Related papers: Pseudorandom Generators for Read-Once Branching Pr…
The generation of pseudorandom elements over finite fields is fundamental to the time, space and randomness complexity of randomized algorithms and data structures. We consider the problem of generating $k$-independent random values over a…
Within the Guessing Random Additive Noise Decoding (GRAND) family, ordered reliability bits GRAND (ORBGRAND) has received considerable attention for its hardware-friendly exploitation of soft information. Existing information-theoretic…
An operating system kernel uses cryptographically secure pseudorandom number generator for creating address space localization randomization offsets to protect memory addresses to processes from exploration, storing users' password securely…
Pseudorandom number generation (PRNG) is a key element in hardware security platforms like field-programmable gate array FPGA circuits. In this article, 18 PRNGs belonging in 4 families (xorshift, LFSR, TGFSR, and LCG) are physically…
One-way state generators (OWSG) are natural quantum analogs to classical one-way functions. We consider statistically-verifiable OWSGs (sv-OWSG), which are potentially weaker objects than OWSGs. We show that O(n/log(n))-copy sv-OWSGs (n…
Pseudorandom number generators have been widely used in Monte Carlo methods, communication systems, cryptography and so on. For cryptographic applications, pseudorandom number generators are required to generate sequences which have good…
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…
Linear-feedback shift register (LFSR) based pseudo-random number generator (PRNG) has applications in a plethora of fields. The issue of being linear is generally circumvented by introducing non-linearities as per the required applications,…
Random linear codes are a workhorse in coding theory, and are used to show the existence of codes with the best known or even near-optimal trade-offs in many noise models. However, they have little structure besides linearity, and are not…
Series and polynomial regression are able to approximate the same function classes as neural networks. However, these methods are rarely used in practice, although they offer more interpretability than neural networks. In this paper, we…
An M-sequence generated by a primitive polynomial has many interesting and desirable properties. A pseudo-random array is the two-dimensional generalization of an M-sequence. There are non-primitive polynomials all of whose non-zero…
In this paper we study a family of algorithms, introduced by Chan [SODA 1999] and called LR-algorithms, for drawing ordered rooted binary trees. In particular, we are interested in constructing LR-drawings (that are drawings obtained via…
Given a circuit $G: \{0, 1\}^n \to \{0, 1\}^m$ with $m > n$, the *range avoidance* problem ($\text{Avoid}$) asks to output a string $y\in \{0, 1\}^m$ that is not in the range of $G$. Besides its profound connection to circuit complexity and…
We show that a black-box construction of a pseudorandom generator from a one-way function needs to make Omega(n/log(n)) calls to the underlying one-way function. The bound even holds if the one-way function is guaranteed to be regular. In…
We connect the study of pseudodeterministic algorithms to two major open problems about the structural complexity of $\mathsf{BPTIME}$: proving hierarchy theorems and showing the existence of complete problems. Our main contributions can be…
Random constraint satisfaction problems (CSPs) such as random $3$-SAT are conjectured to be computationally intractable. The average case hardness of random $3$-SAT and other CSPs has broad and far-reaching implications on problems in…
Reed-Solomon codes are a classic family of error-correcting codes consisting of evaluations of low-degree polynomials over a finite field on some sequence of distinct field elements. They are widely known for their optimal unique-decoding…
Stochastic Gradient Descent (SGD) has proven to be remarkably effective in optimizing deep neural networks that employ ever-larger numbers of parameters. Yet, improving the efficiency of large-scale optimization remains a vital and highly…
NIST SP800-22 (2010) proposes the state of art testing suite for (pseudo) random generators to detect deviations of a binary sequence from randomness. On the one hand, as a counter example to NIST SP800-22 test suite, it is easy to…
The ordered-reliability bits (ORB) variant of guessing random additive noise decoding (GRAND), known as ORBGRAND, achieves remarkably low time complexity at high code rates compared to other GRAND variants. However, its computational…