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How to construct random functions

1986
*
Journal of the ACM
*

A

doi:10.1145/6490.6503
fatcat:v6xme25n2rgtplxkobzpzlehry
*constructive*theory of*randomness*for*functions*, based on computational complexity, is developed, and a pseudorandom*function*generator is presented. ... This generator is a deterministic polynomial-time algorithm that transforms pairs (g, r), where g is any one-way*function*and r is a*random*k-bit string,*to*polynomial-time computable functionsf,: { 1, ... Leonid Levin relentlessly encouraged us*to*get this result and, once obtained, helped us*to*better understand it in the course of so many inspiring discussions. Thank you Lenia! ...##
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How to Construct Quantum Random Functions

2012
*
2012 IEEE 53rd Annual Symposium on Foundations of Computer Science
*

. • The

doi:10.1109/focs.2012.37
dblp:conf/focs/Zhandry12
fatcat:gxoloovb4bet7igx2vswrzbexu
*construction*from pseudorandom synthesizers due*to*Naor and Reingold [NR95]. • The direct*construction*based on the Learning With Errors problem due*to*Banerjee, Peikert, and Rosen [BPR11]. ... The first, which we call standard-security, allows the adversary*to*be quantum, but requires queries*to*the*function**to*be classical. ... Acknowledgments We would like*to*thank Dan Boneh for his guidance and many insightful discussions. This work was supported by NSF and DARPA. ...##
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How to Construct Pseudo-random Permutations from Pseudo-random Functions
[chapter]

*
Lecture Notes in Computer Science
*

Let F " be the set of all

doi:10.1007/3-540-39799-x_34
dblp:conf/crypto/LubyR85
fatcat:aur5valuebfwpibkj4lgyqlkru
*functions*from n bits*to*n bits. Let /" specify is pseudo-.' or each key k of a given length a*function*ft E F " . We say f"*random*if the following two properties hold: ... If a*random*key k is chosen, fc "looks like" a*random**function*chosen from F n*to*any algorithm which is allowed*to*evaiuste j t at polynomial in a input values. ... (1) Given a key k and an input a of length n , the time*to*evaluate ft ( a ) is polynomial in n . ...##
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On Perfect and Adaptive Security in Exposure-Resilient Cryptography
[chapter]

2001
*
Lecture Notes in Computer Science
*

security of AONT

doi:10.1007/3-540-44987-6_19
fatcat:sk7linjhdffareha3guvabryzy
*to*a static property • Main tool: -"Almost-perfect resilient*functions*" (APRF) [Kurosawa-Johansson-Stinson '97] • Simple*construction*of APRF: Pick*random*hash*function*-Will ... • Intuition: A*random**function*is an APRF with high probability (proof by Chernoff bounds) •*Construction*: Pick a*random*(n/log n)-wise independent hash*function*s = k + 2log (1/ε) + O(log n) with high ...##
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To be computable is not the same as to be constructible

2016
*
Filosofia Unisinos
*

It is argued that

doi:10.4013/fsu.2016.172.19
fatcat:ng6q2e6pajgb5ei3p6pdsqamyu
*constructive**functions*cannot be replaced by recursive*functions*. Nonconstructive mathematics (apparently) fail*to*have a computational meaning. But what about the converse? ... Sundholm asks: "Is every*function*used in*constructive*mathematics recursive?" ... Indeed, it is well known that Bishop takes the notion of*constructive**function*as primitive, refusing*to*identify it with any formal notion. ...##
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Construction of normal fuzzy numbers: A case study with earthquake waveform data

2013
*
Journal of Process Management. New Technologies
*

In this article, we have shown

doi:10.5937/jpmnt1301001d
fatcat:b3tfe7lwffdv7hihj2x7waffxm
*how**to**construct*normal fuzzy numbers using data from earthquake waveform and have studied the pattern of the membership curve of the waveform. ... According*to*the*Randomness*-Fuzziness Consistency Principle, two independent laws of*randomness*in [α, β] and [β, γ] are necessary and sufficient*to*define a normal fuzzy number [α, β, γ]. ... But*how*exactly*to**construct*the membership*function*of a fuzzy number mathematically remained a problem. ...##
###
Construction of the membership function of normal fuzzy numbers

2013
*
Journal of Process Management. New Technologies
*

In this article, we have shown

doi:10.5937/jpmnt1302082d
fatcat:qeiihdwzmzgcdfehhlpd52qg4y
*how**to**construct*normal fuzzy number using daily temperature data. ... According*to*the*Randomness*-Fuzziness Consistency Principle, two independent laws of*randomness*in [α, β] and [β, γ] are necessary and sufficient*to*define a normal fuzzy number [α, β, γ]. ... But*how*exactly*to**construct*the membership*function*of a fuzzy number mathematically remained a problem. ...##
###
How to construct a correlated net
[article]

