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Particle Swarm Optimization Algorithm for Integer Factorization Problem (IFP)
"... This paper presents particle swarm optimization (PSO) method to find the prime factors of a composite number. Integer factorization is a well known NP hard problem and security of many cryptosystem is based on difficulty of integer factorization. A particle swarm optimization algorithm for integer f ..."
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This paper presents particle swarm optimization (PSO) method to find the prime factors of a composite number. Integer factorization is a well known NP hard problem and security of many cryptosystem is based on difficulty of integer factorization. A particle swarm optimization algorithm for integer
ForwardSecure Blind Signature Schemes Based on Integer Factorization Problem
, 2006
"... c©2006 by the author ..."
PolynomialTime Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
 SIAM J. on Computing
, 1997
"... A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time by at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. ..."
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Cited by 1277 (4 self)
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. This paper considers factoring integers and finding discrete logarithms, two problems which are generally thought to be hard on a classical computer and which have been used as the basis of several proposed cryptosystems. Efficient randomized algorithms are given for these two problems on a hypothetical
Algorithms for Quantum Computation: Discrete Logarithms and Factoring
, 1994
"... A computer is generally considered to be a universal computational device; i.e., it is believed able to simulate any physical computational device with a cost in computation time of at most a polynomial factol: It is not clear whether this is still true when quantum mechanics is taken into consider ..."
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Cited by 1111 (5 self)
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of steps which is polynomial in the input size, e.g., the number of digits of the integer to be factored. These two problems are generally considered hard on a classical computer and have been used as the basis of several proposed cryptosystems. (We thus give the first examples of quantum cryptanulysis.)
FastSLAM: A Factored Solution to the Simultaneous Localization and Mapping Problem
 In Proceedings of the AAAI National Conference on Artificial Intelligence
, 2002
"... The ability to simultaneously localize a robot and accurately map its surroundings is considered by many to be a key prerequisite of truly autonomous robots. However, few approaches to this problem scale up to handle the very large number of landmarks present in real environments. Kalman filterbase ..."
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Cited by 599 (10 self)
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The ability to simultaneously localize a robot and accurately map its surroundings is considered by many to be a key prerequisite of truly autonomous robots. However, few approaches to this problem scale up to handle the very large number of landmarks present in real environments. Kalman filter
Factoring wavelet transforms into lifting steps
 J. FOURIER ANAL. APPL
, 1998
"... This paper is essentially tutorial in nature. We show how any discrete wavelet transform or two band subband filtering with finite filters can be decomposed into a finite sequence of simple filtering steps, which we call lifting steps but that are also known as ladder structures. This decompositio ..."
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Cited by 584 (8 self)
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in the biorthogonal, i.e, nonunitary case. Like the lattice factorization, the decomposition presented here asymptotically reduces the computational complexity of the transform by a factor two. It has other applications, such as the possibility of defining a waveletlike transform that maps integers to integers.
Proof verification and hardness of approximation problems
 IN PROC. 33RD ANN. IEEE SYMP. ON FOUND. OF COMP. SCI
, 1992
"... We show that every language in NP has a probablistic verifier that checks membership proofs for it using logarithmic number of random bits and by examining a constant number of bits in the proof. If a string is in the language, then there exists a proof such that the verifier accepts with probabilit ..."
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Cited by 797 (39 self)
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in the proof (though this number is a very slowly growing function of the input length). As a consequence we prove that no MAX SNPhard problem has a polynomial time approximation scheme, unless NP=P. The class MAX SNP was defined by Papadimitriou and Yannakakis [82] and hard problems for this class include
Risk and protective factors for alcohol and other drug problems in adolescence and early adulthood: Implications for substance abuse prevention
 Psychological Bulletin
, 1992
"... The authors suggest that the most promising route to effective strategies for the prevention of adolescent alcohol and other drug problems is through a riskfocused approach. This approach requires the identification of risk factors for drug abuse, identification of methods by which risk factors hav ..."
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Cited by 725 (18 self)
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The authors suggest that the most promising route to effective strategies for the prevention of adolescent alcohol and other drug problems is through a riskfocused approach. This approach requires the identification of risk factors for drug abuse, identification of methods by which risk factors
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