Secure multi-party computation protocol allows a set of n-parties to evaluate a joint function of their inputs such that the function is calculated correctly and furthermore no information about their inputs is revealed by the output of the function.Based on the determinate-commutative cryptosystem and under the semi-honest model hypothesis,secure two-party computation protocols for determine whether an element is belong to a certain finite set,whether two finite sets are equal,and whether two equivalence relations are equal are considered.A mathematic method,relates to kernel,image and kernel-classes of mapping,to determine whether two mappings are equal is introduced.Furthermore,two-party computation protocol for determine whether two mappings are equal is given.Correctness,security,and efficiency of our protocols are analyzed.
Secure multi-party computation protocol allows a set of n-parties to evaluate a joint function of their inputs such that the function is calculated correctly and furthermore no information about their inputs is revealed by the output of the function.Based on the determinate-commutative cryptosystem and under the semi-honest model hypothesis,secure two-party computation protocols for determine whether an element is belong to a certain finite set,whether two finite sets are equal,and whether two equivalence relations are equal are considered.A mathematic method,relates to kernel,image and kernel-classes of mapping,to determine whether two mappings are equal is introduced.Furthermore,two-party computation protocol for determine whether two mappings are equal is given.Correctness,security,and efficiency of our protocols are analyzed.
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.
The goal of secure two-party computation is to enable two parties to cooperatively evaluate a function that takes private data from both parties as input without exposing any of the private data. At the end of the computation, the participants learn nothing more than the output of the function. The two-party secure computation systems have three properties: (1) the application involves inputs from two independent parties; (2) each party wants to keep its own data secret; and (3) the participants agree to reveal the output of the computation. That is, the result itself does not imply too much information about either party's private input. Informally, the security requirements are that nothing is learned from the protocol other than the output (privacy), and that the output is distributed according to the prescribed functionality (correctness). The threat models in the two-party computation assume the presence of three different types of adversaries: 1) Semi honest, 2) Malicious and 3) Covert.
Abstract Secure multi-party computation(SMPC) is an important research area in cryptography with many application scenarios, but there are still many problems to be solved. Aiming at security and fairness issues in SMPC, we consider that semi-honest participants are able to execute the protocol according to the specification, but there would be some additional malicious operations such as collusion and refuse to exchange information in the process of information interaction, which leads to deviations in the security and fairness of the protocol. To solve the above problems, we combine information entropy and mutual information to propose an n-round information exchange protocol, in which each participant broadcasts a relevant information value in each round without revealing additional information. The uncertainty of the correct result value is fuzzed by the interactive information in each round, and each participant cannot determine the correct result value until the end of the protocol, which effectively prevents malicious behavior and ensures the correct execution of the protocol. Security analysis and fairness analysis show that under the semi-honest model, our protocol guarantees the security and relative fairness of the output obtained by the participants after completing the protocol.
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.
Abstract. The recently proposed universally composable (UC) security framework, for analyzing security of cryptographic protocols, provides very strong security guarantees. In particular, a protocol proven secure in this framework is guaranteed to maintain its security even when deployed in arbitrary multi-party, multi-protocol, multi-execution environments. Protocols for securely carrying out essentially any cryptographic task in a universally composable way exist, both in the case of an honest majority (in the plain model, i.e., without set-up assumptions) and in the case of no honest majority (in the common reference string model). However, in the plain model, little was known for the case of no honest majority and, in particular, for the important special case of two-party protocols. We study the feasibility of universally composable two-party function evaluation in the plain model. Our results show that very few functions can be computed in this model so as to provide the UC security guarantees. Specifically, for the case of deterministic functions, we provide a full characterization of the functions computable in this model. (Essentially, these are the functions that depend on at most one of the parties’ inputs, and furthermore are “efficiently invertible ” in a sense defined within.) For the case of probabilistic functions, we show that the only functions computable in this model are those where one of the parties can essentially uniquely determine the joint output. 1
In this paper, the problem of secure two-party multiplication of shared secrets is considered, and it is one of problems of secure multi-party computation, where the policy for the shared secrets is based on polynomial interpolation. Firstly, a secure two-party protocol for polynomial multiplication is presented. Secondly, based on the first protocol, a protocol for secure two-party multiplication of shared secrets for semi-honest model is proposed, which is employed to multiply two shared secrets without revealing the private information of two parties. Furthermore, based on the definition of secure two-party computation and Composition Theorem, the proofs of security and analysis of the correctness and the complexity of our two protocols are given.