Determining shared secrets using a blockchain

A computer-implemented method of generating a shared cryptographic key, wherein a first party has a first private key and a corresponding first public key, and a second party has a second private key and corresponding second public key, wherein a blockchain comprises a puzzle blockchain transaction, wherein the puzzle blockchain transaction comprises one or more respective outputs, each respective output comprising a respective puzzle locking script, wherein each respective puzzle locking script comprises a respective target public key and is configured to, when executed together with a respective unlocking script comprising a respective candidate value, convert the respective candidate value into a respective candidate public key and require the respective candidate public key to match the respective target public key, and wherein the method is performed by the second party and comprises:

• obtaining one or more respective reveal blockchain transactions, wherein each respective reveal blockchain transaction comprises one or more respective inputs, each respective input referencing a respective one of the one or more respective outputs of the puzzle blockchain transaction and comprising a respective unlocking script, each respective unlocking script comprising a respective candidate value;
• extracting, from the one or more reveal blockchain transactions, one or more respective candidate values;
• and
• generating the shared cryptographic key by performing elliptic curve operations using the second private key, the first public key, and each respective candidate value, wherein the first party is configured to generate the shared cryptographic key by performing elliptic curve operations using the first private key, the second public key, and each respective target public key.

A computer-implemented method for enabling a second party to determine a shared cryptographic key, wherein a first party has a first private key and corresponding first public key, and the second party has a second private key and corresponding second public key, wherein a blockchain comprises a puzzle blockchain transaction, wherein the puzzle blockchain transaction comprises one or more respective outputs, each respective output comprising a respective puzzle locking script, wherein each respective puzzle locking script comprises a respective target public key and is configured to, when executed together with a respective unlocking script comprising a respective candidate value, convert the respective candidate value into a respective candidate public key and require the respective candidate public key to match the respective target public key, and wherein the method is performed by a third party and comprises:

• generating one or more respective candidate values;
• generating one or more respective reveal blockchain transactions, wherein generating each respective reveal blockchain transaction comprises:
• generating, for one or more respective inputs of the respective reveal blockchain transaction, a respective unlocking script, each respective unlocking script comprising a respective candidate value;
• and
• generating the one or more respective inputs by encoding a respective unlocking script into the respective input and including a respective reference that references a respective one of the one or more respective outputs of the puzzle blockchain transaction;
• and
• sending the one or more respective reveal blockchain transactions to one or more blockchain nodes of a blockchain network, the first party, and/or the second party.