Merged Bitcoin: Proof of Work Blockchains with Multiple Hash Types

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.