Abstract: As one of the core elements of blockchain, the consensus mechanism is different in different fields. For public chain application scenarios, the widely used proof of work（PoW） consensus algorithm still has security and high computing power difficult to regulate. Therefore, the PoW algorithm is studied from the perspective of solution space and adjustment mechanism, and the fuzzy random proof of work（FRMH） consensus algorithm is innovatively proposed. Firstly, for security issues, the FRMH algorithm increases the solution space of the consensus algorithm by introducing technologies such as fuzzy transitive closure matrix in fuzzy mathematics, thereby improving the security of the blockchain consensus mechanism. Secondly, the FRMH algorithm uses a dual adjustment mechanism to deal with high computing power computers, thereby solving the problem of high computing power difficult to control on the blockchain. Finally, it is verified by mathematics that the FRMH algorithm has a significant improvement effect on the solution space and high computing power control.

Key words: fuzzy transitive closure matrix, security, solution space, dual regulation

摘要： 共识机制作为区块链的核心要素之一，在不同领域各不相同。针对公有链应用场景，应用广泛的工作量证明（PoW）共识算法仍然存在安全性及高算力难调控等问题，因此从扩大解空间及优化调节机制等角度对PoW算法进行研究，创新性地提出了模糊随机碰撞工作量证明共识算法（fuzzy random proof of work，FRMH）。针对安全性问题，FRMH算法通过引入模糊数学中的模糊传递闭包阵等技术，增大了共识算法的解空间，从而提高了区块链共识机制的安全性；FRMH算法采用双重调节机制来应对高算力计算机，进而解决了区块链上的高算力难调控问题；通过数学验证了FRMH算法在解空间及高算力调控上有明显的提升效果。

关键词: 模糊传递闭包阵, 安全性, 解空间, 双重调节