Abstract. We deal with the problem of a center sending a message to a group of users such that some subset of the users is considered revoked and should not be able to obtain the content of the message. We concentrate on the stateless receiver case, where the users do not (necessarily) update their state from session to session. We present a framework called the Subset-Cover framework, which abstracts a variety of revocation schemes including some previously known ones. We provide sufficient conditions that guarantees the security of a revocation algorithm in this class. We describe two explicit Subset-Cover revocation algorithms; these algorithms are very flexible and work for any number of revoked users. The schemes require storage at the receiver of log N and 1 2 log 2 N keys respectively (N is the total number of users), and in order to revoke r users the required message lengths are of r log N and 2r keys respectively. We also provide a general traitor tracing mechanism that can be integrated with any Subset-Cover revocation scheme that satisfies a "bifurcation property". This mechanism does not need an a priori bound on the number of traitors and does not expand the message length by much compared to the revocation of the same set of traitors. The main improvements of these methods over previously suggested methods, when adopted to the stateless scenario, are: (1) reducing the message length to O(r) regardless of the coalition size while maintaining a single decryption at the user's end (2) provide a seamless integration between the revocation and tracing so that the tracing mechanisms does not require any change to the revocation algorithm.

server.We describe our implementation, which can be used as an extension of a web server or as a separate server with interface to applications.

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A near-optimal alignment between a pair of sequences is an alignment whose score lies within the neighborhood of the optimal score. We present an efficient method for representing all alignments whose score is within any given delta from the optimal score. The representation is a compact graph that makes it easy to impose additional biological constraints and select one desirable alignment from the large set of alignments. We study the combinatorial nature of near-optimal alignments, and define a set of "canonical" near-optimal alignments. We then show how to enumerate near-optimal alignments efficiently in order of their score, and count their number. When applied to comparisons of two distantly related proteins, near-optimal alignments reveal that the most conserved regions among the near-optimal alignments are the highly structured regions in the proteins. We also show that by counting the number of near optimal alignments as a function of the distance from the optimal score, we can select a good set of parameters that best constraints the biologically relevant alignments.