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Threshold cryptography is essential for many blockchain protocols. For example, many protocols rely on threshold common coin to implement asynchronous consensus, leader elections, and provide support for randomized applications. Similarly,…

The blocks in the Bitcoin blockchain record the amount of work W that went into creating them through proofs of work. When honest parties control a majority of the work, consensus is achieved by picking the chain with the highest recorded…

The security of blockchain systems depends on the distribution of mining power across participants. If sufficient mining power is controlled by one entity, they can force their own version of events. This may allow them to double spend…

Bitcoin provides freshness properties by forming a blockchain where each block is associated with its timestamp and the previous block. Due to these properties, the Bitcoin protocol is being used as a decentralized, trusted, and secure…

Cryptocurrencies have gained popularity due to their transparency, security, and accessibility compared to traditional financial systems, with Bitcoin, introduced in 2009, leading the market. Bitcoin's security relies on blockchain…

In the white book of Bitcion, Satoshi Nakamoto described a bitcoin system that can realize point-to-point online payment without a third-party organization. After supporting this magical application scenario and subverting the traditional…

Bitcoin is a electronic payment system where payment transactions are verified and stored in a data structure called the blockchain. Bitcoin miners work individually to solve a computationally intensive problem, and with each solution a…

Longest-chain blockchain protocols, such as Bitcoin, guarantee liveness even when the number of actively participating users is variable, i.e., they are adaptive. However, they are not safe under network partitions, i.e., they do not…

We study financial transaction confirmation finality in Bitcoin as a function of transaction amount and user risk tolerance. A transaction is recorded in a block on a blockchain. However, a transaction may be revoked due to a fork in the…

It has been known for some time that the Nakamoto consensus as implemented in the Bitcoin protocol is not totally aligned with the individual interests of the participants. More precisely, it has been shown that block withholding mining…

Bitcoin is a peer-to-peer cryptographic currency system. Since its introduction in 2008, Bitcoin has gained noticeable popularity, mostly due to its following properties: (1) the transaction fees are very low, and (2) it is not controlled…

Motivated by the great success and adoption of Bitcoin, a number of cryptocurrencies such as Litecoin, Dogecoin, and Ethereum are becoming increasingly popular. Although existing blockchain-based cryptocurrency schemes can ensure reasonable…

Blokchain is a promising technology to enable distributed and reliable data sharing at the network edge. The high security in blockchain is undoubtedly a critical factor for the network to handle important data item. On the other hand,…

The application of Bitcoin enables people to understand blockchain technology gradually. Bitcoin is a decentralized currency that does not rely on third-party credit institutions, and the core of Bitcoin's underlying technology is…

Bitcoin is a decentralised digital currency that relies on cryptography rather than trusted third parties such as central banks for its security. Underpinning the operation of the currency is a peer-to-peer (P2P) network that facilitates…

Nakamoto invented the longest chain protocol, and claimed its security by analyzing the private double-spend attack, a race between the adversary and the honest nodes to grow a longer chain. But is it the worst attack? We answer the…

While showing great promise, Bitcoin requires users to wait tens of minutes for transactions to commit, and even then, offering only probabilistic guarantees. This paper introduces ByzCoin, a novel Byzantine consensus protocol that…

Bitcoin was recently introduced as a peer-to-peer electronic currency in order to facilitate transactions outside the traditional financial system. The core of Bitcoin, the Blockchain, is the history of the transactions in the system…

The digital currency Bitcoin has had remarkable growth since it was first proposed in 2008. Its distributed nature allows currency transactions without a central authority by using cryptographic methods and a data structure called the…

Bitcoin has emerged in 2008, and after decades of development, it has become the largest trading currency by far. The core of the blockchain is to ensure the anonymity of user transactions. As more and more analysis algorithms for…