General Constructions of Rational Secret Sharing with Expected Constant-Round Reconstruction

We present a general construction of a rational secret-sharing protocol that converts any rational secret-sharing protocol to a protocol with an expected constant-round reconstruction. Our construction can be applied to protocols for synchronous channels, and preserves a strict Nash equilibrium of the original protocol. Combining with an existing protocol, we obtain the first expected constant-round protocol that achieves a strict Nash equilibrium with the optimal coalition resilience \ceil{\frac{n}{2}}-1, where $n$ is the number of players. Our construction can be extended to a construction that preserves the \emph{immunity} to unexpectedly behaving players. Then, for any constant $m \geq 1$, we obtain an expected constant-round protocol that achieves a Nash equilibrium with the optimal coalition resilience \ceil{\frac{n}{2}}-m-1 in the presence of $m$ unexpectedly behaving players. The same protocol also achieves a strict Nash equilibrium with coalition resilience $1$. We show that our protocol with immunity achieves the optimal coalition resilience among constant-round protocols with immunity with respect to both Nash and strict Nash equilibria

08491 Abstracts Collection -- Theoretical Foundations of Practical Information Security

From 30.11. to 05.12.2008, the Dagstuhl Seminar 08491 ``Theoretical Foundations of Practical Information Security \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Resource-Efficient and Robust Distributed Computing

There has been a tremendous growth in the size of distributed systems in the past three decades. Today, distributed systems, such as the Internet, have become so large that they require highly scalable algorithms; algorithms that have asymptotically-small communication, computation, and latency costs with respect to the network size. Moreover, systems with thousands or even millions of parties distributed throughout the world is likely in danger of faults from untrusted parties. In this dissertation, we study scalable and secure distributed algorithms that can tolerate faults from untrusted parties. Throughout this work, we balance two important and often conflicting characteristics of distributed protocols: security and efficiency. Our first result is a protocol that solves the MPC problem in polylogarithmic communication and computation cost and is secure against an adversary than can corrupt a third of the parties. We adapted our synchronous MPC protocol to the asynchronous setting when the fraction of the corrupted parties are less than 1/8. Next, we presented a scalable protocol that solves the secret sharing problem between rational parties in polylogarithmic communication and computation cost. Furthermore, we presented a protocol that can solve the interactive communication problem over a noisy channel when the noise rate in unknown. In this problem, we have focused on the cost of the protocol in the resource-competitive analysis model. Unlike classic models, resource-competitive models consider the cost that the adversary must pay to succeed in corrupting the protocol

Round-Preserving Parallel Composition of Probabilistic-Termination Protocols

An important benchmark for multi-party computation protocols (MPC) is their round complexity. For several important MPC tasks, (tight) lower bounds on the round complexity are known. However, for some of these tasks, such as broadcast, the lower bounds can be circumvented when the termination round of every party is not a priori known, and simultaneous termination is not guaranteed. Protocols with this property are called probabilistic-termination (PT) protocols. Running PT protocols in parallel affects the round complexity of the resulting protocol in somewhat unexpected ways. For instance, an execution of m protocols with constant expected round complexity might take O(log m) rounds to complete. In a seminal work, Ben-Or and El-Yaniv (Distributed Computing \u2703) developed a technique for parallel execution of arbitrarily many broadcast protocols, while preserving expected round complexity. More recently, Cohen et al. (CRYPTO \u2716) devised a framework for universal composition of PT protocols, and provided the first composable parallel-broadcast protocol with a simulation-based proof. These constructions crucially rely on the fact that broadcast is ``privacy free,\u27\u27 and do not generalize to arbitrary protocols in a straightforward way. This raises the question of whether it is possible to execute arbitrary PT protocols in parallel, without increasing the round complexity. In this paper we tackle this question and provide both feasibility and infeasibility results. We construct a round-preserving protocol compiler, secure against a dishonest minority of actively corrupted parties, that compiles arbitrary protocols into a protocol realizing their parallel composition, while having a black-box access to the underlying protocols. Furthermore, we prove that the same cannot be achieved, using known techniques, given only black-box access to the functionalities realized by the protocols, unless merely security against semi-honest corruptions is required, for which case we provide a protocol

Algebraic Techniques for Low Communication Secure Protocols

Internet communication is often encrypted with the aid of mathematical problems that are hard to solve. Another method to secure electronic communication is the use of a digital lock of which the digital key must be exchanged first. PhD student Robbert de Haan (CWI) researched models for a guaranteed safe communication between two people without the exchange of a digital key and without assumptions concerning the practical difficulty of solving certain mathematical problems. In ancient times Julius Caesar used secret codes to make his messages illegible for spies. He upped every letter of the alphabet with three positions: A became D, Z became C, and so on. Usually, cryptographers research secure communication between two people through one channel that can be monitored by malevolent people. De Haan studied the use of multiple channels. A minority of these channels may be in the hands of adversaries that can intercept, replace or block the message. He proved the most efficient way to securely communicate along these channels and thus solved a fundamental cryptography problem that was introduced almost 20 years ago by Dole, Dwork, Naor and Yung

Novel Secret Sharing and Commitment Schemes for Cryptographic Applications

In the second chapter, the notion of a social secret sharing (SSS) scheme is introduced in which shares are allocated based on a player's reputation and the way she interacts with other parties. In other words, this scheme renews shares at each cycle without changing the secret, and it allows the trusted parties to gain more authority. Our motivation is that, in real-world applications, components of a secure scheme have different levels of importance (i.e., the number of shares a player has) and reputation (i.e., cooperation with other parties). Therefore, a good construction should balance these two factors accordingly. In the third chapter, a novel socio-rational secret sharing (SRS) scheme is introduced in which rational foresighted players have long-term interactions in a social context, i.e., players run secret sharing while founding and sustaining a public trust network. To motivate this, consider a repeated secret sharing game such as sealed-bid auctions. If we assume each party has a reputation value, we can then penalize (or reward) the players who are selfish (or unselfish) from game to game. This social reinforcement stimulates the players to be cooperative in the secret recovery phase. Unlike the existing protocols in the literature, the proposed solution is stable and it only has a single reconstruction round. In the fourth chapter, a comprehensive analysis of the existing dynamic secret sharing (DSS) schemes is first provided. In a threshold scheme, the sensitivity of the secret and the number of players may fluctuate due to various reasons. Moreover, a common problem with almost all secret sharing schemes is that they are ``one-time'', meaning that the secret and shares are known to everyone after secret recovery. We therefore provide new techniques where the threshold and/or the secret can be changed multiple times to arbitrary values after the initialization. In addition, we introduce a new application of dynamic threshold schemes, named sequential secret sharing (SQS), in which several secrets with increasing thresholds are shared among the players who have different levels of authority. In the fifth chapter, a cryptographic primitive, named multicomponent commitment scheme (MCS) is proposed where we have multiple committers and verifiers. This new scheme is used to construct different sealed-bid auction protocols (SAP) where the auction outcomes are defined without revealing the losing bids. The main reason for constructing secure auctions is the fact that the values of the losing bids can be exploited in future auctions and negotiations if they are not kept private. In our auctioneer-free protocols, bidders first commit to their bids before the auction starts. They then apply a decreasing price mechanism to define the winner and selling price in an unconditionally secure setting