On the distribution of characteristics in bijective mappings

Differential cryptanalysis is a method of attacking iterated mappings based on differences known as characteristics. The probability of a given characteristic is derived from the XOR tables associated with the iterated mapping. If is a mapping : Z ₂ ^m , then for each , X, Y Z ₂ ^m the XOR table for gives the number of input pairs of difference X=X+X for which gp(X)+(X)=Y.The complexity of a differential attack depends upon two properties of the XOR tables: the density of zero entries in the table, and the size of the largest entry in the table. In this paper we present the first results on the expected values of these properties for a general class of mappings . We prove that if : Z ₂ ^m Z ₂ ^m is a bijective mapping, then the expected size of the largest entry in the XOR table for is bounded by 2m, while the fraction of the XOR table that is zero approaches e ^–1/2=0.60653. We are then able to demonstrate that there are easily constructed classes of iterated mappings for which the probability of a differential-like attack succeeding is very small.The author is presently employed by the Distributed System Technology Center, Brisbane, Australia.     

On singular nonlinearH ∞ control: A state-space approach

A simple state-space approach for the four-block singular nonlinearH control problem is proposed in this paper. This approach combines a (J, J)-lossless and a class of conjugate (J, J)-expansive systems to yield a family of nonlinearH output feedback controllers. The singular nonlinearH control problem is thus transformed into a simple lossless network problem that is easy to deal with in a network-theory context.This work was supported by the National Science Council, Republic of China, under contract NSC 87-2218-E009-026.     

Year 2000 — a Sytems Integration challenge

BT, along with virtually every other IT-dependent business worldwide, is tackling a problem which is quite unique and if not corrected could be disastrous. The problem, sometimes known as the Year 2000 bug or millennium time bomb, has been caused by the use of two digits to represent the year in the majority of our systems and applications. The problem is technically not difficult to fix but the volume of changes occurring, and the need to potentially test every system to ensure that it is year 2000 proof, presents unique and challenging difficulties for integration and testing. Why this is the case, what problems need to be addressed, and an overview of some of the proposed integration and test strategies to tackle these problems, is the subject of this paper.     

Efficient signature generation by smart cards

We present a new public-key signature scheme and a corresponding authentication scheme that are based on discrete logarithms in a subgroup of units in _p where p is a sufficiently large prime, e.g., p 2⁵¹². A key idea is to use for the base of the discrete logarithm an integer in _p such that the order of is a sufficiently large prime q, e.g., q 2¹⁴⁰. In this way we improve the ElGamal signature scheme in the speed of the procedures for the generation and the verification of signatures and also in the bit length of signatures. We present an efficient algorithm that preprocesses the exponentiation of a random residue modulo p.European patent application 89103290.6 from February 24, 1989. U.S. patent number 4995082 of February 19, 1991.     

On the robustness of stability for uncertain large-scale systems subjected to multiple time delays

The robustness problem of stability for large-scale uncertain systems with a class of multiple time delays is addressed in this paper. By applying the complex Lyapunov stability theorem, the matrix measure techniques, and norm inequalities, a new approach for solving a general case of the above problem is proposed. Several robust stability conditions, delay-dependent or delay-independent, are derived to guarantee the asymptotic stability and exponential stability of the uncertain large-scale time-delay systems. Moreover, these obtained results can also be applied to the stabilization design.Notation real number field - complex number field - x x=(x ₁,x ₂,...,x _n ) ^T R ⁿ - x ^T transpose of vectorx - x* complex conjugate transpose of vectorx - Re(·) real part of (·) - x norm of vectorx; x=(x*x)^1/2 - A ^T transpose of matrixA - A* complex conjugate transpose of matrixA - ¯(·) maximal absolute value of eigenvalue of matrixA - (A) matrix measure of matrixA; (A)=¯((A + A*)/2) - A induced norm of matrix A; A=[¯(A*A)]^1/2 - ¦a_ij ¦ absolute value of element a_ij - ¦ A¦ {¦a_ij¦} for matrix A={a_ij} - A >B a_ij > b_ij for alli andj where A={a_ij} andB={b_ij} - z complex number - ¯z complex conjugate ofz Supported by National Science Council, Taiwan, Republic of China, Grant NSC83-0404-E006-001.     

