Secure and fair two-party computation

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

Efficiently Making Secure Two-Party Computation Fair

Secure two-party computation cannot be fair against malicious adversaries, unless a trusted third party (TTP) or a gradual-release type super-constant round protocol is employed. Existing optimistic fair two-party computation protocols with constant rounds are either too costly to arbitrate (e.g., the TTP may need to re-do almost the whole computation), or require the use of electronic payments. Furthermore, most of the existing solutions were proven secure and fair via a partial simulation, which, we show, may lead to insecurity overall. We propose a new framework for fair and secure two-party computation that can be applied on top of any secure two party computation protocol based on Yao's garbled circuits and zero-knowledge proofs. We show that our fairness overhead is minimal, compared to all known existing work. Furthermore, our protocol is fair even in terms of the work performed by Alice and Bob. We also prove our protocol is fair and secure simultaneously, through one simulator, which guarantees that our fairness extensions do not leak any private information. Lastly, we ensure that the TTP never learns the inputs or outputs of the computation. Therefore, even if the TTP becomes malicious and causes unfairness by colluding with one party, the security of the underlying protocol is still preserved

Formal Abstractions for Attested Execution Secure Processors

Realistic secure processors, including those built for academic and commercial purposes, commonly realize an “attested execution” abstraction. Despite being the de facto standard for modern secure processors, the “attested execution” abstraction has not received adequate formal treatment. We provide formal abstractions for “attested execution” secure processors and rigorously explore its expressive power. Our explorations show both the expected and the surprising. On one hand, we show that just like the common belief, attested execution is extremely powerful, and allows one to realize powerful cryptographic abstractions such as stateful obfuscation whose existence is otherwise impossible even when assuming virtual blackbox obfuscation and stateless hardware tokens. On the other hand, we show that surprisingly, realizing composable two-party computation with attested execution processors is not as straightforward as one might anticipate. Specifically, only when both parties are equipped with a secure processor can we realize composable two-party computation. If one of the parties does not have a secure processor, we show that composable two-party computation is impossible. In practice, however, it would be desirable to allow multiple legacy clients (without secure processors) to leverage a server’s secure processor to perform a multi-party computation task. We show how to introduce minimal additional setup assumptions to enable this. Finally, we show that fair multi-party computation for general functionalities is impossible if secure processors do not have trusted clocks. When secure processors have trusted clocks, we can realize fair two-party computation if both parties are equipped with a secure processor; but if only one party has a secure processor (with a trusted clock), then fairness is still impossible for general functionalities

Secure equality testing protocols in the two-party setting

Protocols for securely testing the equality of two encrypted integers are common building blocks for a number of proposals in the literature that aim for privacy preservation. Being used repeatedly in many cryptographic protocols, designing efficient equality testing protocols is important in terms of computation and communication overhead. In this work, we consider a scenario with two parties where party A has two integers encrypted using an additively homomorphic scheme and party B has the decryption key. Party A would like to obtain an encrypted bit that shows whether the integers are equal or not but nothing more. We propose three secure equality testing protocols, which are more efficient in terms of communication, computation or both compared to the existing work. To support our claims, we present experimental results, which show that our protocols achieve up to 99% computation-wise improvement compared to the state-of-the-art protocols in a fair experimental set-up

Secure Multiparty Computation with Partial Fairness

A protocol for computing a functionality is secure if an adversary in this protocol cannot cause more harm than in an ideal computation where parties give their inputs to a trusted party which returns the output of the functionality to all parties. In particular, in the ideal model such computation is fair -- all parties get the output. Cleve (STOC 1986) proved that, in general, fairness is not possible without an honest majority. To overcome this impossibility, Gordon and Katz (Eurocrypt 2010) suggested a relaxed definition -- 1/p-secure computation -- which guarantees partial fairness. For two parties, they construct 1/p-secure protocols for functionalities for which the size of either their domain or their range is polynomial (in the security parameter). Gordon and Katz ask whether their results can be extended to multiparty protocols. We study 1/p-secure protocols in the multiparty setting for general functionalities. Our main result is constructions of 1/p-secure protocols when the number of parties is constant provided that less than 2/3 of the parties are corrupt. Our protocols require that either (1) the functionality is deterministic and the size of the domain is polynomial (in the security parameter), or (2) the functionality can be randomized and the size of the range is polynomial. If the size of the domain is constant and the functionality is deterministic, then our protocol is efficient even when the number of parties is O(log log n) (where n is the security parameter). On the negative side, we show that when the number of parties is super-constant, 1/p-secure protocols are not possible when the size of the domain is polynomial

