Succinct specifications of portable document access policies

When customers need to each be given portable access rights to subset of documents from large universe of n vailable documents, it is often the case that the space vailable for representing each customer's access rights is limited to much less than n, say it is no more than m bits. This is the case when, e.g., limited-capacity inexpensive cards are used to store the access rights to huge multimedia document databases. How does one represent subsets of huge set of n elements,when only m bits re v il ble and m is much smaller than n? We use an approach reminiscent of Bloom filters, by assigning to each document subset of the m bits: If that document is in customer's subset then we set the corresponding bits to 1 on the customer's card. This guarantees that each customer gets the documents he paid for, but it also gives him access to documents he did not pay for ("false positives"). We want to do so in a manner that minimizes the expected total false positives under various deterministic and probabilistic models: In the former model we assume k customers whose respective subsets are known priori, whereas in the latter we assume (more realistically) that each document has probability of being included in customer's subset. We cannot use randomly assigned bits for each document (in the way Bloom filters do), rather we need to consider the priori knowledge (deterministic orprobabilistic) we are given in each model in order to better ssign subset of the m vailable bits to each of the n documents. We analyze and give efficient schemes for this problem.