  S-money [Proc. R. Soc. A 475, 20190170 (2019)] schemes define virtual tokens
designed for networks with relativistic or other trusted signalling
constraints. The tokens allow near-instant verification and guarantee
unforgeability without requiring quantum state storage. We present refined two
stage S-money schemes. The first stage, which may involve quantum information
exchange, generates private user token data. In the second stage, which need
only involve classical communications, users determine the valid presentation
point, without revealing it to the issuer. This refinement allows the user to
determine the presentation point anywhere in the causal past of all valid
presentation points. It also allows flexible transfer of tokens among users
without compromising user privacy.
