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517
Efficient Algorithms for Elliptic Curve Cryptosystems
, 1997
"... Elliptic curves are the basis for a relative new class of publickey schemes. It is predicted that elliptic curves will replace many existing schemes in the near future. It is thus of great interest to develop algorithms which allow efficient implementations of elliptic curve crypto systems. This th ..."
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Cited by 66 (9 self)
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Elliptic curves are the basis for a relative new class of publickey schemes. It is predicted that elliptic curves will replace many existing schemes in the near future. It is thus of great interest to develop algorithms which allow efficient implementations of elliptic curve crypto systems. This thesis deals with such algorithms. Efficient algorithms for elliptic curves can be classified into lowlevel algorithms, which deal with arithmetic in the underlying finite field and highlevel algorithms, which operate with the group operation. This thesis describes three new algorithms for efficient implementations of elliptic curve cryptosystems. The first algorithm describes the application of the KaratsubaOfman Algorithm to multiplication in composite fields GF ((2 n ) m ). The second algorithm deals with efficient inversion in composite Galois fields of the form GF ((2 n ) m ). The third algorithm is an entirely new approach which accelerates the multiplication of points which i...
Agentbased computational models and generative social science
 Complexity
, 1999
"... This article argues that the agentbased computational model permits a distinctive approach to social science for which the term “generative ” is suitable. In defending this terminology, features distinguishing the approach from both “inductive ” and “deductive ” science are given. Then, the followi ..."
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Cited by 64 (0 self)
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This article argues that the agentbased computational model permits a distinctive approach to social science for which the term “generative ” is suitable. In defending this terminology, features distinguishing the approach from both “inductive ” and “deductive ” science are given. Then, the following specific contributions to social science are discussed: The agentbased computational model is a new tool for empirical research. It offers a natural environment for the study of connectionist phenomena in social science. Agentbased modeling provides a powerful way to address certain enduring—and especially interdisciplinary—questions. It allows one to subject certain core theories—such as neoclassical microeconomics—to important types of stress (e.g., the effect of evolving preferences). It permits one to study how rules of individual behavior give rise—or “map up”—to macroscopic regularities and organizations. In turn, one can employ laboratory behavioral research findings to select among competing agentbased (“bottom up”) models. The agentbased approach may well have the important effect of decoupling individual rationality from macroscopic equilibrium and of separating decision science from social science more generally. Agentbased modeling offers powerful new forms of hybrid theoreticalcomputational work; these are particularly relevant to the study of nonequilibrium systems. The agentbased approach invites the interpretation of society as a distributed computational device, and in turn the interpretation of social dynamics as a type of computation. This interpretation raises important foundational issues in social science—some related to intractability, and some to undecidability proper. Finally, since “emergence” figures prominently in this literature, I take up the connection between agentbased modeling and classical emergentism, criticizing the latter and arguing that the two are incompatible. � 1999 John Wiley &
TinyECC: A Configurable Library for Elliptic Curve Cryptography in Wireless Sensor Networks
"... Public Key Cryptography (PKC) has been the enabling technology underlying many security services and protocols in traditional networks such as the Internet. In the context of wireless sensor networks, elliptic curve cryptography (ECC), one of the most efficient types of PKC, is being investigated to ..."
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Cited by 63 (1 self)
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Public Key Cryptography (PKC) has been the enabling technology underlying many security services and protocols in traditional networks such as the Internet. In the context of wireless sensor networks, elliptic curve cryptography (ECC), one of the most efficient types of PKC, is being investigated to provide PKC support in sensor network applications so that the existing PKCbased solutions can be exploited. This paper presents the design, implementation, and evaluation of TinyECC, a configurable library for ECC operations in wireless sensor networks. The primary objective of TinyECC is to provide a readytouse, publicly available software package for ECCbased PKC operations that can be flexibly configured and integrated into sensor network applications. TinyECC provides a number of optimization switches, which can turn specific optimizations on or off based on developers ’ needs. Different combinations of the optimizations have different execution time and resource consumptions, giving developers great flexibility in integrating TinyECC into sensor network applications. This paper also reports the experimental evaluation of TinyECC on several common sensor platforms, including MICAz, Tmote Sky, and Imote2. The evaluation results show the impacts of individual optimizations on the execution time and resource consumptions, and give the most computationally efficient and the most storage efficient configuration of TinyECC.
Recent Advances In Randomized QuasiMonte Carlo Methods
"... We survey some of the recent developments on quasiMonte Carlo (QMC) methods, which, in their basic form, are a deterministic counterpart to the Monte Carlo (MC) method. Our main focus is the applicability of these methods to practical problems that involve the estimation of a highdimensional inte ..."
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Cited by 59 (12 self)
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We survey some of the recent developments on quasiMonte Carlo (QMC) methods, which, in their basic form, are a deterministic counterpart to the Monte Carlo (MC) method. Our main focus is the applicability of these methods to practical problems that involve the estimation of a highdimensional integral. We review several QMC constructions and dierent randomizations that have been proposed to provide unbiased estimators and for error estimation. Randomizing QMC methods allows us to view them as variance reduction techniques. New and old results on this topic are used to explain how these methods can improve over the MC method in practice. We also discuss how this methodology can be coupled with clever transformations of the integrand in order to reduce the variance further. Additional topics included in this survey are the description of gures of merit used to measure the quality of the constructions underlying these methods, and other related techniques for multidimensional integration. 1 2 1.
An objectoriented randomnumber package with many long streams and substreams
 Operations Research
, 2002
"... Multiple independent streams of random numbers are often required in simulation studies, for instance, to facilitate synchronization for variancereduction purposes, and for making independent replications. A portable set of software utilities is described for uniform randomnumber generation. It pro ..."