Performance Monitoring for In-life Capacity Management

The key to providing a meaningful management view of the performance of complex systems lies in having a co-ordinated process for data collection, analysis and presentation. TeleMarketing Services, such as the Freefone service, provide a good example. Managers of diverse, remote subsystems receive summarised performance and customer service information, mostly in the form of simple graphs, in exchange for providing reliable data. The aim is to bring together a structured view of all the components, including a red-amber-green status table, for use by senior customer-facing staff. Generally, the analyses focus on capacity, forecast and measurement, covering a flexible range of parameters. Managers then have an early view of service degradation, potential capacity exhaustion, workload imbalance and resource wastage, enabling timely remedial action, fault clearance and system enhancements.     

Current Operational Amplifier (COA): CMOS Realization and Active Compensation

A methodology for analysis and synthesis of lowpass sigma-delta () converters is presented in this paper. This method permits the synthesis of modulators employing continuous-time filters from discrete-time topologies. The analysis method is based on the discretization of a continuous-time model and using a discrete simulator, which is more efficient than an analog simulator. In our analysis approach, the influence of the sample and hold block and non-idealities of the feedback DAC can be systematically modeled by discrete-time systems. Finally, a realistic design of a second-order modulator with a compensation of the non-ideal behavior of the DAC is given. Moreover, simulation results show a good agreement with the theoretical predictions.     

Index two linear time varying singular systems of differential equations

Linear time varying singular systems of differential equations of the formA(t)x(t) + B(t)x(t)=f(t) whereA(t) is singular and the system has index at most two are considered. Recent results on their analytic solution are improved on. Examples are given that show these results are not easily extended.This work was supported in part by the National Science Foundation under Grant No. DMS-8318026 and the Air Force Office of Scientific Research under Grant No. 84-0240.     

Higher-order terms in asymptotic expansion for information loss in quantized random processes

Uniform quantization of random vectors onto -grids ⁿ is considered. Higherorder terms in asymptotic expansions for the entropy of the -quantized random vector and for the loss of the mutual information between two random vectors under such quantization as 0+are obtained. The coefficients in these asymptotics are explicitly calculated for Gaussian distributed vectors. Taken for initial segments of stationary Gaussian sequences, these factors have limit average values per unit of time. For such sequences governed by state-space equations, computation of these average values is reduced to solutions of algebraic matrix Riccati and Lyapunov equations.Work supported by the Australian Research Council grant A 4970 2246.     

Estimation of Energy Aliasing Error for Nonbandlimited Signals

In this paper, we investigate the problem of approximating a given (not necessarily bandlimited) signal, x(t), by a (bandlimited) interpolation or sampling series of the form:

Input-output systems whose transmission operators furnish nearly best approximations to a given map

Let {S(A):A A}, whereA is a subset of an infinite-dimensional normed linear spaceL, be a class of general nonlinear input-output systems that are governed by operator equations relating the input, state, and output, all of which are in extended spaces. IfQ is a given operator from a specified set ¯D _i, of inputs into the space of outputs ¯H ₀, the problem we consider is to find, for a given >0, a parameterA A such that the transmission operatorR(A ) ofS(A ) furnishes a nearly best (or -best) approximation toQ from allR(A),A A. Here the distance betweenQ andR(A) is defined as the supremum of distances betweenQz andR(A)z taken over allz ¯D _i. In Theorems 2 through 5 we show that ifS(A) is normal (Definition 2),A satisfies some mild requirement andL contains a fundamental sequence, then establishingA A reduces to minimizing a certain continuous functional on a compact subset ofR ⁿ, and thus can be carried out by conventional methods. The applications of results are illustrated by the example of a model-matching problem for a nonlinear system, and of optimal tracking.     

