# Questions tagged [pseudorandomness]

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### $RL=L$ Progress Since 2006

Reingold, Trevisan, and Vadhan's breakthrough 2006 paper (http://dl.acm.org/citation.cfm?id=1132583) reduced the problem of showing $RL=L$ to producing pseudorandom walks on regular digraphs that are ...
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### From Extractors to Pseudorandom Generators?

Luca Trevisan showed how many constructions of pseudorandom generators can in fact be thought of as extractor constructions: http://www.cs.berkeley.edu/~luca/pubs/extractor-full.pdf Is there a ...
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### Explicit balanced matrix

Is it possible to build an explicit $N \times N$ $0/1$-matrix with $N^{1.5}$ ones such that every $N^{0.499} \times N^{0.499}$ submatrix contains less than $N^{0.501}$ ones? Or probably it is ...
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### Are theoretically sound pseudorandom generators used in practice?

As far as I'm aware, most implementations of pseudorandom number generation in practice use methods such as linear shift feedback registers (LSFRs), or these "Mersenne Twister" algorithms. While they ...
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### Fooling arbitrary symmetric functions

A distribution $\mathcal{D}$ is said to $\epsilon$-fool a function $f$ if $|E_{x\in U}(f(x)) - E_{x\in \mathcal{D}}(f(x))| \leq \epsilon$. And it is said to fool a class of functions if it fools every ...
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### Problem-Dependent Derandomization

The famous result of Impagliazzo and Wigderson in '97 cemented our belief that BPP is most likely the same as P; that is, problems that can be efficiently solved with randomness can also be ...
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### Are there any distributions with only polynomially many non-zero Fourier coefficients and a small support?

For a distribution X over $\{0,1\}^n$, we can define the Fourier coefficient of the distribution as $\hat{Y}(s)= \textbf{E}_{y\in Y}({\chi_s(y)})$. The question I have is, do there exist distributions ...
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### Rigorous proof that a random function and a random permutation cannot be distinguished in polynomial time

I have a background in number theory and I'm trying to learn how to reason rigorously about algorithms. I'm reading chapter 2 of Katz and Lindell's Introduction to Modern Cryptography. Show that no ...
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### Where is Yao's original proof that distinguishers imply next-bit-predictors?

In the theory of pseudorandomness, there is a well-known lemma that says roughly the following. Let $X$ be a probability distribution over $\{0, 1\}^n$. Suppose there is an efficient algorithm that ...
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