Allen L. Roginsky

A new analysis of the false positive rate of a Bloom filter

A Bloom filter is a space-efficient data structure used for probabilistic set membership testing. When testing an object for set membership, a Bloom filter may give a false positive. The analysis of the false positive rate is a key to understanding the Bloom filter and applications that use it. We show experimentally that the classic analysis for false positive rate is wrong. We formally derive a correct formula using a balls-and-bins model and show how to numerically compute the new, correct formula in a stable manner. We also prove that the new formula always results in a predicted greater false positive rate than the classic formula. This correct formula is numerically compared to the classic formula for relative error - for a small Bloom filter the prediction of false positive rate will be in error when the classic formula is used.

Performance of packet-to-cell segmentation schemes in input buffered packet switches

Most input buffered packet switches internally segment variable-length packets into fixed-length cells. The last cell in a segmented packet contains overhead bytes if the packet length is not evenly divisible by the cell length. Switch speed-up is used to compensate for this overhead. In this paper, we develop an analytical model of a single-server queue where an input stream of packets is segmented into cells for service. Analytical models are developed for M/M/1, M/H/sub 2//1, and M/E/sub 2//1 queues with a discretized (or quantized) service time. These models and simulation using real packet traces are used to evaluate the effect of speed-up on mean queue length. We propose and evaluate a new method of segmenting a packet trailer and subsequent packet header into a single cell. This cell merging method reduces the required speed-up. No changes to switch-matrix scheduling algorithms are needed. Simulation with a packet trace shows a reduction in the needed speed-up for an iSLIP scheduled input buffered switch.

Report on Pairing-based Cryptography

This report summarizes study results on pairing-based cryptography. The main purpose of the study is to form NIST’s position on standardizing and recommending pairing-based cryptography schemes currently published in research literature and standardized in other standard bodies. The report reviews the mathematical background of pairings. This includes topics such as pairing-friendly elliptic curves and how to compute various pairings. It includes a brief introduction to existing identity-based encryption (IBE) schemes and other cryptographic schemes using pairing technology. The report provides a complete study of the current status of standard activities on pairing-based cryptographic schemes. It explores different application scenarios for pairing-based cryptography schemes. As an important aspect of adopting pairing-based schemes, the report also considers the challenges inherent in validation testing of cryptographic algorithms and modules. Based on the study, the report suggests an approach for including pairing-based cryptography schemes in the NIST cryptographic toolkit. The report also outlines several questions that will require further study if this approach is followed.

Targeted search: reducing the time and cost for searching for objects in multiple-server networks

In many applications-including peer-to-peer (P2P) file sharing, content distribution networks, and grid computing-a single object will be searched for in multiple servers. In this paper, we find the provably optimal search method for such applications and develop analytical models for search time and cost. A client node searching for objects maintains statistics on where (in which servers) it has previously found objects. Using these statistics to target future searches to popular servers is provably optimal. For object location and request distributions that are non-uniform, which has been shown to be the case in P2P file sharing networks, this method of targeted searching is found to be more cost effective (i.e., use less server resources) than broadcast-based searching. Our targeted search method is implemented in a prototype Gnutella servent called Ditella. Ditella can improve the scalability of file sharing in P2P networks and reduce the amount of traffic in the Internet by reducing file search query traffic.