# Research on Progress of Blockchain Consensus Algorithm:
## 1 Introduction  
Blockchain technology is one of the most promising emerging technologies in the 21 st century. It has significant advantages such as decentralization, non-tampering, non-forgery, and traceability [1]. It is very suitable for important anti-counterfeiting data storage, data security, and other realities scenes [2, 3]. Blockchain technology can solve the security problems of data tampering and data loss existing in traditional centralized endorsement agencies, as well as the inefficiency of transaction processing [4, 5, 6], which can be found in finance [7, 8, 9], medical [10], Internet of Things [11], property rights protection [12], privacy protection [13] and other fields. Blockchain technology has produced great value, so it has been attracting attention since it appeared [14]. Blockchain technology originated from the paper \"Bitcoin: A Peer-to-Peer Electronic Cash System\" written by the scholar \"[PERSON]\" in 2008 [15]. In 2009, the creation of the genesis block in Bitcoin marked the birth of the blockchain. The emergence of blockchain technology announced the birth of a new scientific field and an innovative distributed technology. With the gradual application of blockchain technology, it is increasingly known and understood, and some of its inherent drawbacks were gradually exposed by people. For example, in terms of performance, the ability to handle high concurrent transactions is too low, the data throughput is too small, and there is insufficient capacity to defend from malicious nodes [16] of a chain, etc. In terms of energy consumption, there are problems such as waste of power resources caused by excessive computing power consumption. These problems have greatly hindered the development of blockchain technology. So, how to solve these thorny problems has become a hotspot in the research of blockchain. The consensus algorithm is one of the core technologies of blockchain, which is essential to theefficiency, security, and stability of blockchain data processing [17]. When the blockchain consensus algorithm promotes the consensus of blockchain nodes, it also needs to pay great attention to the security, scalability, resource consumption and performance efficiency of the algorithm, and it can constantly pursue high performance, low energy consumption, high security and scalability. In fact, the consensus algorithm has always been one of the key research directions of blockchain. The research work of consensus algorithms precedes the concept of blockchain. It can be traced back to the research work carried out by [PERSON] et al. in 1959 [18]. That is, a special probability space represents a collection of event probabilities and includes sample space, event space, and probability function, a group of subjective individual probability distributions, and how to reach a consensus probability distribution. According to whether or not to consider the existence of malicious nodes in a blockchain network, consensus algorithms can be divided into non-Byzantine fault-tolerant algorithms and Byzantine fault-tolerant algorithms [19]. Most of the early consensus algorithms did not consider the possibility of malicious nodes in the system, so they are generally non-Byzantine algorithms, such as the VR (Viewstamped Replication) consensus algorithm proposed by [PERSON] et al. in 1988 [20], the Paxos algorithm proposed by [PERSON] in 1989 [21], the PBFT (Practical Byzantine Fault Tolerance) algorithm proposed by [PERSON] in 1999 [22], and so on. Non-Byzantine algorithms such as VR, Paxos, and PBFT have certain limitations, which are only applicable to blockchains with a limited number of nodes and relatively trustworthy nodes. In 2008, [PERSON] proposed the concept of \"Bitcoin\". The Bitcoin system he designed uses the POW (Proof of Work) consensus algorithm proposed by [PERSON] [23], which fully considers the possible existence of malicious nodes in a blockchain. Since then, Byzantine algorithms began to develop rapidly.