In some situations, the transfer of authentication authority is necessary for user authentication. In traditional authentication, a trust mechanism based on a trusted party establishes trust between two unfamiliar entities. However, a trusted party's failure or malicious behavior could undermine the trust system. Additionally, traditional authentication methods often involve complex and time-consuming procedures and may incur high costs. With the advancement of technology, more decentralized authentication methods and blockchain-based identity verification solutions have been proposed to address these limitations and enhance the security and efficiency of trust establishment. There are still cases where the number of transfers of their authentication authority should be limited for authentication in blockchain networks. Meanwhile, an authentication scheme consisting only of efficient operations such as hash functions is desirable. However, to the best of our knowledge, blockchain networks have no authentication schemes that consist of only hash functions and allow the transfer of authentication authority. In this paper, we propose an efficient authentication scheme based on only a hash function that can limit the number of times authentication authority can be transferred by using hash chains and Hashcash techniques in a blockchain network. As a result, our scheme has the advantage of reducing the computational complexity and gas costs in smart contracts. Furthermore, we deployed the smart contracts on the Goerli test network and completed authentication, proving the solution's effectiveness. On the Goerli testnet, our smart contract consumed 304.6kgas when deployed and 29.9kgas when performing authentication.