Proof of work blockchain protocols using multiple hash types are considered. It is proven that the security region of such a protocol cannot be the AND of a 51\% attack on all the hash types. Nevertheless, a protocol called Merged Bitcoin is introduced, which is the Bitcoin protocol where links between blocks can be formed using multiple different hash types. Closed form bounds on its security region in the $Δ$-bounded delay network model are proven, and these bounds are compared to simulation results. This protocol is proven to maximize cost of attack in the linear cost-per-hash model. A difficulty adjustment method is introduced, and it is argued that this can partly remedy asymmetric advantages an adversary may gain in hashing power for some hash types, including from algorithmic advances, quantum attacks like Grover's algorithm, or hardware backdoor attacks.

翻译：本文探讨了采用多种哈希类型的工作量证明区块链协议。研究证明，此类协议的安全区域不能简单地等同于对所有哈希类型同时发动51%攻击的合取条件。尽管如此，本文提出了一种名为"合并比特币"的协议，该协议在比特币原有框架基础上，允许使用多种不同哈希类型建立区块间的链接。在Δ有界延迟网络模型中，我们推导出该协议安全区域的闭式界，并将理论边界与仿真结果进行对比。在线性哈希成本模型下，该协议被证明能够最大化攻击成本。本文还提出了一种难度调整方法，论证了该方法可部分缓解攻击者因算法进步（如Grover算法等量子攻击）或硬件后门攻击，在特定哈希类型上获得算力不对称优势的问题。