Based on the verifiable encryption and zero-knowledge proof protocols of Jarecki and Shmatikov and Pedersen’s verifiable threshold secret sharing scheme, this paper proposes a new full fair secure two-party computation protocols. For getting full fair, the new protocol employs a group of third-party servers. We prove that when more than two-thirds of the third-party servers are honest, the new protocol guarantees that two parties can get their correct outputs full fairly. In the new protocol, the computation is performed in the form of garbled circuit, and only two added interaction rounds are needed for full fairness.
Based on the verifiable encryption and zero-knowledge proof protocols of Jarecki and Shmatikov and Pedersen’s verifiable threshold secret sharing scheme, this paper proposes a new full fair secure two-party computation protocols. For getting full fair, the new protocol employs a group of third-party servers. We prove that when more than two-thirds of the third-party servers are honest, the new protocol guarantees that two parties can get their correct outputs full fairly. In the new protocol, the computation is performed in the form of garbled circuit, and only two added interaction rounds are needed for full fairness.
Yao first introduced a constant-round protocol for secure two-party computation (2PC) withstanding semi-honest adversaries by using a tool called "garbled circuit". Later, many protocols based on garbled circuit approach have been presented, most of which discussed malicious adversaries and efficiency about 2PC. However, there only have a few protocols dealing with the fundamental property of fairness for Yao's garbled circuit approach, in which one involved a trusted third party and the others are very expensive. In the paper, we propose' an efficient Yao's garbled circuit protocol for fair secure 2PC based on ElGamal encryption, Pedersen commitment, Cachin et al.'s verifiable oblivious transfer and Ou-Ruan et al.'s gradual release homomorphic timed commitment. The protocol achieves two advantages: it doesn't need the third party and it is more efficient than other fair secure Yao's protocols.
Abstract. We present an efficient and fair protocol for secure two-party computation in the optimistic model, where a partially trusted third party T is available, but not involved in normal protocol executions. T is needed only if communication is disrupted or if one of the two parties misbehaves. The protocol guarantees that although one party may terminate the protocol at any time, the computation remains fair for the other party. Communication is over an asynchronous network. All our protocols are based on efficient proofs of knowledge and involve no general zero-knowledge tools. As intermediate steps we describe efficient verifiable oblivious transfer and verifiable secure function evaluation protocols, whose security is proved under the decisional Diffie-Hellman assumption. 1
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 fairness of multi-party computation has been investigated for long time. Classic results demonstrate that fair exchange can be achieved by utilizing cryptographic tools, as most of them are based on garbled circuits. For the secret-sharing schemes, such as SPDZ, it may incur significant overhead to simply apply a fair escrow scheme, since it encrypts all the shares of delivered results. To address this issue, we design a twolevel secret-sharing mechanism. The escrow encryption is only for the first level of sharing and performed in preprocessing. The second level of sharing is used for computation and always handled by plaintexts, such that the online phase is still efficient. Our work also employs a semi-trusted third party (TTP) which provide optimistic escrow for output delivery. The verification and delivery procedures prevent the malicious parties from corrupting the outcome or aborting, when there is at least one honest party. Furthermore, the TTP has no knowledge of output, so even if he is malicious and colluding, we only lose fairness. The escrow decryption is needed only when misconduct is detected for opening the first-level shares.
Cramer, Damgard, and Nielsen [CDN01] show how to construct an efficient secure multiparty computation scheme using a threshold homomorphic encryption scheme that has four properties i) a honest-verifier zero-knowledge proof of knowledge of encrypted values, ii) proving multiplications correct iii) threshold decryption and iv) trusted shared key setup. Naor and Nissim [NN01a] show how to construct secure multi-party protocols for a function f whose communication is proportional to the communication required to evaluate f without security, albeit at the cost of computation that might be exponential in the description of f . Gentry [Gen09a] shows how to combine both ideas with fully homomorphic encryption in order to construct secure multi-party protocol that allows evaluation of a function f using communication that is independent of the circuit description of f and computation that is polynomial in | f |. This paper addresses the major drawback’s of Gentry’s approach: we eliminate the use of non-black box methods that are inherent in Naor and Nissim’s compiler. To do this we show how to modify the fully homomorphic encryption construction of van Dijk et al. [vDGHV10] to be threshold fully homomorphic encryption schemes. We directly construct (information theoretically) secure protocols for sharing the secret key for our threshold scheme (thereby removing the setup assumptions) and for jointly decrypting a bit. All of these constructions are constant round and we thoroughly analyze their complexity; they address requirements (iii) and (iv). The fact that the encryption scheme is fully homomorphic addresses requirement (ii). To address the need for an honest-verifier zero-knowledge proof of knowledge of encrypted values, we instead argue that a weaker solution suffices. We provide a 2-round blackbox protocol that allows us to prove knowledge of encrypted bits. Our protocol is not zeroknowledge, but it provably does not release any information about the bit being discussed, and this is sufficient to prove the correctness of a simulation in a method similar to Cramer et al. Altogether, we construct the first black-box secure multi-party computation protocol that allows evaluation of a function f using communication that is independent of the circuit description of f .
The techniques of verifiable secret sharing and verifiable encryption are used in the construction of two party fair exchange protocols.The novelty of the construction lies in the introduction of the distributed semi-trusted third party.Compared to the previous fair exchange protocols with a single semi-trusted third party,the newly constructed fair exchange protocol can further guarantee the security and fairness of the transaction due to the existence of the distributed semi-trusted third party.