Fast threshold ECDSA with honest majority

ECDSA is a widely adopted digital signature standard. A number of threshold protocols for ECDSA have been developed that let a set of parties jointly generate the secret signing key and compute signatures, without ever revealing the signing key. Threshold protocols for ECDSA have seen recent interest, in particular due to the need for additional security in cryptocurrency wallets where leakage of the signing key is equivalent to an immediate loss of money. We propose a threshold ECDSA protocol secure against an active adversary in the honest majority model with abort. Our protocol is efficient in terms of both computation and bandwidth usage, and it allows the parties to pre-process parts of the signature, such that once the message to sign becomes known, they can compute a secret sharing of the signature very efficiently, using only local operations. We also show how to obtain guaranteed output delivery (and hence also fairness) in the online phase at the cost of some additional pre-processing work, i.e., such that it either aborts during the pre-processing phase, in which case nothing is revealed, or the signature is guaranteed to be delivered to all honest parties online.

Majority Vote in Social Networks: Make Random Friends or Be Stubborn to Overpower Elites

Consider a graph G, representing a social network. Assume that initially each node is colored either black or white, which corresponds to a positive or negative opinion regarding a consumer product or a technological innovation. In the majority model, in each round all nodes simultaneously update their color to the most frequent color among their connections. Experiments on the graph data from the real world social networks (SNs) suggest that if all nodes in an extremely small set of high-degree nodes, often referred to as the elites, agree on a color, that color becomes the dominant color at the end of the process. We propose two countermeasures that can be adopted by individual nodes relatively easily and guarantee that the elites will not have this disproportionate power to engineer the dominant output color. The first countermeasure essentially requires each node to make some new connections at random while the second one demands the nodes to be more reluctant towards changing their color (opinion). We verify their effectiveness and correctness both theoretically and experimentally. We also investigate the majority model and a variant of it when the initial coloring is random on the real world SNs and several random graph models. In particular, our results on the Erdős-Rényi, and regular random graphs confirm or support several theoretical findings or conjectures by the prior work regarding the threshold behavior of the process. Finally, we provide theoretical and experimental evidence for the existence of a poly-logarithmic bound on the expected stabilization time of the majority model.

OPINION DYNAMICS IN POPULATIONS WITH IMPLICIT COMMUNITY STRUCTURE

Web encounter facilitate contacts between people from different communities outside space and time. Implicit Community Structure is exhibited because of highly connected links within community and sparse encounters between communities. Considering the imperceptible influence of encounter on opinions, Sznajd updating rules are used to mimic people's behaviors after encountering a stranger in another community. We introduce a model for opinion evolution, in which the interconnectivity between different communities is represented as encounter frequency, and leadership is introduced to control the strength of community's opinion guide. In this scenario, the effects of Implicit Community Structure of contact network on opinion evolution, for asymmetric and random initial distribution but with heterogeneous opinion guide, are investigated respectively. It is shown that large encounter frequency favors consensus of the whole populations and successful opinion spreading, which is qualitatively agree with the results observed in Majority model defined on substrates with predefined community structure.