Brief Announcement: Brokering with Hashed Timelock Contracts is NP-Hard

In recent years, many different cryptocurrencies have risen in popularity. Since coins vary in fiat value and functionality, it has become important to securely exchange between them. A common exchange method is hashed timelock contracts (HTLC). However, this method did not support brokerage transactions that allow parties to leverage assets they gain during the transaction. We consider HTLC with brokering. The transaction fees for HTLC is a direct function of the size of the leader set. Thus, brokers are interested in finding the minimum leader set of a given transaction graph. We show that finding the minimum leader set on general transaction graphs with brokering is NP-hard. We then introduce flower transaction graphs, a common type of transaction graphs with brokering, and show that finding the minimum leader set of a flower graph is also NP-hard through a reduction from the knapsack problem.