S-money: virtual tokens for a relativistic economy

We propose definitions and implementations of 'S-money'-virtual tokens designed for high-value fast transactions on networks with relativistic or other trusted signalling constraints, defined by inputs that in general are made at many network points, some or all of which may be space-like separated. We argue that one significant way of characterizing types of money in space-time is via the 'summoning' tasks they can solve: that is, how flexibly the money can be propagated to a desired space-time point in response to relevant information received at various space-time points. We show that S-money is more flexible than standard quantum or classical money in the sense that it can solve deterministic summoning tasks that they cannot. It requires the issuer and user to have networks of agents with classical data storage and communication, but no long-term quantum state storage, and is feasible with current technology. User privacy can be incorporated by secure bit commitment and zero-knowledge proof protocols. The level of privacy feasible in given scenarios depends on efficiency and composable security questions that remain to be systematically addressed.