A Direct Digital Synthesizer with Tunable Delta Sigma Modulator

In direct digital synthesizer (DDS) applications, the drawback of the conventional delta sigma () modulator structure is that its signal band is fixed. In the new architecture presented in this paper, the signal band of the modulator is tuned according to the DDS output frequency. We use a hardware efficient phase-to-sine amplitude converter in the DDS that approximates the first quadrant of the sine function with sixteen equal length second degree polynomial segments. The DDS is capable of frequency, phase, and quadrature amplitude modulation. Two DDSs with tunable 1-bit D/A converters (real and complex) were designed and implemented on a programmable logic device (PLD); experimental results show their desired operation and performance.     

Quality Determination for Gate Delay Fault Tests Considering Three-State Elements

Most industrial digital circuits contain three-state elements besides pure logic gates. This paper presents a gate delay fault simulator for combinational circuits that can handle three-state elements like bus drivers, transmission gates and pulled busses. The well known delay faults--slow-to-rise and slow-to-fall--are considered as well as delayed transitions from isolating signal state high impedance to binary states 0 and 1 and vice versa. The presented parallel delay fault simulator distinguishes between non-robust, robust and hazard free tests and determines the quality of a test. Experimental results for ISCAS85/89 benchmark circuits are presented as well as results for industrial circuits containing three-state elements.     

Pervasive Home Environments

For decades, technologists have been promising the intelligent house. The vision is usually portrayed as a house filled with technology which will do the dweller's bidding and take all domestic drudgery out of their lives. The truly intelligent house is still some way off, but the emergence of broadband, availability of faster, smaller and ever cheaper computing equipment and a variety of wired and wireless network technologies are enabling technologies that bring this vision closer to reality. These technology trends lead to the concept that computing and other smart devices will become pervasive, fully networked and disappear into the infrastructure of the home. People will carry out their tasks unaware of the complexity of the infrastructure that supports their activities in much the same way as people today use mains electricity.This paper introduces these concepts and discusses the technological challenges to be overcome. We present our vision of the pervasive home environment where inhabitants can focus on tasks rather than the technology: I need to create X and send it to Y rather than I need to use this computer and this application which needs access to service A and resource B. Although this sounds simple, the environment needs to understand who I is, and who or what Y is. Appropriate permissions must be in place and resources allocated, if available. The most appropriate interface for the task and user must be determined.The pervasive, intelligent home will make available new ways to access and share information. It will herald new services, such as care and support of people in the home, entertainment, educational and security services. The final part of the paper discusses the commercial opportunities and challenges which must be met, not least the need for industry to agree on open standards and interfaces.     

Systematic Width-and-Length Dependent CMOS Transistor Mismatch Characterization and Simulation

This paper presents a methodology for characterizing the random component of transistor mismatch in CMOS technologies. The methodology is based on the design of a special purpose chip which allows automatic characterization of arrays of NMOS and PMOS transistors of different sizes. Up to 30 different transistor sizes were implemented in the same chip, with varying transistors width W and length L. A simple strong inversion large signal transistor model is considered, and a new five parameters MOS mismatch model is introduced. The current mismatch between two identical transistors is characterized by the mismatch in their respective current gain factors /, V _TO threshold voltages , bulk threshold parameters , and two components for the mobility degradation parameter mismatch ₀ and _e. These two components modulate the mismatch contribution differently, depending on whether the transistors are biased in ohmic or in saturation region. Using this five parameter mismatch model, an extraordinary fit between experimental and computed mismatch is obtained, including minimum length (1 m) transistors for both ohmic and saturation regions. Standard deviations for these five parameters are obtained as well as their respective correlation coefficients, and are fitted to two dimensional surfaces f(W, L) so that their values can be predicted as a function of transistor sizes. These functions are used in an electrical circuit simulator (Hspice) to predict transistor mismatch. Measured and simulated data are in excellent agreement.     

