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.
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.
Secure multi-party multiplication is a special secure multi-party computation problem, which can be used by multi-party to share the multiplication result. Present protocols frequently using the secure two-party multiplication protocol which has high communication cost and large amount of data. Based on the homomorphic encryption technology, a serial secure multi-party multiplication protocol in the complex communication environment and a parallel secure multi-party multiplication protocol in the ideal communication environment are presented for this problem in the semi-honest model.At last, correctness and security of those protocols are analyzed. Compared with the present protocols, the analysis shows that the proposed protocols have better advantages in the communication cost and the execution efficiency.
Two-party computation allows two clients to jointly compute an arbitrary function of their inputs without revealing these inputs to each other. In this study, we adopt a server-aided model, in which a set of computing servers performs computation using the inputs of two clients. In the (k, n) threshold secret sharing scheme, input s is divided into n shares and can be recovered from k shares, where k is a threshold. Typically, the multiplication of shares increases the polynomial's degree from (k-1) to (2k-2), thus increasing the number of shares required from k to 2k-1. Because each server typically holds only one share, the number of servers required also increases to 2k-1. Therefore, a set of n servers can compute multiplication securely only if the adversary corrupts at most k-1 <; n/2 servers. In this study, we differentiate N, which is the number of required servers, and n, which is the parameter of the (k, n) threshold secret sharing scheme. We propose a method of multiplication by using only N ≥ k servers. This is implemented by sending two shares of the same input to each server. In a “normal” method, sending multiple shares to one server violates security because k shares can be leaked from k-1 servers. We overcome this by implementing a different functionality, where each share is first encrypted with a different random number (encrypted share) before being sent to a server. Instead of the “normal shares” of ab, our protocol computes the encrypted shares of ab using the encrypted shares of a and b. We show that the proposed method is secure against a non-colluding semi-honest adversary. Moreover, we implement our method in MATLAB and show its efficiency.
A secure multi-party computation problem deals with computing a function on any input, in a distributed network, ensuring that no more information is revealed to a player in the computation. New protocols are developed for the following interesting variation on a typical problem of secure multi-party computation: Given secrets shared among a group of players, compute the function value of basic computations, such as interpolation, addition, multiplication or inversion, in the exponent. The protocols can be proven robust and secure in standard computation models.
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.
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.