Related papers: A Pseudorandom Generator for Functions of Low-Degr…
In this paper we present several heuristic algorithms, including a Genetic Algorithm (GA), for obtaining polynomial threshold function (PTF) representations of Boolean functions (BFs) with small number of monomials. We compare these among…
We give a pseudorandom generator that fools $m$-facet polytopes over $\{0,1\}^n$ with seed length $\mathrm{polylog}(m) \cdot \log n$. The previous best seed length had superlinear dependence on $m$. An immediate consequence is a…
We construct pseudorandom generators of seed length $\tilde{O}(\log(n)\cdot \log(1/\epsilon))$ that $\epsilon$-fool ordered read-once branching programs (ROBPs) of width $3$ and length $n$. For unordered ROBPs, we construct pseudorandom…
A technique for controlling errors in the functioning of nodes for the formation of $q$-valued pseudo-random sequences (PRS) operating under both random errors and errors generated through intentional attack by an attacker is provided, in…
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…
Pseudorandom bit generators (PRBG) can be designed to take the advantage of some hard number theoretic problems such as the discrete logarithm problem (DLP). Such type of generators will have good randomness and unpredictability properties…
With the widespread use of communication technologies, cryptosystems are therefore critical to guarantee security over open networks as the Internet. Pseudo-random number generators (PRNGs) are fundamental in cryptosystems and information…
We show that there is a randomized algorithm that, when given a small constant-depth Boolean circuit $C$ made up of gates that compute constant-degree Polynomial Threshold functions or PTFs (i.e., Boolean functions that compute signs of…
The hardness vs.~randomness paradigm aims to explicitly construct pseudorandom generators $G:\{0,1\}^r \rightarrow \{0,1\}^m$ that fool circuits of size $m$, assuming the existence of explicit hard functions. A ``high-end PRG'' with seed…
A Pseudo-Random Number Generator (PRNG) is any algorithm generating a sequence of numbers approximating properties of random numbers. These numbers are widely employed in mid-level cryptography and in software applications. Test suites are…
The $\epsilon$-approximate degree $deg_\epsilon(f)$ of a Boolean function $f$ is the least degree of a real-valued polynomial that approximates $f$ pointwise to error $\epsilon$. The approximate degree of $f$ is at least $k$ iff there…
We construct a pseudorandom generator which fools read-$k$ oblivious branching programs and, more generally, any linear length oblivious branching program, assuming that the sequence according to which the bits are read is known in advance.…
Polynomial threshold functions (PTFs) are an important low-complexity class of Boolean functions, with strong connections to learning theory and approximation theory. Recent work on learning and testing PTFs has exploited structural and…
Gaussian processes have been successful in both supervised and unsupervised machine learning tasks, but their computational complexity has constrained practical applications. We introduce a new approximation for large-scale Gaussian…
This project develops a pseudo-random number generator (PRNG) using the logistic map, implemented in Verilog HDL on an FPGA and processes its output through a Central Limit Theorem (CLT) function to achieve a Gaussian distribution. The…
Introduced in [CG24], pseudorandom error-correcting codes (PRCs) are a new cryptographic primitive with applications in watermarking generative AI models. These are codes where a collection of polynomially many codewords is computationally…
We study weighted pseudorandom generators (WPRGs) and derandomizations for read-once branching programs (ROBPs). Denote $n$ and $w$ as the length and the width of a ROBP. We have the following results. For standard ROBPs, we give an…
For Boolean functions computed by read-once, depth-$D$ circuits with unbounded fan-in over the de Morgan basis, we present an explicit pseudorandom generator with seed length $\tilde{O}(\log^{D+1} n)$. The previous best seed length known…
Let X be randomly chosen from {-1,1}^n, and let Y be randomly chosen from the standard spherical Gaussian on R^n. For any (possibly unbounded) polytope P formed by the intersection of k halfspaces, we prove that |Pr [X belongs to P] - Pr [Y…
Deep Gaussian Processes (DGP) are hierarchical generalizations of Gaussian Processes (GP) that have proven to work effectively on a multiple supervised regression tasks. They combine the well calibrated uncertainty estimates of GPs with the…