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The Nakamoto longest chain protocol is remarkably simple and has been proven to provide security against any adversary with less than 50% of the total hashing power. Proof-of-stake (PoS) protocols are an energy efficient alternative; however existing protocols adopting Nakamotos longest chain design achieve provable security only by allowing long-term predictability (which have serious security implications). In this paper, we prove that a natural longest chain PoS protocol with similar predictability as Nakamotos PoW protocol can achieve security against any adversary with less than 1/(1+e) fraction of the total stake. Moreover we propose a new family of longest chain PoS protocols that achieve security against a 50% adversary, while only requiring short-term predictability. Our proofs present a new approach to analyzing the formal security of blockchains, based on a notion of adversary-proof convergence.
Off-chain protocols constitute one of the most promising approaches to solve the inherent scalability issue of blockchain technologies. The core idea is to let parties transact on-chain only once to establish a channel between them, leveraging later
Fault-tolerant distributed systems move the trust in a single party to a majority of parties participating in the protocol. This makes blockchain based crypto-currencies possible: they allow parties to agree on a total order of transactions without a
The blockchain data structure maintained via the longest-chain rule---popularized by Bitcoin---is a powerful algorithmic tool for consensus algorithms. Such algorithms achieve consistency for blocks in the chain as a function of their depth from the
Proof-of-stake (PoS) is a promising approach for designing efficient blockchains, where block proposers are randomly chosen with probability proportional to their stake. A primary concern with PoS systems is the rich getting richer phenomenon, whereb
We propose a method for engineering security protocols that are aware of timing aspects. We study a simplified version of the well-known Needham Schroeder protocol and the complete Yahalom protocol, where timing information allows the study of differ