainly one-dimensional data.There are few researches on secure multiparty computation of multi-dimensional data in the rational number field, but they can’t be generalized.Based on the fractional representation of rational numbers, the new encoding schemes about rational numbers and rational number vectors were proposed, which could encode multi-dimensional data in the rational number field and provided new solutions for other SMC problems in the rational number field.Based on the encoding scheme and one-way hash function, some protocols were designed for equality problems and set problems in the rational number field.These protocols used basic arithmetic operation and hash operation to guarantee efficiency than existing related protocols.And these protocols didn’t limit the range of research data and they were more widely applicable.It proves that these protocols are secure in the semi-honest model using simulation paradigm, and demonstrates the efficiency and the applicability of these protocols by theoretical analysis and experiment.A practical example was also given to illustrate that approaches are more versatile, and they could also be directly used to solve some secure multiparty computational geometry problems in the rational number field.