Many emerging network applications are based upon a group communications model. As a result, securing group communications, i.e., providing confidentiality, authenticity, and integrity of messages delivered between group members, will become a critical networking issue. We present, in this paper, a novel solution to the scalability problem of group/multicast key management. We formalize the notion of a secure group as a triple (U,K,R) where U denotes a set of users, K a set of keys held by the users, and R a user-key relation. We then introduce key graphs to specify secure groups. For a special class of key graphs, we present three strategies for securely distributing rekey messages after a join/leave and specify protocols for joining and leaving a secure group. The rekeying strategies and join/leave protocols are implemented in a prototype key server we have built. We present measurement results from experiments and discuss performance comparisons. We show that our group key management service, using any of the three rekeying strategies, is scalable to large groups with frequent joins and leaves. In particular, the average measured processing time per join/leave increases linearly with the logarithm of group size.

We present chaining techniques for signing/verifying multiple packets using a single signing/verification operation. We then present flow signing and verification procedures based upon a tree-chaining technique. Since a single signing/verification operation is amortized over many packets, these procedures improve signing and verification rates by one to two orders of magnitude, compared to the approach of signing/verifying packets individually. Our procedures do not depend upon reliable delivery of packets. They also provide delay-bounded signing, and are thus suitable for delay-sensitive flows and multicast applications. To further improve our procedures, we propose several extensions to the Feige-Fiat-Shamir (1987) digital signature scheme to substantially speed up both the signing and verification operations, as well as to allow "adjustable and incremental" verification. The extended scheme, called eFFS, is compared to four other digital signature schemes (RSA, DSA, ElGamal (1985), and Rabin). We compare their signing and verification times, as well as key and signature sizes. We observe that: (1) eFFS is the fastest in signing (by a large margin over any of the other four schemes) and as fast as RSA in verification (tie for a close second behind Rabin (1979)); (2) eFFS allows a tradeoff between memory and signing/verification time; and (3) eFFS allows adjustable and incremental verification by receivers.

We present chaining techniques for signing/verifying multiple packets using a single signing/verification operation. We then present flow signing and verification procedures based upon a tree chaining technique. Since a single signing/verification operation is amortized over many packets, these procedures improve signing and verification rates by one to two orders of magnitude compared to the approach of signing/verifying packets individually. Our procedures do not depend upon reliable delivery of packets, provide delay-bounded signing, and are thus suitable for delay-sensitive flows and multicast applications. To further improve our procedures, we propose several extensions to the Feige-Fiat-Shamir digital signature scheme to speed up both the signing and verification operations, as well as to allow "adjustable and incremental" verification. The extended scheme, called eFFS, is compared to four other digital signature schemes (RSA, DSA, ElGamal, Rabin). We compare their signing and verification times, as well as key and signature sizes. We observe that (i) the signing and verification operations of eFFS are highly efficient compared to the other schemes, (ii) eFFS allows a tradeoff between memory and signing/verification time, and (iii) eFFS allows adjustable and incremental verification by receivers.

Many emerging applications (e.g., teleconference, real-time information services, pay per view, distributed interactive simulation, and collaborative work) are based upon a group communications model, i.e., they require packet delivery from one or more authorized senders to a very large number of authorized receivers. As a result, securing group communications (i.e., providing confidentiality, integrity, and authenticity of messages delivered between group members) will become a critical networking issue.In this paper, we present a novel solution to the scalability problem of group/multicast key management. We formalize the notion of a secure group as a triple (U,K,R) where U denotes a set of users, K a set of keys held by the users, and R a user-key relation. We then introduce key graphs to specify secure groups. For a special class of key graphs, we present three strategies for securely distributing rekey messages after a join/leave, and specify protocols for joining and leaving a secure group. The rekeying strategies and join/leave protocols are implemented in a prototype group key server we have built. We present measurement results from experiments and discuss performance comparisons. We show that our group key management service, using any of the three rekeying strategies, is scalable to large groups with frequent joins and leaves. In particular, the average measured processing time per join/leave increases linearly with the logarithm of group size.