An Efficient Rational Secret Sharing Scheme Based on the Chinese Remainder Theorem (Revised Version)

The design of rational cryptographic protocols is a recently created research area at the intersection of cryptography and game theory. At TCC\u2710, Fuchsbauer \emph{et al.} introduced two equilibrium notions (computational version of strict Nash equilibrium and stability with respect to trembles) offering a computational relaxation of traditional game theory equilibria. Using trapdoor permutations, they constructed a rational $t$-out-of $n$ sharing technique satisfying these new security models. Their construction only requires standard communication networks but the share bitsize is $2 n |s| + O(k)$ for security against a single deviation and raises to $(n-t+1)\cdot (2n|s|+O(k))$ to achieve $(t-1)$-resilience where $k$ is a security parameter. In this paper, we propose a new protocol for rational $t$-out-of $n$ secret sharing scheme based on the Chinese reminder theorem. Under some computational assumptions related to the discrete logarithm problem and RSA, this construction leads to a $(t-1)$-resilient computational strict Nash equilibrium that is stable with respect to trembles with share bitsize $O(k)$. Our protocol does not rely on simultaneous channel. Instead, it only requires synchronous broadcast channel and synchronous pairwise private channels

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