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Topic: Pseudorandomness

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	Pseudorandomness - Wikipedia, the free encyclopedia
		Pseudorandom sequences typically exhibit statistical randomness while being generated by an entirely deterministic causal process.
		Pseudorandom distributions can be generated deterministically from short random seeds, which are much shorter than the length of the pseudorandom output.
		This definition of pseudorandomness is used primarily in the study of pseudorandom generators.
	en.wikipedia.org /wiki/Pseudorandomness (1023 words)

	Abstracts: DIMACS Workshop on Pseudorandomness and Explicit Combinatorial Constructions
		A pseudorandom generator for such rectangles is a deterministic function maping short strings to elements in [m]^d such that these elements form a good sample space for approximating each rectangle's volume.
		Pseudorandom generators for combinatorial rectangles have been actively studied for a while in theoretical computer science.
		Explicit constructions of extractors have a variety of important applications, such as the simulation of randomized algorithms using weak random sources; the explicit construction of expanders and superconcentrators; randomness-efficient reduction of error in sampling and in randomized algorithms; and simpler proofs of certain complexity-theoretic results.
	dimacs.rutgers.edu /Workshops/Pseudorandom/abstract.html (2105 words)

	Encryption Software: Books: Pseudorandomness and Cryptographic Applications (Princeton Computer Science Notes), ...
		Pseudorandomness and Cryptographic Applications, by Michael Luby, presents the mathematical underpinnings of one-way hash functions, which can be used to implement pseudorandom number generators.
		A pseudorandom generator is an easy-to-compute function that stretches a short random string into a much longer string that "looks" just like a random string to any efficient adversary.
		One immediate application of a pseudorandom generator is the construction of a private key cryptosystem that is secure against chosen plaintext attack.
	www.primasoft.com /book_encryption/cryptography_book_11.htm (318 words)

	Table of Contents for Luby, M.: Pseudorandomness and Cryptographic Applications.
		Definition of a pseudorandom generator, the next bit test, and the proof that the two definitions are equivalent.
		Construction of a pseudorandom generator that stretches by a polynomial amount from a pseudorandom generator that stretches by one bit.
		Definition of a pseudorandom invertible permutation generator and discussion of applications to the construction of a block private key cryptosystern secure against chosen plaintext attack.
	press.princeton.edu /TOCs/c5154.html (644 words)

	Cortona Lectures on Pseudorandomness and Combinatorial Constructions
		A series of 11 lectures on pseudorandomness, derandomization, average-case complexity, and the explicit constructions of expanders and other combinatorial objects.
		We will then see the Nisan-Wigderson construction of a pseudorandom generator under considerably weaker complexity assumption, and then show how to further weaken those assumptions by proving a connection between the average-case complexity and the worst-case complexity of certain problems.
		Pseudorandomness and combinatorial constructions David Zuckerman, UT Austin
	www.cs.berkeley.edu /~luca/cortona (487 words)

	P versus NP:Natural Proofs - QEDen (Site not responding. Last check: 2007-09-08)
		They furthermore demonstrated that every complexity-theoretic lower bound proven thus far is natural in this sense, except for those obtained by simulation and diagonalization (these are in a certain sense covered by the result that P vs. NP does not relativize).
		Pseudorandomness is a concept that was developed primarily with cryptography in mind, although it has found other applications.
		Thus, the "hardness" property doubles as a "not pseudorandom" property, proving that pseudorandom function generators do not exist, since if they did we could by definition not detect them.
	www.qeden.com /wiki/P_versus_NP:Natural_Proofs (617 words)

	Pseudorandomness and Combinatorial Constructions
		This course will have two main, tightly woven, threads: the study of conditional results about pseudorandomness and derandomization, showing that if certain complexity-theoretic conjectures are true then every probabilistic algorithm has an efficient deterministic simulations; and the study of (unconditional) explicit construction of pseudorandom objects, such as randomness extractors and expander graphs.
		Cryptographically strong pseudorandom generators: the Blum-Micali-Yao construction, the Goldreich-Levin theorem, the coding-theoretic and Fourier-analytic interpretations of the Goldreich-Levin theorem.
		Pseudorandom generators for derandomization: the Nisan-Wigderson generator and the Impagliazzo-Wigderson worst-case to average case reduction.
	www.cs.berkeley.edu /~luca/pacc (1029 words)

	Amazon.com: Pseudorandomness and Cryptographic Applications (Princeton Computer Science Notes): Books: Michael Luby (Site not responding. Last check: 2007-09-08)
		The concept of a pseudorandom distribution is introduced as a distribution where no efficient procedure or program can distinguish it from a uniform distribution.
		Pseudorandom generators are polynomial-time deterministic programs that take a randomly selected seed and expand it into a pseudorandom bit sequence.
		Pseudorandom generators are introduced as a solution to the problem of sending secure messages that are longer than the private key.
	www.amazon.com /Pseudorandomness-Cryptographic-Applications-Princeton-Computer/dp/0691025460 (1150 words)

