collisions is limited, it is of greater concern than random collisions for MD5. In this note we sketch our construction. To illustrate its practicality, we present two MD5 based X.509 certificates with identical signatures but different public keys and different Distinguished Name fields, whereas our

values P �S and P ′ �S ′ collide under MD5. Although the practical attack potential of this construction of chosen-prefix collisions is limited, it is of greater concern than random collisions for MD5. To illustrate the practicality of our method, we constructed two MD5 based X.509 certificates

Intrusion detection/prevention systems (IDSs/IPSs) heavily rely on signature databases and pattern matching (PM) techniques to identify network attacks. The engines of such systems often employ traditional PM algorithms to search for telltale patterns in network flows. The observations that real-world network traffic is largely legitimate and that telltales manifested by exploits rarely appear in network streams lead us to the proposal of Fingerprinter. This framework integrates fingerprinting and PM methods to rapidly distinguish well-behaved from malicious traffic. Fingerprinter produces concise digests or fingerprints for attack signatures during its programming phase. In its querying phase, the framework quickly identifies attack-free connections by transforming input traffic into its fingerprint space and matching its digest against those of attack signatures. If the legitimacy of a stream cannot be determined by fingerprints alone, our framework uses the Boyer–Moore algorithm to ascertain whether attack signatures appear in the stream. To reduce false matches, we resort to multiple fingerprinting techniques including Bloom–Filter and Rabin–Fingerprint. Experimentation with a prototype and a variety of traces has helped us establish that Fingerprinter significantly accelerates the attack detection process.

@ Printed on acid-free paper which falls within the guidelines of the ANSI

In this thesis, two sets of experimental studies in bosonic and fermionic gases are described. In the first part of the thesis, itinerant ferromagnetism was studied in a strongly interacting Fermi gas of ultracold atoms. The observation of nonmonotonic behavior of lifetime, kinetic energy, and size for increasing repulsive interactions pro-vides strong evidence for a phase transition to a ferromagnetic state. Our observations imply that itinerant ferromagnetism of delocalized fermions is possible without lattice and band structure, and our data validate the most basic model for ferromagnetism introduced by Stoner. In the second part of the thesis, the coherence properties of a Bose-Einstein con-densate (BEC) was studied in a radio frequency induced double-well potential imple-mented on a microfabricated atom chip. We observed phase coherence between the separated condensates for times up to 200 ms after splitting, a factor of 10 longer than the phase diffusion time expected for a coherent state for our experimental con-ditions. The enhanced coherence time is attributed to number squeezing of the initial