Towards a Multi-Chain Future of Proof-of-Space

Proof-of-Space provides an intriguing alternative for consensus protocol of permissionless blockchains due to its recyclable nature and the potential to support multiple chains simultaneously. However, a direct shared proof of the same storage, which was adopted in the existing multi-chain schemes based on Proof-of-Space, could give rise to newborn attack on new chain launching. To fix this gap, we propose an innovative framework of single-chain Proof-of-Space and further present a novel multi-chain scheme which can resist newborn attack effectively by elaborately combining shared proof and chain-specific proof of storage. Moreover, we analyze the security of the multi-chain scheme and prove that it is incentive-compatible. This means that participants in such multi-chain system can achieve their greatest utility with our proposed strategy of storage resource partition.Comment: This paper is accepted by 15th EAI International Conference on Security and Privacy in Communication Networks (SecureComm 2019

Bipartite Expander Matching is in NC

A work-efficient deterministic NC algorithm is presented for finding a maximum matching in a bipartite expander graph with any expansion factor fi ? 1. This improves upon a recently presented deterministic NC maximum matching algorithm which is restricted to those bipartite expanders with large expansion factors (fi \Delta ffl ; ffl ? 0), and is not work-efficient [1]. Keywords: Bipartite Matching, Expander Graphs, NC, Network Flow. 1. Introduction Finding maximum cardinality matchings in bipartite expander graphs has many applications such as routing networks, sorting networks, permutation networks, and path selection. Note that by Hall's Theorem there is a perfect matching in a bipartite expander graph with expansion factor fi ? 1. Thus we are really finding one of the (potentially many) perfect matchings. Bipartite expander graphs are an important part of the design of routing networks such as concentrators and superconcentrators [2]. They are also used in self-routing permuta..