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724
Universality in quantum computation
 Proc. R. Soc. London A
, 1995
"... We show that in quantum computation almost every gate that operates on two or more bits is a universal gate. We discuss various physical considerations bearing on the proper definition of universality for computational components such as logic gates. ..."
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Cited by 74 (3 self)
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We show that in quantum computation almost every gate that operates on two or more bits is a universal gate. We discuss various physical considerations bearing on the proper definition of universality for computational components such as logic gates.
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 69 (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...
Monte Carlo simulation and numerical integration
, 1996
"... not be cited or distributed without the author's permission. Section 7 of this draft is incomplete. Suggestions and corrections will be gratefully received and acknowledged. ..."
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Cited by 64 (11 self)
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not be cited or distributed without the author's permission. Section 7 of this draft is incomplete. Suggestions and corrections will be gratefully received and acknowledged.
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 60 (13 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 56 (7 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 Lâ€™Ecuyer et al. (2001).
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 OEF ..."
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Cited by 53 (9 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...
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 52 (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.
Asymptotic Experimental Analysis for the HeldKarp Traveling Salesman Bound
, 1996
"... The HeldKarp (HK) lower bound is the solution to the linear programming relaxation of the standard integer programming formulation of the traveling salesman problem (TSP). For numbers of cities N up to 30,000 or more it can be computed exactly using the Simplex method and appropriate separation alg ..."
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Cited by 51 (5 self)
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The HeldKarp (HK) lower bound is the solution to the linear programming relaxation of the standard integer programming formulation of the traveling salesman problem (TSP). For numbers of cities N up to 30,000 or more it can be computed exactly using the Simplex method and appropriate separation algorithms, and for N up to a million good approximations can be obtained via iterative Lagrangean relaxation techniques first suggested by Held and Karp. In this paper, we consider three applications of our ability to compute/approximate this bound. First, we provide empirical evidence in support of using the HK bound as a standin for the optimal tour length when evaluating the quality of nearoptimal tours. We show that for a wide variety of randomly generated instance types the optimal tour length averages less than 0.8% over the HK bound, and even for the realworld instances in TSPLIB the gap is almost always less than 2%. Moreover, our data indicates that the HK bound can provide substa...
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 48 (15 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...