Blockchains the previous blocks being modified in a

Blockchains today are mostly recognized in the context of cryptocurrencies but serve some other purposes too. One of the earlier designs for blockchains was from a pseudonym called Satoshi Nakamoto who created the Bitcoin cryptocurrencies and solved some problems existing at this time (for example double-spend problem). The fundamental concept of constrcuting such a data structure is based on blocks and hash functions. Blocks is consist of block header and a list of transactions. These blocks are linked sequentially and each block contains the hash value from the previous block. This prevents the previous blocks being modified in a later time and ensures therefore some integrity. It is working because of the security aspects of hash functions which are the pre-image resistance, second pre-image resistance and collision resistance. The transactions can have many different meanings and usages, the most common one is it contains the information of a currency transfer from one account to another. Besides, a transaction also can be the certificate information for a single user cite{qin2017cecoin}. To prevent that malicious users can create transactions for other users there needs to be a mechanism such as signing so that other users can verify the transaction. This leads to the problem how these transactions can be included in a blockchain. The most common usage of blockchains is in a decentralized setting implemented in a peer-to-peer network.When a participant creates a transaction he needs to broadcast it to the network. A deterministic rule is needed to decide about the order of transactions and also to prevent problems such as double-spending. Every blockchain with a global state has a consensus in form of proof-of-work, proof-of-stake and Byzantine Agreement. Proof-of-work is more commonly and lets the participants, which are called miners, solve a problem. The first one who has solved this problem becomes the next block leader and he also gets a reward to give some incentive. Proof-of-stake on the other hand selects the next block creator with a specific algorithm and gives him the right to validate the next block and set of transactions. One idea of this algorithm is that the next leader is chosen based on the amount of coins he put at stake because a rich participant has an incentive to do nothing malicious otherwise he would reduce his own wealth. This is especially interesting because it does not require a lot of computation power which results in a high energy consumption. Byzantine Agreement is considered as a centralized approach to reach consensus. The consensus are made by some pre-selected server and these servers negotiate with each other for making an agreement. Each of these consensus mechanisms have some problems of their own and trust is needed in the system to guarantee that they work. In proof-of-work a so called 51\%-attack can be performed as soon as one user or group has more than 50\% of the computation power. This allows to dismiss transactions or modify some of the last blocks. In reality this has occurred for bitcoin and can let the whole system appear untrustworthy. Proof-of-stake suffers from a selected malicious block creator because there is often no punishment for faulty behavior and also little cost in doing so. Byzantine agreement has a higher requiremnt of the number of honset nodes. There are already some attempts to solve this problem in different kind of ways proposed by Ethereumcite{wood2014ethereum} or PeerCoincite{king2012ppcoin}, for example.


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