Embodiments may include a two-round-trip protocol by which two parties can securely conduct an already-agreed-upon exchange of digital assets (i.e., in the provable absence of settlement risk). For example, in the first round of the protocol, each party may send to a specially designed “settlement contract” the “statement” corresponding to the party's portion of the proposed bilateral transaction (e.g., how much asset the party will transfer, and to whom), as well as a hash of the party's “proof”. Between rounds, each party checks that the other party's statement transfers to the party the agreed-upon amount. The settlement contract may then lock the proof hashes against future misuse, and in particular against use by unauthorized parties. In the second round, each party sends its proof to the settlement contract. The settlement contract then dispatches both statement-proof pairs and executes the bilateral exchange.