	Random Number Generators
		Handbook of Applied Cryptography; Chapter 5, Pseudorandom Bits and Sequences (22 pages), Alfred J. Menezes, Paul C. van Oorschot and Scott A. Vanstone, July 1999.
		On Pseudorandomness with respect to Deterministic Observers, O. Goldreich and A. Wigderson, May 4, 2000.
		Inversive pseudorandom number generators: concepts, results, and links, Peter Hellekalek, Proceedings of the 1995 Winter Simulation Conference, pp.
	cnscenter.future.co.kr /crypto/algorithm/random.html (703 words)

	ECCC Report TR00-056 and related Papers
		Abstract: In the theory of pseudorandomness, potential (uniform) observers are modeled as probabilistic polynomial-time machines.
		We conclude that randomness of the observer is essential to the theory of pseudorandomness.
		What we actually prove is that the hypotheses of two central theorems (in the theory of pseudorandomness) hold unconditionally when stated with respect to deterministic polynomial-time algorithms.
	eccc.hpi-web.de /eccc-reports/2000/TR00-056/index.html (172 words)

	Pseudorandom numbers
		To overcome these problems, the concept of pseudorandom numbers has been proposed: simply substitute the physical device by a computer algorithm that generates numbers in a deterministic, fast and reproducible way.
		We have to start in the limited world of algorithms in order to characterize the pseudorandom numbers in a way that is both mathematically precise and practically relevant.
		One difference between PRNs and RNs is that in the former case we know the deterministic character of the numbers, whereas this is left open to philosophical discussion in the latter case.
	random.mat.sbg.ac.at /~ste/dipl/node10.html (539 words)

	in theory: Pseudorandomness and more pseudorandomness
		For example, in the setting of looking for arithmetic progressions of length 3, a subset of {1,...,N} is "structured" if it has a large Fourier coefficient and it is pseudorandom if it has approximately the same number of length-3 progressions of a random subset of {1,...,N} with the same density.
		If what remains is pseudorandom, we are fine, otherwise we subtract another structured part, and so on.
		The advantage of this type of decomposition (whether it is done explicitely or it is implicit in the proof) is that one can use techniques from analysis and probability to analyse the pseudorandom part and (depending on the definition of "structure") techniques from analysis and geometry to analyse the structured part.
	in-theory.blogspot.com /2006/08/pseudorandomness-and-more.html (1136 words)

	Pseudorandomness and Combinatorial Constructions
		Randomization is very useful in almost all areas of computer science, such as algorithms, cryptography, and distributed computing.
		A pseudorandom generator is a deterministic algorithm that takes as input a short random seed and outputs a long string which is ``random'' enough for the purpose at hand.
		In fact, a pseudorandom generator is such an object.
	www.cs.utexas.edu /users/diz/395T/01 (502 words)

	in theory: The primes are random except when they are not
		The idea is to start by thinking of the following probabilistic "model" for prime numbers: a number N is "prime" with probability 1/ln N, and to observe that certain properties of the primes (for example, the prime number theorem) hold in this model.
		These results and conjectures are part of an even bigger set of results whose spirit is that "multiplicative structure is pseudorandom with respect to addition," that can be seen in various results that have applications to combinatorial constructions.
		This comes up most directly in sum-product results in finite fields and over the integers, used to construct extractors, in Weil's result on character sums, which is used to construct eps-biased generators, in certain expander constructions related to Ramanujan graphs, and so on.
	in-theory.blogspot.com /2006/10/primes-are-random-except-when-they-are.html (1144 words)

	Pseudorandomness (expositions by Oded Goldreich) (Site not responding. Last check: 2007-09-08)
		A fresh view at the question of randomness was taken in the theory of computing: It has been postulated that a distribution is pseudorandom if it cannot be told apart from the uniform distribution by any efficient procedure.
		This paradigm, originally associating efficient procedures with polynomial-time algorithms, has been applied also with respect to a variety of limited classes of such distinguishing procedures.
		Chapter 3 in Foundations of Cryptography focuses on the archetypical case of pseudorandom generators (withstanding any polynomial-time distinguisher).
	www.wisdom.weizmann.ac.il /~oded/c-indist.html (185 words)

	Modern Cryptography, Probabilistic Proofs and Pseudorandomness
		Starting with the general paradigm, we survey the archetypical case of pseudorandom generators (withstanding any polynomial-time distinguisher), as well as generators withstanding space-bounded distinguishers, the derandomization of complexity classes such as BPP, and some special-purpose generators.
		In particular, we survey the basic tools of cryptography -- computational difficulty, pseudorandomness and zero-knowledge proofs -- and the basic utilities -- encryption, signatures, and general cryptographic protocols.
		(The overlap with Chapter 1 is small, and the presentation is quite different.) Likewise, Chapter 3 surveys various notions of pseudorandom generators, viewing the one discussed in Chapter 1 as an archetypical instantiation of a general paradigm.
	www.wisdom.weizmann.ac.il /~oded/book1.html (1682 words)

