A system for performing transaction mixing between a plurality of users on a blockchain is provided. The blockchain may be, for example, the Bitcoin blockchain. The system is configured to carry out the steps of: (i) preparing a first commitment transaction arranged to transmit control of a resource from a source address of a first user to a receiving address of a second user; (ii) preparing a second commitment transaction arranged to transmit control of a resource from a source address of the second user to a receiving address of a further user; (iii) preparing a further commitment transaction arranged to transmit control of a resource from a source address of the further user to either: (a) a receiving address of the first user; or (b) a receiving address of a yet further user and repeating step (iii) until option (a) is performed to complete a transaction chain; and (iv) executing the transaction chain. At least one of the users is randomly chosen from the plurality.