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### How to construct random functions

Oded Goldreich, Shafi Goldwasser, Silvio Micali
1986 Journal of the ACM
A 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!  ...

### How to Construct Quantum Random Functions

Mark Zhandry
2012 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science
. • The 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.  ...

### How to Construct Pseudo-random Permutations from Pseudo-random Functions [chapter]

Michael Luby, Charles Rackoff
Lecture Notes in Computer Science
Let F " be the set of all 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 .  ...

### On Perfect and Adaptive Security in Exposure-Resilient Cryptography [chapter]

Yevgeniy Dodis, Amit Sahai, Adam Smith
2001 Lecture Notes in Computer Science
security of AONT 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  ...

### To be computable is not the same as to be constructible

Walter Carnielli
2016 Filosofia Unisinos
It is argued that 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.  ...

### Construction of normal fuzzy numbers: A case study with earthquake waveform data

Dhruba Das, Anamika Dutta, Supahi Mahanta, Hemanta Baruah
2013 Journal of Process Management. New Technologies
In this article, we have shown 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

Anamika Dutta, Dhruba Das, Hemanta Baruah
2013 Journal of Process Management. New Technologies
In this article, we have shown 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]

S.N. Dorogovtsev, J.F.F. Mendes, A.N. Samukhin
2002 arXiv   pre-print
(a) We propose a "static" 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 ?  ...

### The Generalized Randomized Iterate and Its Application to New Efficient Constructions of UOWHFs from Regular One-Way Functions [chapter]

Scott Ames, Rosario Gennaro, Muthuramakrishnan Venkitasubramaniam
2012 Lecture Notes in Computer Science
This paper presents the Generalized 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  ...

### Modern architecture of random graphs: Constructions and correlations [article]

S.N. Dorogovtsev, J.F.F. Mendes, A.N. Samukhin
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 .  ...

### Chosen Ciphertext Security via UCE [chapter]

Takahiro Matsuda, Goichiro Hanaoka
2014 Lecture Notes in Computer Science
Bellare, Hoang, and Keelveedhi (CRYPTO'13) introduced a security notion for a family of (hash) 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.  ...

### How to Construct a Random Probability Measure

Michael Monticino
2001 International Statistical Review
Dubins & Freedman (1967) note that any method for generating a probability measure at 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

Michael Monticino
2001 International Statistical Review
Dubins & Freedman (1967) note that any method for generating a probability measure at 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.  ...

### Multivariate Gaussian Random Fields with Oscillating Covariance Functions using Systems of Stochastic Partial Differential Equations [article]

Xiangping Hu, Finn Lindgren, Daniel Simpson, Håvard Rue
2013 arXiv   pre-print
We discuss 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.  ...

### Secure Signatures and Chosen Ciphertext Security in a Quantum Computing World [chapter]

Dan Boneh, Mark Zhandry
2013 Lecture Notes in Computer Science
We 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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