Atomic cross-chain swaps using equivalent secret values

A method for performing a swap using equivalent secret values across a first blockchain and a second blockchain, the first blockchain being based on a first elliptic curve and the second blockchain being based on a second elliptic curve, comprising:

• receiving a first public key and a second public key from a transferring party, the first public key being on the first elliptic curve and the second public key being on the second elliptic curve;
• generating, by the computing device, a third public key and a fourth public key from the recipient, the third public key being on the first elliptic curve and the fourth public key being on the second elliptic curve, the third public key being associated with a third private key and the fourth public key being associated with a fourth private key;
• transmitting the third public key and the fourth public key to the transferring party;
• creating a second transaction on the second blockchain, the second transaction being associated with a second asset and a second signature comprising the second public key and the fourth public key;
• verifying a zero-knowledge proof using generated public keys received from the transferring party, the generated public keys both being derived from a selected bitstring, where a first generated public key is associated with the first elliptic curve and the second generated public key is associated with the second elliptic curve, the zero-knowledge proof verifying that the generated public keys are both derived from the selected bitstring without revealing the bitstring itself;
• verifying that an encrypted first partial signature and an encrypted second partial signature received from the transferring party include valid private keys for the first transaction and a second transaction, where the first private key corresponds to the first public key and the second private key corresponds to the second public key, the verifying being performed using the generated public keys, the first public key, and the second public key;
• transmitting a fourth partial signature corresponding to the fourth public key;
• determining the selected bitstring from a second signature associated with a second transaction on the second blockchain, the determining being further based on the encrypted second partial signature and the fourth partial signature;
• and
• signing a first transaction with a first signature comprising a first partial signature and a third partial signature on the first blockchain, thereby transferring a first asset, the published first signature being generated using the selected bitstring.