When the information allowing transfer of value is created for the anonymous refund agents, cryptographic protocols provably ensure each phone that it is correct and double-blind. This means that in the rare case information is sent to refund agents, the information is valid and allows transfer only to the correct party under the agreed conditions. It also ensures that refund agents cannot be communicated with unless the signatures are actually sent them.

(Without property 4: parties could intercept messages intended for refund agents or some refund agents could collude with one party against the other party.)