1. A method for performing secure information processing operations utilizing a plurality of processing devices, the method comprising the steps of: performing a setup procedure to permit interactions of a designated type to be carried out between a first participant associated with at least a first one of the processing devices and a second participant associated with at least a second one of the processing devices; initiating in the first processing device a particular interaction with the second participant, by sending designated initiation information to the second processing device associated with the second participant, the particular interaction being configured based at least in part on one or more results of the setup procedure; receiving as part of the interaction response information from the second processing device associated with the second participant; and sending as part of the interaction additional information from the first processing device to the second processing device based at least in part on the received response information; wherein the interaction is configured such that transcripts of the interaction can be used to determine rights of the first and second participants in a publicly verifiable manner, the rights being based upon particular results of the interaction.