Secure multi-party computation of Chebyshev distance represents a crucial method for confidential distance measurement, holding significant theoretical and practical implications. Especially within electronic archival management systems, secure computation of Chebyshev distance is employed for similarity measurement, classification, and clustering of sensitive archival information, thereby enhancing the security of sensitive archival queries and sharing. This paper proposes a secure protocol for computing Chebyshev distance under a semi-honest model, leveraging the additive homomorphic properties of the NTRU cryptosystem and a vector encoding method. This protocol transforms the confidential computation of Chebyshev distance into the inner product of confidential computation vectors, as demonstrated through the model paradigm validating its security under the semi-honest model. Addressing potential malicious participant scenarios, a secure protocol for computing Chebyshev distance under a malicious model is introduced, utilizing cryptographic tools such as digital commitments and mutual decryption methods. The security of this protocol under the malicious model is affirmed using the real/ideal model paradigm. Theoretical analysis and experimental simulations demonstrate the efficiency and practical applicability of the proposed schemes.
Secure multi-party computation of Chebyshev distance represents a crucial method for confidential distance measurement, holding significant theoretical and practical implications. Especially within electronic archival management systems, secure computation of Chebyshev distance is employed for similarity measurement, classification, and clustering of sensitive archival information, thereby enhancing the security of sensitive archival queries and sharing. This paper proposes a secure protocol for computing Chebyshev distance under a semi-honest model, leveraging the additive homomorphic properties of the NTRU cryptosystem and a vector encoding method. This protocol transforms the confidential computation of Chebyshev distance into the inner product of confidential computation vectors, as demonstrated through the model paradigm validating its security under the semi-honest model. Addressing potential malicious participant scenarios, a secure protocol for computing Chebyshev distance under a malicious model is introduced, utilizing cryptographic tools such as digital commitments and mutual decryption methods. The security of this protocol under the malicious model is affirmed using the real/ideal model paradigm. Theoretical analysis and experimental simulations demonstrate the efficiency and practical applicability of the proposed schemes.
Manhattan distance is mainly used to calculate the total absolute wheelbase of two points in the standard coordinate system. The secure computation of Manhattan distance is a new geometric problem of secure multi-party computation. At present, the existing research secure computing protocols for Manhattan distance cannot resist the attack of malicious participants. In the real scene, the existence of malicious participants makes it necessary to study a solution that can resist malicious attacks. This paper first analyzes malicious attacks of the semi-honest model protocol of computing Manhattan distance and then designs an advanced protocol under the malicious model by using the Goldwasser–Micali encryption system and Paillier encryption algorithm, and utilizing some cryptographic tools such as the cut-choose method and zero-knowledge proof. Finally, the real/ideal model paradigm method is used to prove the security of the malicious model protocol. Compared with existing protocols, the experimental simulation shows that the proposed protocol can resist malicious participant attacks while maintaining high efficiency. It has practical value.
Bringer et al. proposed two cryptographic protocols for the computation of Hamming distance. Their first scheme uses oblivious transfer and provides security in the semi-honest model. The other scheme uses committed oblivious transfer and is claimed to provide full security in the malicious case. The proposed protocols have direct implications to biometric authentication schemes between a prover and a verifier where the verifier has biometric data of the users in plain form. In this paper, we show that their protocol is not actually fully secure against malicious adversaries. More precisely, our attack breaks the soundness property of their protocol where a malicious user can compute a Hamming distance, which is different from the actual value. For biometric authentication systems, this attack allows a malicious adversary to pass the authentication without knowledge of the honest user's input with at most O(n) complexity instead of O(2n), where n is the input length. We propose an enhanced version of their protocol where this attack is eliminated. The security of our modified protocol is proven using the simulation-based paradigm. Furthermore, as for efficiency concerns, the modified protocol utilizes verifiable oblivious transfer, which does not require the commitments to outputs, which improves its efficiency significantly.
Secure two-party computation is always the focus in the international cryptographic community, and establishing a secure two-party computation for determining the equality of data is a fundamental and crucial task within this field.There is still substantial room for improvement in terms of efficiency and security, so it is worth exploring further.In this paper, two theorems are proved from camera imaging of straight lines on a flat surface and the equality judgement of data between the two-party is innovatively converted into judging whether the inner products of the vectors owned by the two parties are zeroes.Based on the specific property of these vectors, a security protocol is established to determine whether those inner products are zeroes, which realizes the protocol scheme of judging the data equality of two-party under the semi-honest model and analyses its security theoretically.The scheme needs key stream for dynamic data encoding, since only basic arithmetic operations (integer addition, subtraction and multiplication) and a final modulus operation are required after encode without high-order and decimal operations, and the communication complexity is O(1), which greatly improves the efficiency.This scheme may not fit for malicious model, we could use the existing agreements of malicious model to determine whether those inner products are zeroes, by the conversion in this paper we also could complete the equality judgement.
With the rapid development of the Internet and information technology, the problem of zero-trust networks has become increasingly prominent, and secure multi-party computation has become a research hotspot to solve the problem of zero-trust networks. The secure judgment of point and line relationship is an important research branch of secure computing set geometry. However, most of resent secure computing protocols of point and line relationship are designed in the semi-honest model and cannot resist malicious attacks. Therefore, this paper analyzes the possible malicious adversary behaviors and designs a secure protocol in the malicious model. In this paper, the Paillier cryptosystem, zero- knowledge proof, and cut-choose method are used to resist malicious behavior, and the real/ideal model paradigm method is used to prove the security of the protocol. Compared with the existing solutions, the malicious model protocol is still efficient and widely used in real applications.
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.