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41,814
Logarithmic space and permutations
, 2013
"... In a recent work, Girard [1] proposed a new and innovative approach to computational complexity based on the proofsasprograms correspondence. In a previous paper [2], the authors showed how Girard proposal succeeds in obtaining a new characterization of coNL languages as a set of operators acting ..."
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Cited by 4 (2 self)
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acting on a Hilbert Space. In this paper, we extend this work by showing that it is also possible to define a set of operators characterizing the class L of logarithmic space languages.
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 increase in computation time of at most a polynomial factor. It is not clear whether this is still true when quantum mechanics is taken into consi ..."
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Cited by 1103 (7 self)
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into consideration. Several researchers, starting with David Deutsch, have developed models for quantum mechanical computers and have investigated their computational properties. This paper gives Las Vegas algorithms for finding discrete logarithms and factoring integers on a quantum computer that take a number
Gradient flows in metric spaces and in the space of probability measures
 LECTURES IN MATHEMATICS ETH ZÜRICH, BIRKHÄUSER VERLAG
, 2005
"... ..."
A Digital Signature Scheme Secure Against Adaptive ChosenMessage Attacks
, 1995
"... We present a digital signature scheme based on the computational diculty of integer factorization. The scheme possesses the novel property of being robust against an adaptive chosenmessage attack: an adversary who receives signatures for messages of his choice (where each message may be chosen in a ..."
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Cited by 985 (43 self)
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were considered in the folklore to be contradictory. More generally, we show how to construct a signature scheme with such properties based on the existence of a "clawfree" pair of permutations  a potentially weaker assumption than the intractibility of integer factorization. The new scheme
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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. This paper considers factoring integers and finding discrete logarithms, two problems which are generally thought to be hard on a classical computer and have been used as the basis of several proposed cryptosystems. Efficient randomized algorithms are given for these two problems on a hypothetical quantum
Greedy Function Approximation: A Gradient Boosting Machine
 Annals of Statistics
, 2000
"... Function approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest{descent minimization. A general gradient{descent \boosting" paradigm is developed for additi ..."
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Cited by 951 (12 self)
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Function approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest{descent minimization. A general gradient{descent \boosting" paradigm is developed
String theory and noncommutative geometry
 JHEP
, 1999
"... We extend earlier ideas about the appearance of noncommutative geometry in string theory with a nonzero Bfield. We identify a limit in which the entire string dynamics is described by a minimally coupled (supersymmetric) gauge theory on a noncommutative space, and discuss the corrections away from ..."
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Cited by 801 (8 self)
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We extend earlier ideas about the appearance of noncommutative geometry in string theory with a nonzero Bfield. We identify a limit in which the entire string dynamics is described by a minimally coupled (supersymmetric) gauge theory on a noncommutative space, and discuss the corrections away from
Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
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Cited by 5350 (67 self)
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long time, ‘variational ’ problems have been identified mostly with the ‘calculus of variations’. In that venerable subject, built around the minimization of integral functionals, constraints were relatively simple and much of the focus was on infinitedimensional function spaces. A major theme
Fuzzy extractors: How to generate strong keys from biometrics and other noisy data. Technical Report 2003/235, Cryptology ePrint archive, http://eprint.iacr.org, 2006. Previous version appeared at EUROCRYPT 2004
 34 [DRS07] [DS05] [EHMS00] [FJ01] Yevgeniy Dodis, Leonid Reyzin, and Adam
, 2004
"... We provide formal definitions and efficient secure techniques for • turning noisy information into keys usable for any cryptographic application, and, in particular, • reliably and securely authenticating biometric data. Our techniques apply not just to biometric information, but to any keying mater ..."
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Cited by 532 (38 self)
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We provide formal definitions and efficient secure techniques for • turning noisy information into keys usable for any cryptographic application, and, in particular, • reliably and securely authenticating biometric data. Our techniques apply not just to biometric information, but to any keying material that, unlike traditional cryptographic keys, is (1) not reproducible precisely and (2) not distributed uniformly. We propose two primitives: a fuzzy extractor reliably extracts nearly uniform randomness R from its input; the extraction is errortolerant in the sense that R will be the same even if the input changes, as long as it remains reasonably close to the original. Thus, R can be used as a key in a cryptographic application. A secure sketch produces public information about its input w that does not reveal w, and yet allows exact recovery of w given another value that is close to w. Thus, it can be used to reliably reproduce errorprone biometric inputs without incurring the security risk inherent in storing them. We define the primitives to be both formally secure and versatile, generalizing much prior work. In addition, we provide nearly optimal constructions of both primitives for various measures of “closeness” of input data, such as Hamming distance, edit distance, and set difference.
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 particular realization of the N = 2 theories, the resulting string field theory is equivalent to a topological theory in six dimensions, the Kodaira– Spencer theory, which may be viewed as the closed string analog of the Chern–Simon theory. Using the mirror map this leads to computation of the ‘number ’ of holomorphic curves of higher genus curves in Calabi–Yau manifolds. It is shown that topological amplitudes can also be reinterpreted as computing corrections to superpotential terms appearing in the effective 4d theory resulting from compactification of standard 10d superstrings on the corresponding N = 2 theory. Relations with c = 1 strings are also pointed out.
Results 1  10
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41,814