# The Evolution and Optimization Strategies of a PBFT Consensus Algorithm for Consortium Blockchains
## 3 An Introduction to Mainstream Consensus Algorithms
### The Mainstream Consensus Algorithms of Public Blockchains
#### 3.1.1 Pow  
Proof of Work (PoW), as the fundamental consensus mechanism of distributed ledger technology [19], relies on solving cryptographic puzzles and computational resource competition to achieve transaction validation and ledger consistency in a decentralized environment. In terms of technical implementation, the PoW mechanism requires participating nodes to perform high-intensity hash calculations on the block header parameters, which include a random number (Nonce). Nodes search for a valid hash solution by iterating through different Nonce values to meet a preset difficulty threshold (such as a constraint on the number of leading zeros) [20]. The first node to complete the computation gains the right to add the block to the ledger and distributes the new block across the network through a broadcast mechanism. Other nodes can quickly verify the validity of the computation based on the one-way nature of the hash function and synchronize the global state by following the \"longest chain rule\", thus constructing a distributed consensus system with resistance to Sybil attacks. From a security perspective, PoW establishes a dual-defense mechanism by introducing a competitive computational model. The PoW consensus process schematic is shown in Figure 5. This security architecture based on mathematical certainty allows public blockchains such as Bitcoin to ensure censorship resistance and data finality even in the  
Figure 4: An overview of blockchain consensus algorithms. absence of centralized regulation. However, the PoW mechanism's high reliance on computing power brings about huge energy consumption, which has become a major bottleneck restricting the widespread application of blockchain technology. Therefore, the industry is gradually exploring more energy-efficient consensus schemes, such as Proof of Stake (PoS). By optimizing the verification process and redesigning the incentive mechanism, researchers are pushing the distributed system towards sustainability. Although PoW is still the core consensus mechanism of blockchain, its high energy consumption has prompted academics to actively seek more efficient alternatives. To reduce the environmental impact of PoW, [PERSON] et al. [21] proposed the Green-PoW algorithm, which grants the runner-up in a mining competition the exclusive right to compute the subsequent blocks, in order to reduce unnecessary energy consumption while maintaining network security. In addition to energy-saving optimization, research also focuses on the dual utilization of computational resources. For example, the Proof of Learning (PoLe) consensus mechanism proposed by [PERSON] et al. [22] attempts to combine the PoW computation process with neural network optimization so that blockchain computing can serve machine learning tasks at the same time. Further innovations address emerging security challenges within the blockchain ecosystem. [PERSON] et al. [23] developed a post-quantum PoW variant tailored for smart city applications, integrating quantum-resistant cryptographic primitives to defend against future quantum computing threats. Similarly, [PERSON] et al. [24] improved PoW's energy efficiency with the Computation-and-Waiting PoW (CW-PoW) protocol, introducing multi-round proof verification to minimize redundant computation. The adaptability of PoW to different network architectures has also been explored. In decentralized opportunity networks (OppNets), [PERSON] et al. [25] demonstrated the feasibility of PoW through a blockchain-based secure routing protocol (BDRP), ensuring tamper-proof and decentralized routing decisions. For hierarchical data ecosystems, [PERSON] et al. [26] designed a federated ledger framework (Fed-DDM) using scalable PoW to synchronize multiple private sub-ledgers, enabling secure cross-network data markets. PoW's applications have expanded to specific blockchain implementations across various fields. In healthcare IoT systems, [PERSON] et al. [27] proposed an enhanced PoW  
Figure 5: A PoW consensus process schematic.