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 .
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 .
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.
Abstract. We show how two existing paradigms for two-party secure function evaluation (SFE) in the semi-honest model can be combined securely and efficiently – those based on additively homomorphic encryption (HE) with those based on garbled circuits (GC) and vice versa. Additionally, we propose new GC constructions for addition, subtraction, multiplication, and comparison functions. Our circuits are approximately two times smaller (in terms of garbled tables) than previous constructions. This implies corresponding computation and communication improvements in SFE of functions using the above building blocks (including the protocols for combining HE and GC). Based on these results, we present efficient constant-round protocols for secure integer comparison, and the related problems of minimum selection and minimum distance, which are crucial building blocks of many cryptographic schemes such as privacy preserving biometric authentication (e.g., face recognition, fingerprint matching, etc).
Secure comparison is a fundamental problem in multiparty computation. There are two different parties, each holding an l-bit integer, denoted by a and b, respectively. The goal of secure comparison is to compute the order relationship between a and b, say (a>b)∈{0,1}, without revealing their inputs to any others. Since previous solutions based on homomorphic encryption need at least Ω(l) encryptions for each l-bit comparison, the total encryption time leads to a computational bottleneck for these protocols. This work presents a fast, semi-honest, secure comparison protocol based on the BFV encryption scheme. With its vector-like plaintext space, the number of required encryptions can be significantly reduced; actually, only six encryptions are needed for each comparison in our protocol. In other words, the proposed protocol can achieve the time complexity O˜(λ+l) for a given security parameter λ. As a result, 4096-bit integers can be securely compared within 12.08 ms, which is 280 times faster than the state-of-the-art homomorphic encryption-based secure comparison protocol. Furthermore, we can compare k pairs of l⋅k−1-bit integers with almost the same execution time as comparing l-bit integers and achieve higher throughput regardless of the compared integer size.
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 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 multi-party computation (MPC) allows a set of parties to compute a function jointly while keeping their inputs private. Compared with the MPC based on garbled circuits, some recent research results show that MPC based on secret sharing (SS) works at a very high speed. Moreover, SS-based MPC can be easily vectorized and achieve higher throughput. In SS-based MPC, however, we need many communication rounds for computing concrete protocols like equality check, less-than comparison, etc. This property is not suited for large-latency environments like the Internet (or WAN). In this paper, we construct semi-honest secure communication-efficient two-party protocols. The core technique is Beaver triple extension, which is a new tool for treating multi-fan-in gates, and we also show how to use it efficiently. We mainly focus on reducing the number of communication rounds, and our protocols also succeed in reducing the number of communication bits (in most cases). As an example, we propose a less-than comparison protocol (under practical parameters) with three communication rounds. This is less than a half compared with the previous work. Moreover, the number of communication bits is also 38.4% fewer. As a result, total online execution time is 56.1% shorter than the previous work adopting the same settings. Although the computation costs of our protocols are more expensive than those of previous work, we confirm via experiments that such a disadvantage has small effects on the whole online performance in the typical WAN environments.