	Papers on Pseudorandomness by Oded Goldreich
		Goldreich and S. Micali, Increasing the Expansion of Pseudorandom Generators, 1984.
		Goldreich and A. Wigderson, Improved derandomization of BPP using a hitting set generator, May 1999.
		Goldreich and A. Wigderson, On Pseudorandomness with respect to Deterministic Observers, May 2000.
	www.wisdom.weizmann.ac.il /~oded/pp_pseudo.html (476 words)

	CiteULike: Pseudorandomness and Combinatorial Constructions (Site not responding. Last check: 2007-09-08)
		In computer science, probabilistic algorithms are sometimes simpler and more efficient than the best known deterministic algorithms for the same problem.
		<br />Despite this evidence for the power of random choices, the computational theory of pseudorandomness shows that, under certain complexity-theoretic assumptions, every probabilistic algorithm has an efficient deterministic simulation and a large class of applications of the the probabilistic method can be converted into explicit constructions.
		Despite this evidence for the power of random choices, the computational theory of pseudorandomness shows that, under certain complexity-theoretic assumptions, every probabilistic algorithm has an efficient deterministic simulation and a large class of applications of the the probabilistic method can be converted into explicit constructions.
	www.citeulike.org /user/BarrosH/article/502045 (287 words)

	Report 4, 2000 Abstract (Site not responding. Last check: 2007-09-08)
		However, the harnessing and use of randomness from physical processes is not an easy problem.
		In this survey paper we examine the use (and sometimes misuse) of pseudorandomness in achieving security (secrecy, identification, authentication, etc.) and robustness (error detection, error correction, routing, etc.) in modern electronic communication systems.
		Using the wrong type of pseudorandomness can be catastrophic.
	www.ma.rmit.edu.au /kepler/reports/2000/r4_2000.html (107 words)

	Amazon.ca: Modern Cryptography, Probalistic Proofs and Pseudorandomness: Books: Oded Goldreich (Site not responding. Last check: 2007-09-08)
		The areas are modern cryptography, the study of probabilistic proof systems, and the theory of computational pseudorandomness.
		These areas are modern cryptography, the study of probabilistic proof systems, & the theory of computational pseudorandomness.
		Cryptography is concerned with the construction of schemes which are robust against malicious attempts to make these schemes deviate from their prescribed functionality. Read the first page
	www.amazon.ca /Modern-Cryptography-Probalistic-Proofs-Pseudorandomness/dp/354064766X (765 words)

	Canisius College - Willem Fouché
		Course Abstract: The application of ideas from number theory to the theory of error-correction codes, cryptography and the design of efficient algorithms which are based on discrete patterns which are “pseudorandom”, rank among the deepest aspects of the information sciences.
		The efficient simulation of randomness have incredibly interesting applications, not only to the design of information systems but also to the understanding of the intrinsic time complexity of algorithms.
		In addition, he studied the recursive aspects of Ramsey theory which soon led to an interest in the role of symmetry in Ramsey theory.
	www.canisius.edu /topos/fouche.asp (626 words)

	On the Pseudorandomness of KASUMI Type Permutations - Iwata, Yagi, Kurosawa (ResearchIndex)
		In this paper, we study the pseudorandomness of idealized KASUMI type permutations for adaptive adversaries.
		1 the pseudorandomness of KASUMI type permutations - Iwata, Yagi et al.
		1 Pseudorandomness of MISTY-type transformations and the block..
	citeseer.ist.psu.edu /684283.html (354 words)

	Seminar (Site not responding. Last check: 2007-09-08)
		In this survey talk we describe connections between the conditional "derandomization" results of the computational theory of pseudorandomness and unconditional explicit constructions of certain combinatorial objects such as error-correcting codes and "randomness extractors."
		Luca Trevisan is an associate professor of computer science at U.C. Berkeley.
		Luca's research is in theoretical computer science, and most of his work has been in two areas: (i) the relation between pseudorandomness, derandomization, average-case complexity, coding theory, and the explicit construction of expander-like graphs; and (ii) the theory of probabilistically checkable proofs and its relation to the approximability of combinatorial optimization problems.
	www.cse.cuhk.edu.hk /~temmy/seminar/070111a.htm (289 words)

	FreeTechBooks.com - Computational Complexity: A Conceptual Perspective
		This effort may be viewed as a "high-level" study of computation.
		The theory of NP-completeness as well as the studies of approximation, probabilistic proof systems, pseudorandomness and cryptography all fall within this category.
		The current book focuses on the latter effort (or direction).
	www.freetechbooks.com /about411.html (639 words)

	Randomness and Pseudorandomness in Secure and Robust Communications (ResearchIndex)
		Randomness and Pseudorandomness in Secure and Robust Communications (2000)
		Because of this, pseudorandomness is substituted for randomness in many cases.
		In this survey paper we examine the use (and sometimes misuse) of pseudorandomness in achieving security (secrecy, identification, authentication, etc.) and robustness (error detection, error correction, routing, etc.) in modern...
	citeseer.ist.psu.edu /boztas00randomness.html (511 words)

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