We study the problem of privacy-preserving planarity testing of distributed graphs. The setting involves several parties that hold private graphs on the same set of vertices, and an external mediator that helps with performing the computations. Their goal is to test whether the union of their private graphs is planar, but in doing so each party wishes to deny from his peers any information on his own private edge set beyond what is implied by the final output of the computation. We present a privacy-preserving protocol for that purpose which is based on the Hanani-Tutte Theorem. That theorem enables translating the planarity question into the question of whether a specific system of linear equations over the field F2 is solvable. Our protocol uses a diverse cryptographic toolkit which includes techniques such as homomorphic encryption, oblivious Gaussian elimination, and private set intersection. This is the first time that a solution to this problem is presented.
Battleships is a well known traditional board game for two players which dates from World War I. Though, the game has several digital version implementations, they are affected by similar major drawbacks such as fairness and a trust model that relies on third party. In this paper, we demonstrate how to implement a fair, resistant to denial-ofservice, where the honest winner earns the deposit money immediately. The game is built on a permissionless Blockchain that supports Turing complete smart-contract computation. Furthermore, we provide a full working game implementation 1 of this proposition over the Ethereum Blockchain.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.