In recent years, we have seen the development of key assignment schemes that use cryptography to enforce time-based authorization policies. One of the most important aspects of these schemes is the balance between the time required to derive keys and the amount of storage required for the public information from which keys are derived. The derivation time and storage are dependent on the number of time periods used in the authorization policy. In this paper, we discuss novel schemes that achieve good trade-offs between these competing parameters and for which explicit bounds can be given in terms of the number of time periods.
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