Discrete Mathematics
Practical network support for IP traceback
Proceedings of the conference on Applications, Technologies, Architectures, and Protocols for Computer Communication
Using router stamping to identify the source of IP packets
Proceedings of the 7th ACM conference on Computer and communications security
Tradeoffs in probabilistic packet marking for IP traceback
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Efficient packet marking for large-scale IP traceback
Proceedings of the 9th ACM conference on Computer and communications security
Tracing Anonymous Packets to Their Approximate Source
LISA '00 Proceedings of the 14th USENIX conference on System administration
A theoretical approach to parameter value selection of probabilistic packet marking for IP traceback
AINTEC '09 Asian Internet Engineering Conference
Nonexistence of 2-reptile simplices
JCDCG'04 Proceedings of the 2004 Japanese conference on Discrete and Computational Geometry
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There has been considerable recent interest in probabilistic packet marking schemes for sending information from nodes (routers) along one or more paths traveled by a stream of packets to the end-host receiving that stream. A central consideration for such schemes is the tradeoff between the number B of possible states of the marking bits in a packet, the number of bits n of information being sent by the nodes, and the expected number of packets T required to reconstruct this information. For the case where the packets all travel along the same path, we prove a lower bound of T ≥ Ω(B22n/(B-1)), roughly the square of an earlier lower bound of Adler.For an upper bound, we consider a model where each of m nodes along a single path must send one of s possible messages (thus n = m log2 s total bits are sent). We prove that T ≤ O(m • 22m(log2 s)/(B-1)) suffices (the implicit constant depends on B and s); this almost matches the lower bound, and is roughly the square root of an earlier upper bound of Adler. The new bound holds for all B and s in two slightly relaxed models, while under the strictest requirements we prove it only for some special values of B and s. This is related to a challenging geometric problem: the existence of an s-reptile (B-1)-dimensional simplex, i.e. a simplex S that can be tiled by s congruent simplices similar to S.We also consider the case where the packets travel along multiple paths to the same destination. In this case, we present a new protocol and analysis technique that together allow us to significantly generalize over previous work the scenarios where the protocol is effective.