Recent proliferation of cryptocurrencies that allow for pseudo-anonymous transactions has resulted in a spike of various e-crime activities and, particularly, cryptocurrency payments in hacking attacks demanding ransom by encrypting sensitive user data. Currently, most hackers use Bitcoin for payments, and existing ransomware detection tools depend only on a couple of heuristics and/or tedious data gathering steps. By capitalizing on the recent advances in Topological Data Analysis, we propose a novel efficient and tractable framework to automatically predict new ransomware transactions in a ransomware family, given only limited records of past transactions. Moreover, our new methodology exhibits high utility to detect emergence of new ransomware families, that is, detecting ransomware with no past records of transactions.