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.
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.
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.
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.
Consider several parties that do not trust each other, yet they wish to correctly compute some common function of their local inputs while keeping these inputs private. This problem is known as "Secure Multi-Party Computation", and was introduced by Andrew Yao in 1982. Secure multi-party computations have some real world examples like electronic auctions, electronic voting or fingerprinting. In this thesis we consider the case where there are only two parties involved. This is known as "Secure Two-Party Computation". If there is a trusted third party called Carol, then the problem is pretty straightforward. The participating parties could hand their inputs in Carol who can compute the common function correctly and could return the outputs to the corresponding parties. The goal is to achieve (almost) the same result when there is no trusted third party. Cryptographic protocols are designed in order to solve these kinds of problems. These protocols are analyzed within an appropriate model in which the behavior of parties is structured. The basic level is called the Semi-Honest Model where parties are assumed to follow the protocol specification, but later can derive additional information based on the messages which have been received so far. A more realistic model is the so-called Malicious Model. The common approach is to first analyze a protocol in the semi-honest model and then later extend it into the malicious model. Any cryptographic protocol for secure two-party computation must satisfy the following security requirements: correctness, privacy and fairness. It must guarantee the correctness of the result while preserving the privacy of the parties’ inputs, even if one of the parties is malicious and behaves arbitrarily throughout the protocol. It must also guarantee fairness. This roughly means that whenever a party aborts the protocol prematurely, he or she should not have any advantage over the other party in discovering the output. The main question for researchers is to construct new protocols that achieve the above mentioned goals for secure multi-party computation. Of course, such protocols must be secure in a given model, as well as be as efficient as possible. In 1986, Yao presented the first general protocol for secure two-party computation which was applicable only to the semi-honest model. He uses a tool called "Garbled Circuit". Yao’s protocol uses the underlying primitives ("Pseudorandom Generator" and "Oblivious Transfer") as blackboxes which lead to efficient results. After Yao’s work many variants and improvements have been proposed for the malicious model. In this thesis, we design several new protocols for secure two-party computation based on Yao’s garbled circuit. Before we present the details of our new designs, we first show several weaknesses, security flaws or problems with the existing protocols in the literature. We first work in the semi-honest model and then extend it into the malicious model by presenting new protocols. Finally we add fairness to our protocol. Oblivious transfer (OT) is a fundamental primitive in modern cryptography which is useful for implementing protocols for secure multi-party computation. We study several variants of oblivious transfer in this thesis. We present a new protocol for the so-called "Committed OT". This protocol is very efficient in the sense that it is quite good in comparison to the most efficient committed OT protocols in the literature. The abovementioned flaw with the use of OT can be fixed with our committed oblivious transfer protocol. Furthermore, it is more general than all previous protocols, and, therefore, it is of independent interest. We also deal with fairness in this thesis. For protocols based on garbled circuit, so far only Benny Pinkas has presented a protocol in the literature for achieving fairness. We show a subtle problem with this protocol where the privacy of the inputs of one party can be compromised. We also describe this problem in detail which is in fact related to the fairness, and finally propose a more efficient scheme that does achieve fairness.
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 scalar product protocol is an important fundamental protocol in secure multi-party computation. Serving as a basic building block for many other secure protocols, it is widely used in data mining, statistical analysis and scientific computation. Based on additive homomorphism public key cryptosystem, we develop a new secure scalar product protocol under semi-honest model with low communication complexity which is easy to implement and understanding. Furthermore, we firstly apply it to position relationship decision for privacy preserving space vectors.
In this paper, we propose memory- and round-efficient protocols for securely evaluating arithmetic primitives. We focus on secure two-party computation over the ring ℤ2k that achieves security against semi-honest adversaries and works in the pre-processing model. Our protocols rely on the unit vectorization technique introduced by Boyle et al. (TCC 2019). The unit vectorization technique provides online-optimal protocols for several fundamental operations in the pre-processing model. However, a relatively large memory cost for correlated randomness is required, which might become an obstacle in a large-scale application. In order to achieve both memory and communication efficiency, we propose a size reduction method that uses unit vectorization only for short-length inputs, and based on this, construct two-round protocols for equality test, detecting the most significant non-zero bit, detecting wrap-around, and less-than comparison. In addition, as applications of these results, we provide practically efficient protocols for integer division, integer square root, integer logarithm, and modular exponentiation.