The prime and generalized nullspaces of right regular pencils

The classical notion of the -generalized nullspace, defined on a matrixA R ^n×n,where is an eigenvalue, is extended to the case of ordered pairs of matrices(F, G), F, G R ^m×nwhere the associated pencilsF – G is right regular. It is shown that for every C {} generalized eigenvalue of (F, G), an ascending nested sequence of spaces {P ⁱ ,i=1, 2,...} and a descending nested sequence of spaces {ie495-02 i=1, 2,...} are defined from the -Toeplitz matrices of (F, G); the first sequence has a maximal elementM ^* , the -generalized nullspace of (F, G), which is the element of the sequence corresponding to the index , the -index of annihilation of (F, G), whereas the second sequence has the first elementP ^* as its maximal element, the -prime space of (F, G). The geometric properties of the {M ⁱ ,i=1, 2,..., and {P ⁱ ,i=1, 2,...sets, as well as their interrelations are investigated and are shown to be intimately related to the existence of nested basis matrices of the nullspaces of the -Toeplitz matrices of (F, G). These nested basis matrices characterize completely the geometry ofM ^* and provide a systematic procedure for the selection of maximal length linearly independent vector chains characterizing the-Segre characteristic of (F, G).     

Gaussian radial basis functions and inner product spaces

An approximation result is given concerning Gaussian radial basis functions in a general inner product space. Applications are described concerning the classification of the elements of disjoint sets of signals, and also the approximation of continuous real functions defined on all of ⁿ using radial basis function (RBF) networks. More specifically, it is shown that an important large class of classification problems involving signals can be solved using a structure consisting of only a generalized RBF network followed by a quantizer. It is also shown that Gaussian radial basis functions defined on ⁿ can uniformly approximate arbitrarily well over all of ⁿ any continuous real functionalf on ⁿ that meets the condition that |f(x)|0 as x.     

Performance of a joint CDMA/PRMA protocol with heavy‐tailed ON/OFF source

The performance of a joint CDMA/PRMA protocol with heavy-tailed ON/OFF source has been studied. Compared with the random access scheme, the PRMA protocol improves the system performance (such as packet loss, throughput) whether the traffic is SRD or LRD. The less bursty traffic is, the greater the improvement. The buffer design should take into account knowledge about the network traffic such as the presence or absence of the Noah effect in a typical source, especially of _on, the intensity of the Noah effect of ONperiod. The smaller _on is, the smaller the buffering gain, and the more packets will be lost. LRD has impacts on the overall system performance. The Noah effect, especially _off, the intensity of the Noah effect of OFFperiod, has significant impact on the overall system performance such as capacity, time delay, etc. As _off gets closer to 1, the traffic becomes more bursty, the system capacity is decreased and time delay is increased.     

A framework for delivering multicast messages in networks with mobile hosts

To accommodatemobile hosts (MHs) within existing data networks, the static network is augmented with mobile support stations (MSSs) that communicate directly with MHs, usually via wireless links. Connectivity of the overall network changes dynamically as MHs connect to the static network from different locations (MSSs) at different times. Compared to their desktop counterparts, mobile hosts face a new set of constraints namely, low bandwith of the wireless links, tight constraints on power consumption and a significantly lower computing capability. Thus, even without considering failures, integration of mobile computer within existing networks pose a new set of problems. In this paper, we look at the problems associated with delivering multicast meassages to mobile hosts. First, we identify how a mobile host's ability to connect to different MSSs at different times, affects delivery of multicast messages and present schemes to deliver multicast messages to MHs fromatleast-one location, fromatmost-one location, and fromexactly-one location. Next, we introduce multicast groups of mobile hosts wherein each multicast group is associated with a host view, a set of MSSs representing theaggregate location information of the group. A host-view membership algorithm is then presented and combined with the multicast scheme for exactly-once delivery. As a result, to deliver a multicast message to a specified group, copies of the message need be propagated only to the MSSs in the group's host-view.This work was done while the author was a graduate student at Rutgers University.This research work was supported in part by ARPA under contract number DAAH04-95-1-0596, NSF grant numbers CCR 95-09620, IRIS 95-09816 and sponsors of WINLAB.     

High Dynamic Range Design for ΣΔM with Wide Input Ranges

A new design algorithm is introduced to improve the input ranges of Sigma-Delta Modulation (M). Modified digital error correction techniques are proposed and employed to carry out the wide range DAC of a modulator. This design algorithm includes the advantages from both single-bit M and multi-bit M. This paper utilizes a second order lowpass modulator as an explanatory example to demonstrate our design process as well as the performance improvement. The analytical results from a quasilinear model are described to offer a theoretical explanation of the system performance. This algorithm can also be applied to bandpass and MASH architectures.