Weighted average problem revisited under hybrid and malicious model

It is getting more common for two or more parties to jointly compute some statistics, say for marketing, by combining information on their private databases without disclosing the private data to the others. The core problem is usually known as secure multi-party computation (SMC). A number of solutions have been proposed. However, almost all of them assume a semi-honest model which is unrealistic. On the other hand, protocols that work under the malicious model (all participating parties can be malicious) are usually complicated and expensive in terms of communication and computation. In this paper, we try to consider a more reasonable model, the hybrid security model, in which at least one party is semi-honest. We want to make sure that the malicious parties will not get the correct final result if they perform malicious behaviors. We propose a scheme to solve the two-party weighted average problem (WAP) under this hybrid security model. We also show that the scheme can be extended to work under the malicious model using any fair exchange scheme. We formally show that our schemes are secure. We also implemented the schemes and showed that our scheme under the hybrid security model is reasonably fast and efficient for practical use. © 2012 AICIT.published_or_final_versio

Legally Fair Contract Signing Without Keystones

International audienceIn two-party computation, achieving both fairness and guaranteed output delivery is well known to be impossible. Despite this limitation , many approaches provide solutions of practical interest by weakening somewhat the fairness requirement. Such approaches fall roughly in three categories: " gradual release " schemes assume that the aggrieved party can eventually reconstruct the missing information; " optimistic schemes " assume a trusted third party arbitrator that can restore fairness in case of litigation; and " concurrent " or " legally fair " schemes in which a breach of fairness is compensated by the aggrieved party having a digitally signed cheque from the other party (called the keystone). In this paper we describe and analyse a new contract signing paradigm that doesn't require keystones to achieve legal fairness, and give a concrete construction based on Schnorr signatures which is compatible with standard Schnorr signatures and provably secure

Instantaneous Decentralized Poker

We present efficient protocols for amortized secure multiparty computation with penalties and secure cash distribution, of which poker is a prime example. Our protocols have an initial phase where the parties interact with a cryptocurrency network, that then enables them to interact only among themselves over the course of playing many poker games in which money changes hands. The high efficiency of our protocols is achieved by harnessing the power of stateful contracts. Compared to the limited expressive power of Bitcoin scripts, stateful contracts enable richer forms of interaction between standard secure computation and a cryptocurrency. We formalize the stateful contract model and the security notions that our protocols accomplish, and provide proofs using the simulation paradigm. Moreover, we provide a reference implementation in Ethereum/Solidity for the stateful contracts that our protocols are based on. We also adopt our off-chain cash distribution protocols to the special case of stateful duplex micropayment channels, which are of independent interest. In comparison to Bitcoin based payment channels, our duplex channel implementation is more efficient and has additional features

A Rational Approach to Cryptographic Protocols

This work initiates an analysis of several cryptographic protocols from a rational point of view using a game-theoretical approach, which allows us to represent not only the protocols but also possible misbehaviours of parties. Concretely, several concepts of two-person games and of two-party cryptographic protocols are here combined in order to model the latters as the formers. One of the main advantages of analysing a cryptographic protocol in the game-theory setting is the possibility of describing improved and stronger cryptographic solutions because possible adversarial behaviours may be taken into account directly. With those tools, protocols can be studied in a malicious model in order to find equilibrium conditions that make possible to protect honest parties against all possible strategies of adversaries