A cryptographic system enables a user securely to access a resource from an issuer at a first space-time point selected by the user, but not at a second (or other) space-time point. The parties (the issuer and the user) pre-agree representations of the future space-time points, which may include any number of future space-time points. The system then comprises a commitment device for use in a commitment protocol between the user and the issuer in which the user makes a secure commitment to the issuer, the commitment comprising the agreed representation of the space-time point selected by the user. The commitment device is configured to generate commitment data at a first output associated with the user and validation data at a second output associated with the issuer Respective redemption devices at each of the space-time points each have an input for receiving a token presented by the user, the token being derived from the commitment data. Each redemption device is configured to validate the token if, and only if, the token is presented at the space-time point selected by the user and represented in the commitment.
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