Pseudorandomness

Pseudorandomness refers to the property of sequences of numbers that appear to be random but are generated by a deterministic process, typically using algorithms. These sequences are called pseudorandom sequences, and they are produced by mathematical algorithms known as pseudorandom number generators (PRNGs).

The Ehrenfeucht–Mycielski sequence is a mathematical construct that originates from the field of combinatorial set theory and is typically studied in the context of discrete mathematics and graph theory. Specifically, it is often related to the study of properties of graphs and their corresponding sequences. The definition of the Ehrenfeucht–Mycielski sequence is connected to the concept of constructing new objects (like graphs or sequences) from existing ones while preserving certain properties.

A hard-core predicate is a concept from cryptography, particularly in the context of cryptographic primitives like pseudorandom generators and one-way functions. It refers to a function or value that is difficult to compute when given only limited information about a related hard problem, typically the output of a one-way function.

PRF advantage refers to the advantage of a particular algorithm (or adversary) in distinguishing a pseudorandom function (PRF) from a truly random function. In cryptography, a pseudorandom function is a function that is efficient to compute and indistinguishable from a random function by any efficient (polynomial-time) adversary. The concept is crucial in evaluating the security of cryptographic primitives.

A Pseudorandom Binary Sequence (PRBS) is a binary sequence that appears to be random but is generated by a deterministic process. This means that, although the sequence may exhibit properties similar to those of truly random sequences (such as having a uniform distribution of ones and zeros, or correlational properties), it is produced using a specific algorithm or mathematical formula, which allows the sequence to be reproduced exactly if the initial conditions (or seed) are known.

A **pseudorandom function family** (PRF family) is a fundamental concept in cryptography and computer science, particularly in the field of secure communication and data protection. Here's a breakdown of the concept: ### Definition - A pseudorandom function family is a collection of functions—typically indexed by a secret key—such that, given a random key from that family, the function behaves like a truly random function to any efficient adversary (e.g., a polynomial time algorithm).

The Pseudorandom Generator Theorem is a fundamental result in theoretical computer science, particularly in the field of complexity theory and cryptography. It establishes a connection between pseudorandomness and the complexity classes of algorithms.

Pseudorandom generators for polynomials are a class of algorithms or mathematical constructions that produce sequences that appear random, based on a smaller set of initial values (or "seeds") while remaining efficiently computable. In the context of polynomials, these generators are used to create outputs that can simulate the behavior of random polynomial evaluations.

Pseudorandom noise (PRN) is a deterministic sequence of numbers that appears to be random but is generated by a predictable algorithm. This means that while the sequence may have properties similar to truly random noise, it can be reproduced exactly if the initial conditions (often referred to as the seed) are known. PRN is commonly used in various applications, particularly in fields such as communications, cryptography, and simulations. **Key Characteristics of Pseudorandom Noise:** 1.

Stochastic screening refers to a probabilistic approach often used in various fields, including statistics, optimization, and machine learning. While the specific context can vary, it generally involves using stochastic methods—techniques that incorporate randomness or probabilistic elements—to sample or evaluate solutions to problems.