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Finding Small Solutions of a Class of Simultaneous Modular Equations and Applications to Modular Inversion Hidden Number Problem and Inversive Congruential Generator
"... Abstract. In this paper we revisit the modular inversion hidden number problem and the inversive congruential pseudo random number generator and consider how to more efficiently attack them in terms of fewer samples or outputs. We reduce the attacking problem to finding small solutions of systems ..."
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in previous methods, a part of polynomials chosen in our strategies are linear combinations of some polynomials generated in advance and this enables us to achieve a larger upper bound for the desired root. Applying the solving of the above equations to analyze the modular inversion hidden number problem
The modular inversion hidden number problem
 In ASIACRYPT 2001, volume 2248 of LNCS
, 2001
"... Abstract. We study a class of problems called Modular Inverse Hidden Number Problems (MIHNPs). The basic problem in this class is the following: Given many pairs � � � � −1 xi, msbk (α + xi) mod p for random xi ∈ Zp the problem is to find α ∈ Zp (here msbk(x) refers to the k most significant bits o ..."
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Cited by 16 (1 self)
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Abstract. We study a class of problems called Modular Inverse Hidden Number Problems (MIHNPs). The basic problem in this class is the following: Given many pairs � � � � −1 xi, msbk (α + xi) mod p for random xi ∈ Zp the problem is to find α ∈ Zp (here msbk(x) refers to the k most significant bits
PseudoRandom Generation from OneWay Functions
 PROC. 20TH STOC
, 1988
"... Pseudorandom generators are fundamental to many theoretical and applied aspects of computing. We show howto construct a pseudorandom generator from any oneway function. Since it is easy to construct a oneway function from a pseudorandom generator, this result shows that there is a pseudorandom gene ..."
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Cited by 887 (22 self)
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Pseudorandom generators are fundamental to many theoretical and applied aspects of computing. We show howto construct a pseudorandom generator from any oneway function. Since it is easy to construct a oneway function from a pseudorandom generator, this result shows that there is a pseudorandom
A solution to Plato’s problem: The latent semantic analysis theory of acquisition, induction, and representation of knowledge
 PSYCHOLOGICAL REVIEW
, 1997
"... How do people know as much as they do with as little information as they get? The problem takes many forms; learning vocabulary from text is an especially dramatic and convenient case for research. A new general theory of acquired similarity and knowledge representation, latent semantic analysis (LS ..."
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Cited by 1772 (10 self)
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rate to schoolchildren. LSA uses no prior linguistic or perceptual similarity knowledge; it is based solely on a general mathematical learning method that achieves powerful inductive effects by extracting the right number of dimensions (e.g., 300) to represent objects and contexts. Relations to other
Simulating Physics with Computers
 SIAM Journal on Computing
, 1982
"... 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 of at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. ..."
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Cited by 601 (1 self)
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computer. These algorithms take a number of steps polynomial in the input size, e.g., the number of digits of the integer to be factored. AMS subject classifications: 82P10, 11Y05, 68Q10. 1 Introduction One of the first results in the mathematics of computation, which underlies the subsequent development
Large margin methods for structured and interdependent output variables
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2005
"... Learning general functional dependencies between arbitrary input and output spaces is one of the key challenges in computational intelligence. While recent progress in machine learning has mainly focused on designing flexible and powerful input representations, this paper addresses the complementary ..."
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Cited by 612 (12 self)
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that solves the optimization problem in polynomial time for a large class of problems. The proposed method has important applications in areas such as computational biology, natural language processing, information retrieval/extraction, and optical character recognition. Experiments from various domains
KodairaSpencer theory of gravity and exact results for quantum string amplitudes
 Commun. Math. Phys
, 1994
"... We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particu ..."
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Cited by 545 (60 self)
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We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a
A Tutorial on Visual Servo Control
 IEEE Transactions on Robotics and Automation
, 1996
"... This paper provides a tutorial introduction to visual servo control of robotic manipulators. Since the topic spans many disciplines our goal is limited to providing a basic conceptual framework. We begin by reviewing the prerequisite topics from robotics and computer vision, including a brief review ..."
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Cited by 822 (25 self)
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review of coordinate transformations, velocity representation, and a description of the geometric aspects of the image formation process. We then present a taxonomy of visual servo control systems. The two major classes of systems, positionbased and imagebased systems, are then discussed. Since any
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