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Reed-Muller codes encode an $m$-variate polynomial of degree $r$ by evaluating it on all points in $\{0,1\}^m$. We denote this code by $RM(m,r)$. The minimal distance of $RM(m,r)$ is $2^{m-r}$ and so it cannot correct more than half that…
Random graph generation is an important tool for studying large complex networks. Despite abundance of random graph models, constructing models with application-driven constraints is poorly understood. In order to advance state-of-the-art…
Pseudorandomness has played a central role in modern cryptography, finding theoretical and practical applications to various fields of computer science. A function that generates pseudorandom strings from shorter but truly random seeds is…
In this paper we study the problem of testing of constrained samplers over high-dimensional distributions with $(\varepsilon,\eta,\delta)$ guarantees. Samplers are increasingly used in a wide range of safety-critical ML applications, and…
Despite their ubiquity in language generation, it remains unknown why truncation sampling heuristics like nucleus sampling are so effective. We provide a theoretical explanation for the effectiveness of the truncation sampling by proving…
For an arbitrary degree distribution pair (DDP), we construct a sequence of low-density parity-check (LDPC) code ensembles with girth growing logarithmically in block-length using Ramanujan graphs. When the DDP has minimum left degree at…
One of the pivotal security threats for the embedded computing systems is malicious software a.k.a malware. With efficiency and efficacy, Machine Learning (ML) has been widely adopted for malware detection in recent times. Despite being…
A new framework is introduced for examining and evaluating the fundamental limits of lossless data compression, that emphasizes genuinely non-asymptotic results. The {\em sample complexity} of compressing a given source is defined as the…
De, Trevisan and Tulsiani [CRYPTO 2010] show that every distribution over $n$-bit strings which has constant statistical distance to uniform (e.g., the output of a pseudorandom generator mapping $n-1$ to $n$ bit strings), can be…
We model (interactive) resources that provide Alice with a string $X$ and a guarantee that any Eve interacting with her interface of the resource obtains a (quantum) system $E$ such that the conditional (smooth) min-entropy of $X$ given $E$…
We provide a new upper bound for sampling numbers $(g_n)_{n\in \mathbb{N}}$ associated to the compact embedding of a separable reproducing kernel Hilbert space into the space of square integrable functions. There are universal constants…
Low-depth random circuit codes possess many desirable properties for quantum error correction but have so far only been analyzed in the code capacity setting where it is assumed that encoding gates and syndrome measurements are noiseless.…
We give the best known pseudorandom generators for two touchstone classes in unconditional derandomization: an $\varepsilon$-PRG for the class of size-$M$ depth-$d$ $\mathsf{AC}^0$ circuits with seed length $\log(M)^{d+O(1)}\cdot…
Generating secure random numbers is a central problem in cryptography that needs a reliable source of enough computing entropy. Without enough entropy available - meaning no good source of secure random numbers - a device is susceptible to…
Key extraction via measuring a physical quantity is a class of information theoretic key exchange protocols that rely on the physical characteristics of the communication channel to enable the computation of a shared key by two (or more)…
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…
The behavior of malware threats is gradually increasing, heightened the need for malware detection. However, existing malware detection methods only target at the existing malicious samples, the detection of fresh malicious code and…
This paper studies the parameters for which Reed-Muller (RM) codes over $GF(2)$ can correct random erasures and random errors with high probability, and in particular when can they achieve capacity for these two classical channels.…
Iterative decoders used for decoding low-density parity-check (LDPC) and moderate-density parity-check (MDPC) codes are not characterized by a deterministic decoding radius and their error rate performance is usually assessed through…
In this paper we design non-uniform bit-wise puncturing distributions for irregular non-binary LDPC (NB-LDPC) codes. The puncturing distributions are optimized by minimizing the decoding threshold of the punctured LDPC code, the threshold…