In order to improve efficiency and solve the security vulnerabilities of the secure set computation protocols in practical applications, two secure two-party protocols for set membership and set intersection were proposed based on discrete logarithm problem and the polynomial representation of sets with which the set operation problem could be transformed into a polynomial evaluation problem. Firstly, a latest efficient secure set membership protocol was analyzed, and a security vulnerability of leaking the privacy of the participants by obtaining the element of participants on the brute attack was found. To overcome the security vulnerability, a new method was introduced by representing sets by polynomials and randomizing the polynomials, which could ensure the security of the participants without any leakage of interactions. Based on the discrete logarithm problem and the new method, a new secure set membership protocol was presented. The protocol could judge set-element membership with high-efficiency, and did not leak any other information about the participants besides the size of the set. Further, a secure set intersection protocol was showed according to the same technique. The security proofs of both protocols were given under the semi-honest model by using the probability polynomial time simulator, which indicated that the simulator views were computationally indistinguishable from the original protocols’ execution views. Finally, the detailed analysis about the protocols’ performance was presented, showing that both protocols were more efficient than other protocols since their communication complexity and computational complexity were smaller.
In order to improve efficiency and solve the security vulnerabilities of the secure set computation protocols in practical applications, two secure two-party protocols for set membership and set intersection were proposed based on discrete logarithm problem and the polynomial representation of sets with which the set operation problem could be transformed into a polynomial evaluation problem. Firstly, a latest efficient secure set membership protocol was analyzed, and a security vulnerability of leaking the privacy of the participants by obtaining the element of participants on the brute attack was found. To overcome the security vulnerability, a new method was introduced by representing sets by polynomials and randomizing the polynomials, which could ensure the security of the participants without any leakage of interactions. Based on the discrete logarithm problem and the new method, a new secure set membership protocol was presented. The protocol could judge set-element membership with high-efficiency, and did not leak any other information about the participants besides the size of the set. Further, a secure set intersection protocol was showed according to the same technique. The security proofs of both protocols were given under the semi-honest model by using the probability polynomial time simulator, which indicated that the simulator views were computationally indistinguishable from the original protocols’ execution views. Finally, the detailed analysis about the protocols’ performance was presented, showing that both protocols were more efficient than other protocols since their communication complexity and computational complexity were smaller.
A secure function evaluation protocol allows two parties to jointly compute a function f(x; y) of their inputs in a manner not leaking more information than necessary. A major result in this field is: "any function f that can be computed using polynomial resources can be computed securely using polynomial resources" (where `resources' refers to communication and computation). This result follows by a general transformation from any circuit for f to a secure protocol that evaluates f . Although the resources used by protocols resulting from this transformation are polynomial in the circuit size, they are much higher (in general) than those required for an insecure computation of f . We propose a new methodology for designing secure protocols, utilizing the communication complexity tree (or branching program) representation of f . We start with an efficient (insecure) protocol for f and transform it into a secure protocol. In other words, "any function f that can be computed using communication complexity c can be can be computed securely using communication complexity that is polynomial in c and a security parameter". We show several simple applications of this new methodology resulting in protocols efficient either in communication or in computation. In particular, we exemplify a protocol for the "millionaires problem ", where two participants want to compare their values but reveal no other information. Our protocol is more efficient than previously known ones in either communication or computation. 1.
Private set intersection (PSI) has important application value, however, current quantum PSI protocols are either unsuitable for multi-party scenarios or inefficient. Recently, Imran (arXiv: 2303.17196v3 , 2023) proposed two quantum secure multi-party greatest common divisor (GCD) protocols that can be used for PSI, but with the downside of information leakage and resource consumption. In this paper, we propose a novel quantum secure multi-party GCD protocol that has higher security and lower complexity. To hide privacy, each party randomly selects a coefficient within a range determined by his input integer, and with the assistance of a semi-honest third party TP, all parties secretly calculate the linear combination of their inputs under these coefficients. Once enough linear combinations are collected, TP calculates the GCD of these combinations, which is equal to the GCD of all input integers. To verify the honesty of participants, a quantum zero-knowledge proof sub-protocol is designed. Analysis shows that our GCD protocol is correct and has security against malicious attacks. Moreover, its complexity is polynomial level and lower than Imran’s. Furthermore, we demonstrate the scalability of our GCD protocol in private set operations, such as private set intersection, private set intersection cardinality, private multi-set intersection, etc.
Private set intersection (PSI) is a valuable technique with various practical applications, including secure matching of communication packets in the Internet of Things. However, most of the currently available two-party PSI protocols are based on the oblivious transfer (OT) protocol, which is computationally expensive and results in significant communication overhead. In this paper, we propose a new coding method to design a two-party PSI protocol under the semi-honest model. We analyze possible malicious attacks and then develop a PSI protocol under the malicious model using the Paillier cryptosystem, cut-and-choose, zero-knowledge proof, and other cryptographic tools. By adopting the real/ideal model paradigm, we prove the protocol’s security under the malicious model, which is more efficient compared to the existing related schemes.
In this paper we study the two fundamental functionalities oblivious polynomial evaluation in the exponent and set-intersection, and introduce a new technique for designing efficient secure protocols for these problems (and others). Our starting point is the [BGV11] technique (CRYPTO 2011) for verifiable delegation of polynomial evaluations, using algebraic PRFs. We use this tool, that is useful to achieve verifiability in the outsourced setting, in order to achieve privacy in the standard two-party setting. Our results imply new simple and efficient oblivious polynomial evaluation (OPE) protocols. We further show that our OPE protocols are readily used for secure set-intersection, implying much simpler protocols in the plain model. As a side result, we demonstrate the usefulness of algebraic PRFs for various search functionalities, such as keyword search and oblivious transfer with adaptive queries. Our protocols are secure under full simulation-based definitions in the presence of malicious adversaries.
We revisit the problem of constructing efficient secure two-party protocols for the problems of setintersection and set-union, focusing on the model of malicious parties. Our main results are constantround protocols that exhibit linear communication and a (practically) linear number of exponentiations with simulation based security. In the heart of these constructions is a technique based on a combination of a perfectly hiding commitment and an oblivious pseudorandom function evaluation protocol. Our protocols readily transform into protocols that are UC-secure, and we discuss how to perform these transformations. Keywords: Secure two-party computation, Simulation-based security, Set-intersection, Set-union, Oblivious pseudorandom function evaluation.
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.