Abstract: 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.

Abstract: Systems and methods for anonymous cryptocurrency transactions are disclosed. A method may include: receiving, from the electronic device associated with a sender of a cryptocurrency transaction, a zero-knowledge statement comprising a shuffled and anonymized list of participants comprising the sender, a receiver of the cryptocurrency transaction, and a plurality of decoy participants, a transfer amount, and a remaining balance, and a secret witness, wherein each participant is associated with an index; generating one-out-of-many proofs for the sender and the receiver based on their associated indices; generating a Basic Zether proof for the transfer amount and the remaining balance; conducting many-out-of-many proofs with parameters chosen for an anonymous payment setting; and constructing a zero-knowledge proof for the zero-knowledge statement.

Abstract: A method for privacy-preserving inventory matching may include: (1) receiving a plurality of axe submissions; (2) arranging the parties into data structures based on a direction in the party's axe submission; (3) sending each party's commitment to the other party; (4) receiving, from each party, output secret-shares of an arithmetized comparison circuit; (5) verifying that the output secret-shares of the arithmetized comparison circuit received from the parties match commitments to the output secret-shares sent by the respective opposite party; (6) identifying a minimal party based on the outputs of the arithmetized comparison circuit; (7) generating and sending a proof of the minimal party identification to the minimal party; (8) receiving a minimal quantity integer from the minimal party; (9) revealing the minimal quantity integer to the first party and the second party; and (10) executing the trade for the minimal quantity integer.

Abstract: 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.

Abstract: Systems and methods for anonymous cryptocurrency transactions are disclosed. A method may include: receiving, from the electronic device associated with a sender of a cryptocurrency transaction, a zero-knowledge statement comprising a shuffled and anonymized list of participants comprising the sender, a receiver of the cryptocurrency transaction, and a plurality of decoy participants, a transfer amount, and a remaining balance, and a secret witness, wherein each participant is associated with an index; generating one-out-of-many proofs for the sender and the receiver based on their associated indices; generating a Basic Zether proof for the transfer amount and the remaining balance; conducting many-out-of-many proofs with parameters chosen for an anonymous payment setting; and constructing a zero-knowledge proof for the zero-knowledge statement.