Related papers: Pseudorandom Bits for Oblivious Branching Programs
We study the Fourier spectrum of functions $f\colon \{0,1\}^{mk} \to \{-1,0,1\}$ which can be written as a product of $k$ Boolean functions $f_i$ on disjoint $m$-bit inputs. We prove that for every positive integer $d$, \[ \sum_{S \subseteq…
The paper develops techniques in order to construct computer programs, pseudorandom number generators (PRNG), that produce uniformly distributed sequences. The paper exploits an approach that treats standard processor instructions…
The paper study counter-dependent pseudorandom generators; the latter are generators such that their state transition function (and output function) is being modified dynamically while working: For such a generator the recurrence sequence…
Short integer linear programs are programs with a relatively small number of constraints. We show how recent improvements on the running-times of solvers for such programs can be used to obtain fast pseudo-polynomial time algorithms for…
We prove that any oblivious algorithm using space $S$ to find the median of a list of $n$ integers from $\{1,...,2n\}$ requires time $\Omega(n \log\log_S n)$. This bound also applies to the problem of determining whether the median is odd…
Pseudo-random number generators (PRNG) are a fundamental element of many security algorithms. We introduce a novel approach to their implementation, by proposing the use of generative adversarial networks (GAN) to train a neural network to…
Subsets of F_2^n that are eps-biased, meaning that the parity of any set of bits is even or odd with probability eps close to 1/2, are powerful tools for derandomization. A simple randomized construction shows that such sets exist of size…
In this paper we prove a space lower bound of $n^{\Omega(k)}$ for non-deterministic (syntactic) read-once branching programs ({\sc nrobp}s) on functions expressible as {\sc cnf}s with treewidth at most $k$ of their primal graphs. This lower…
We give improved hitting sets for two special cases of Read-once Oblivious Arithmetic Branching Programs (ROABP). First is the case of an ROABP with known order of the variables. The best previously known hitting set for this case had size…
A $c$-short program for a string $x$ is a description of $x$ of length at most $C(x) + c$, where $C(x)$ is the Kolmogorov complexity of $x$. We show that there exists a randomized algorithm that constructs a list of $n$ elements that…
We introduce several classes of pseudorandom sequences which represent a natural extension of classical methods in random number generation. The sequences are obtained from constructions on labeled binary trees, generalizing the well-known…
Expander graphs are among the most useful combinatorial objects in theoretical computer science. A line of work studies random walks on expander graphs for their pseudorandomness against various classes of test functions, including…
We present results of extensive statistical and bit level tests on three implementations of a pseudorandom number generator algorithm using the lagged Fibonacci method with an occasional addition of an extra bit. First implementation is the…
Pseudo-random number generators are widely used in many branches of science, mainly in applications related to Monte Carlo methods, although they are deterministic in design and, therefore, unsuitable for tackling fundamental problems in…
Kernel methods are fundamental in machine learning, and faster algorithms for kernel approximation provide direct speedups for many core tasks in machine learning. The polynomial kernel is especially important as other kernels can often be…
Oblivious RAM (ORAM) is a cryptographic primitive that allows a client to securely execute RAM programs over data that is stored in an untrusted server. Distributed Oblivious RAM is a variant of ORAM, where the data is stored in $m>1$…
Pseudo-random arrays and perfect maps are the two-dimensional analogs of M-sequences and de Bruijn sequences, respectively. We modify the definitions to be applied to codes. These codes are also the two-dimensional analogs of certain…
Pseudo-Random Numbers Generators (PRNGs) are algorithms produced to generate long sequences of statistically uncorrelated numbers, i.e. Pseudo-Random Numbers (PRNs). These numbers are widely employed in mid-level cryptography and in…
We present a new approach to constructing of pseudo-random binary sequences (PRS) generators for the purpose of cryptographic data protection, secured from the perpetrator's attacks, caused by generation of masses of hardware errors and…
We study pseudorandomness properties of permutations on $\{0,1\}^n$ computed by random circuits made from reversible $3$-bit gates (permutations on $\{0,1\}^3$). Our main result is that a random circuit of depth $n \cdot \tilde{O}(k^2)$,…