2002
*
arXiv
*
pre-print

(a) We propose a "static"

arXiv:cond-mat/0206131v1
fatcat:fwqa6mgt7bco7nzj5eyt72jvuq
*construction*procedure for*random*networks with given correlations of the degrees of the nearest-neighbor vertices. ... (b) We generalize the notion of preferential linking and introduce a new category, pair preference and a pair preference*function*for the attaching of edges*to*pairs of vertices. ... [7] we called such*constructions*a microcanonical ensemble of*random*graphs.*How*can such graphs be*constructed*for large N ? ...##
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The Generalized Randomized Iterate and Its Application to New Efficient Constructions of UOWHFs from Regular One-Way Functions
[chapter]

2012
*
Lecture Notes in Computer Science
*

This paper presents the Generalized

doi:10.1007/978-3-642-34961-4_11
fatcat:motsd4mllfdh3h4dblc23xjsou
*Randomized*Iterate of a (regular) one-way*function*f and show that it can be used*to*build Universal One-Way Hash*Function*(UOWHF) families with O(n 2 ) key length. ... We then show that Shoup's technique for UOWHF domain extension can be used*to*improve the efficiency of the previous*construction*. ... Haitner, et. al [7] simplified the*construction**to*use just pair-wise hashing and further derandomized the*construction*by showing*how**to*generate the n hash-*functions*required at the*randomization*steps ...##
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Modern architecture of random graphs: Constructions and correlations
[article]

2002
*
arXiv
*
pre-print

*How*

*to*

*construct*an equilibrium net with given degree-degree correlations. 10. ...

*How*

*to*

*construct*a growing scale-free net with a given clustering (towards a real-space renormalization group for networks). ...

*How*

*to*

*construct*an equilibrium net with given degree-degree correlations. 10 . ...

##
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Chosen Ciphertext Security via UCE
[chapter]

2014
*
Lecture Notes in Computer Science
*

Bellare, Hoang, and Keelveedhi (CRYPTO'13) introduced a security notion for a family of (hash)

doi:10.1007/978-3-642-54631-0_4
fatcat:m2opqcuys5c4xewszq2lynml3m
*functions*called universal computational extractor (UCE), and showed*how*it can be used*to*realize various ... Then, as our main positive result, we show*how**to**construct*a CCA secure PKE scheme using only CPA secure PKE and a UCE as building blocks. ... The authors would like*to*thank Pooya Farshim for giving us a detailed overview of their attack [12] on UCE security using indistinguishability obfuscation. ...##
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How to Construct a Random Probability Measure

2001
*
International Statistical Review
*

Dubins & Freedman (1967) note that any method for generating a probability measure at

doi:10.1111/j.1751-5823.2001.tb00484.x
fatcat:cf6subncvzfhzgksyvcurptjyu
*random*is equivalent*to*selecting a non-decreasing right continuous*function*at*random*, and generating a continuous ... onto an interval [a, f] is a one-*to*-one*function*, f, from [a, b] onto [a, P] such that f and its inverse*function*are continuous. ... So*how*do you generate a probability distribution at*random*? (Or,*how*do you*construct*a homeomorphism or a convex*function*at*random*?) That is the topic of this article. ...##
###
How to Construct a Random Probability Measure

2001
*
International Statistical Review
*

Dubins & Freedman (1967) note that any method for generating a probability measure at

doi:10.2307/1403534
fatcat:khm7j73cdzaytf472wsv6m7fum
*random*is equivalent*to*selecting a non-decreasing right continuous*function*at*random*, and generating a continuous ... onto an interval [a, f] is a one-*to*-one*function*, f, from [a, b] onto [a, P] such that f and its inverse*function*are continuous. ... So*how*do you generate a probability distribution at*random*? (Or,*how*do you*construct*a homeomorphism or a convex*function*at*random*?) That is the topic of this article. ...##
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Multivariate Gaussian Random Fields with Oscillating Covariance Functions using Systems of Stochastic Partial Differential Equations
[article]

2013
*
arXiv
*
pre-print

We discuss

arXiv:1307.1384v1
fatcat:f6hq4f3zpncrdkmr3weracnavu
*how**to*build systems of SPDEs that introduces oscillation characteristics in the covariance*functions*of the multivariate GRFs. ... In this paper we propose a new approach for*constructing*multivariate Gaussian*random*fields (GRFs) with oscillating covariance*functions*through systems of stochastic partial differential equations (SPDEs ... In this section we are going*to*discuss*how**to**construct*multivariate GRFs where some components of the*random*fields have oscillating covariance*functions*. ...##
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Secure Signatures and Chosen Ciphertext Security in a Quantum Computing World
[chapter]

2013
*
Lecture Notes in Computer Science
*

We

doi:10.1007/978-3-642-40084-1_21
fatcat:3ovse3btfjg5xon7tcv46csq2m
*construct*classical systems that remain secure when exposed*to*such quantum queries. ... For signatures, we*construct*two compilers that convert classically secure signatures into signatures secure in the quantum setting and apply these compilers*to*existing post-quantum signatures. ... Along these lines, Zhandry [Zha12b] showed*how**to**construct*pseudorandom*functions*(PRFs) that remain secure even when the adversary is allowed*to*issue quantum queries*to*the PRF. ...
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