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Cited by 51 (8 self)
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Multiple independent streams of random numbers are often required in simulation studies, for instance, to facilitate synchronization for variancereduction purposes, and for making independent replications. A portable set of software utilities is described for uniform randomnumber generation. It provides for multiple generators (streams) running simultaneously, and each generator (stream) has its sequence of numbers partitioned into many long disjoint contiguous substreams. The basic underlying generator for this implementation is a combined multiple recursive generator with period length of approximately 2 191, proposed in a previous paper. A C++ interface is described here. Portable implementations are available in C, C++, and Java via the Online Companion to this paper on the Operations Research website. This report is an expanded version of the article by L’Ecuyer et al. (2001).
Evaluation of sampling for data mining of association rules
 In 7th Intl. Wkshp. Research Issues in Data Engg
, 1997
"... Discovery of association rules is a prototypical problem in data mining. The current algorithms proposed for data mining of association rules make repeated passes over the database to determine the commonly occurring itemsets (or set of items). For large databases, the I/O overhead in scanning the d ..."
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Cited by 50 (10 self)
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Discovery of association rules is a prototypical problem in data mining. The current algorithms proposed for data mining of association rules make repeated passes over the database to determine the commonly occurring itemsets (or set of items). For large databases, the I/O overhead in scanning the database can be extremely high. In this paper we show that random sampling of transactions in the database is an effective method for finding association rules. Sampling can speed up the miningprocess by more than an order of magnitudeby reducing I/O costs and drastically shrinking the number of transaction to be considered. We may also be able to make the sampled database resident in mainmemory. Furthermore, we show that sampling can accurately represent the data patterns in the database with high confidence. We experimentally evaluate the effectiveness of sampling on different databases, and study the relationship between the performance, and the accuracy and confidence of the chosen sample. 1.
Tables Of Linear Congruential Generators Of Different Sizes And Good Lattice Structure
, 1999
"... . We provide sets of parameters for multiplicative linear congruential generators (MLCGs) of different sizes and good performance with respect to the spectral test. For ` = 8; 9; : : : ; 64; 127; 128, we take as a modulus m the largest prime smaller than 2 ` , and provide a list of multipliers a ..."
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Cited by 49 (16 self)
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. We provide sets of parameters for multiplicative linear congruential generators (MLCGs) of different sizes and good performance with respect to the spectral test. For ` = 8; 9; : : : ; 64; 127; 128, we take as a modulus m the largest prime smaller than 2 ` , and provide a list of multipliers a such that the MLCG with modulus m and multiplier a has a good lattice structure in dimensions 2 to 32. We provide similar lists for poweroftwo moduli m = 2 ` , for multiplicative and nonmultiplicative LCGs. 1. Introduction A multiplicative linear congruential generator (MLCG) is defined by a recurrence of the form xn = axn\Gamma1 mod m (1) where m and a are integers called the modulus and the multiplier , respectively, and xn 2 Zm = f0; : : : ; m \Gamma 1g is the state at step n. To obtain a sequence of "random numbers" in the interval [0; 1), one can define the output at step n as un = xn=m: (2) We use the expression "the MLCG (m; a)" to denote a sequence that obeys (1) and (2). Th...
A brief history of cellular automata
, 2000
"... Cellular automata are simple models of computation which exhibit fascinatingly complex behavior. They have captured the attention of several generations of researchers, leading to an extensive body of work. Here we trace a history of cellular automata from their beginnings with von Neumann to the pr ..."
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Cited by 46 (2 self)
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Cellular automata are simple models of computation which exhibit fascinatingly complex behavior. They have captured the attention of several generations of researchers, leading to an extensive body of work. Here we trace a history of cellular automata from their beginnings with von Neumann to the present day. The emphasis is mainly on topics closer to computer science and mathematics rather than physics, biology or other applications. The work should be of interest to both new entrants into the field as well as researchers working on particular aspects of cellular automata.
Efficient Arithmetic in Finite Field Extensions with Application in Elliptic Curve Cryptography
 Journal of Cryptology
, 2000
"... . This contribution focuses on a class of Galois field used to achieve fast finite field arithmetic which we call an Optimal Extension Field (OEF), first introduced in [3]. We extend this work by presenting an adaptation of Itoh and Tsujii's algorithm for finite field inversion applied to OEFs. I ..."
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Cited by 46 (7 self)
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. This contribution focuses on a class of Galois field used to achieve fast finite field arithmetic which we call an Optimal Extension Field (OEF), first introduced in [3]. We extend this work by presenting an adaptation of Itoh and Tsujii's algorithm for finite field inversion applied to OEFs. In particular, we use the facts that the action of the Frobenius map in GF (p m ) can be computed with only m 1 subfield multiplications and that inverses in GF (p) may be computed cheaply using known techniques. As a result, we show that one extension field inversion can be computed with a logarithmic number of extension field multiplications. In addition, we provide new extension field multiplication formulas which give a performance increase. Further, we provide an OEF construction algorithm together with tables of Type I and Type II OEFs along with statistics on the number of pseudoMersenne primes and OEFs. We apply this new work to provide implementation results using these me...
Detecting Perfect Powers In Essentially Linear Time
 Math. Comp
, 1998
"... This paper (1) gives complete details of an algorithm to compute approximate kth roots; (2) uses this in an algorithm that, given an integer n>1, either writes n as a perfect power or proves that n is not a perfect power; (3) proves, using Loxton's theorem on multiple linear forms in logarithms, th ..."
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Cited by 41 (12 self)
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This paper (1) gives complete details of an algorithm to compute approximate kth roots; (2) uses this in an algorithm that, given an integer n>1, either writes n as a perfect power or proves that n is not a perfect power; (3) proves, using Loxton's theorem on multiple linear forms in logarithms, that this perfectpower decomposition algorithm runs in time (log n) . 1.