Wai Wan Tsang

Evaluating Kolmogorov's Distribution

Kolmogorovs goodness-of-fit measure, Dn , for a sample CDF has consistently been set aside for methods such as the D+n or D-n of Smirnov, primarily, it seems, because of the difficulty of computing the distribution of Dn . As far as we know, no easy way to compute that distribution has ever been provided in the 70+ years since Kolmogorovs fundamental paper. We provide one here, a C procedure that provides Pr(Dn

Toward a universal random number generator

This article describes an approach towards a random number generator that passes all of the stringent tests for randomness we have put to it, and that is able to produce exactly the same sequence of uniform random variables in a wide variety of computers, including TRS80, Apple, Macintosh, Commodore, Kaypro, IBM PC, AT, PC and AT clones, Sun, Vax, IBM , 3090, Amdahl, CDC Cyber and even 205 and ETA supercomputers.

A simple method for generating gamma variables

We offer a procedure for generating a gamma variate as the cube of a suitably scaled normal variate. It is fast and simple, assuming one has a fast way to generate normal variables. In brief: generate a normal variate <italic>x</italic> and a uniform variate <italic>U</italic> until In (<italic>U</italic>)<0.5<italic>x</italic><supscrpt>2</supscrpt> + <italic>d</italic> - <italic>dv</italic> + <italic>d</italic>ln(italic>v</italic>), then return <italic>dv</italic>. Here, the gamma parameter is α ≥ 1, and <italic>v</italic> = (1 + <italic>x</italic>/ *** with <italic>d</italic> = α - 1/3. The efficiency is high, exceeding 0.951, 0.981, 0.992, 0.996 at α = 1,2,4,8. The procedure can be made to run faster by means of a simple squeeze that avoids the two logarithms most of the time; return <italic>dv</italic> if <italic>U</italic> < 1-0.0331<italic>x</italic><supscrpt>4</supscrpt>. We give a short C program for any α ≥ 1, and show how to boost an α <1 into an α > 1. The gamma procedure is particularly fst for C implementation if the normal variate is generated in-line, via the #define feature. We include such an inline version, based on our ziggurat method. With it, and an inline uniform generator, gamma variates can be produced in 400MHz CPUs at better than 1.3 million per second, with the parameter α changing from call to call.

A Fast, Easily Implemented Method for Sampling from Decreasing or Symmetric Unimodal Density Functions

The fastest computer methods for sampling from a given density are those based on a mixture of a fast and slow part. This paper describes a new method of this type, suitable for any decreasing or symmetric unimodal density. It differs from others in that it is faster and more easily implemented, thereby providing a standard procedure for developing both the fast and the slow part for many given densities. It is called the ziggurat method, after the shape of a single, convenient density that provides for both the fast and the slow parts of the generating process. Examples are given for REXP and RNOR, subroutines that generate exponential and normal variates that, as assembler routines, are nearly twice as fast as the previous best assembler routines, and that, as Fortran subroutines, approach the limiting possible speed: the time for Fortran subroutine linkage conventions plus the time to generate one uniform variate.

IDR: an intrusion detection router for defending against distributed denial-of-service (DDoS) attacks

Distributed denial-of-service (DDoS) attack has turned into one of the major security threats in recent years. Usually the only solution is to stop the services or shut down the victim and then discard the attack traffic only after the DDoS attack characteristics (such as the destination ports of the attack packets) are known. In this paper, we introduce a generic DDoS attack detection mechanism as well as the design and setup of a testbed for performing experiments and analysis. Our results showed that the mechanism can detect DDoS attack. This enables us to proceed to the next steps of packet classification and traffic control.

An improved authenticated key agreement protocol with perfect forward secrecy for wireless mobile communication

To provide secure communication for mobile devices, an authenticated key agreement protocol is an important primitive for establishing session keys. However, most existing authenticated key agreement protocols are not designed for wireless mobile communication for which bandwidth and device storage capacity are limited. Also, as mobile devices are more vulnerable to attack, providing forward secrecy becomes an essential element in the protocol. Based on Seo and Sweeneys simple authenticated key agreement algorithm (SAKA), we develop an improved authenticated key agreement protocol that eliminates the disadvantages of SAKA and provides identity authentication, key validation, and perfect forward secrecy. Also, our protocol can foil man-in-the-middle attacks. We also show how our proposed protocol can be included in the current 3GPP2 specifications for OTASP to improve A-key (authentication key) distribution, which is the master key in IS-95 and cdma2000 mobile networks. The proposed protocol requires significantly less bandwidth, and less computational and storage overhead, while having higher security compared to 3GPP2 specifications. The proposed protocol can also be applied to other wireless communication scenarios.

Separable and Anonymous Identity-Based Key Issuing

In identity-based (ID-based) cryptosystems, a local registration authority (LRA) is responsible for authentication of users while the key generation center (KGC) is responsible for computing and sending the private keys to users and therefore, a secure channel is required. For privacy-oriented applications, it is important to keep in secret whether the private key corresponding to a certain identity has been requested. All of the existing ID-based key issuing schemes have not addressed this anonymity issue. Besides, the separation of duties of LRA and KGC has not been discussed as well. We propose a novel separable and anonymous ID-based key issuing scheme without secure channel. Our protocol supports the separation of duties between LRA and KGC. The private key computed by the KGC can be sent to the user in an encrypted form such that only the legitimate key requester authenticated by LRA can decrypt it. and any eavesdropper cannot know the identity corresponding to the secret key

The Monty Python method for generating random variables

We suggest an interesting and fast method for generating normal, exponential, t, von Mises, and certain other important random variables used in Monte Carlo studies. The right half of a symmetric density is cut into pieces, then, using simple area-preserving transformations, reassembled into a rectangle from which the x-coordinate—or a linear function of the x-coordinate—of a random point provides the required variate. To illustrate the speed and simplicity of the Monty Python method, we provide a small C program, self-contained, for rapid generation of normal (Gaussian) variables. It is self-contained in the sense that required uniform variates are generated in-line, as pairs of 16-bit integers by means of the remarkable new multiply-with-carry method.

BTM - An Automated Rule-based BT Monitoring System for Piracy Detection

With the advent of peer-to-peer communication technologies, individuals can easily connect to one another over Internet for file sharing and online chatting. Although these technologies provide wonderful platforms for users to share their digital materials, its illegitimate use on unauthorized sharing of copyrighted files is increasingly rampant. With the BitTorrent (BT) technology, the tracking down of these illegal activities is even more difficult as the downloaders can also act as the distributors and cooperate to provide different parts of the same file for sharing. It is close to impossible for law enforcement agencies to trace these distributed and short-duration Internet piracy activities with limited resources. In this paper, we present the first automated rule-based software system, the BitTorrent monitoring (BTM) system, for monitoring, recording, and analyzing suspicious BT traffic on the Internet. From a preliminary experiment on a real case, the system successfully located 126 distributors (a.k.a. seeders) for some Cantonese pop songs within 90 minutes.

Intrusion Detection Routers: Design, Implementation and Evaluation Using an Experimental Testbed

In this paper, we present the design, the implementation details, and the evaluation results of an intrusion detection and defense system for distributed denial-of-service (DDoS) attack. The evaluation is conducted using an experimental testbed. The system, known as intrusion detection router (IDR), is deployed on network routers to perform online detection on any DDoS attack event, and then react with defense mechanisms to mitigate the attack. The testbed is built up by a cluster of sufficient number of Linux machines to mimic a portion of the Internet. Using the testbed, we conduct real experiments to evaluate the IDR system and demonstrate that IDR is effective in protecting the network from various DDoS attacks