A pseudorandom generator is usually found in systems such as Linux or in related programming language libraries. The pseudorandom generator used today for most operating systems and various programming languages exhibits similar behavior. What Is a Pseudorandom Generator (PRG) Application? Given the initial seed value, the numbers generated by the algorithm follow one after another, and the successive numbers appear to be independent and random. Pseudorandom number generation allows these deterministic algorithms to work with a seed value as a starting point. Computers don't generate truly random numbers because the algorithms involved in computers are deterministic processes. Pseudorandom is a concept used in computer science. Pseudorandom numbers can be predictable and in some cases lead to unintended consequences. However, for security-critical applications, it is recommended to choose hardware or physical sources that generate true random numbers. For instance, in game development, cryptography, simulations, statistical analysis, and testing. Pseudorandom numbers are used in many applications. They are generated by the number generator and are based on a seed value that is used as a starting point. Pseudorandom numbers represent numbers that are not easily correlated when analyzed. Pseudorandom numbers are not completely random but behave like random numbers. Therefore, in most cases, random functions in programming languages generate pseudorandom numbers. True randomness is considered an elusive property because computers perform deterministic operations. In computer science, it is often used to refer to operations that are associated with randomness. Random, the concept of randomness, can be used to mean unpredictability, randomness, and uncertainty. For example, the movements of the planets initially seemed random and accidental, but early astronomers were able to make predictions by discovering a pattern in the planets. Different ideas have been put forward about what it means for data to be random and about the nature of probability. The axiomatic unpredictability definition and the cryptographically secure definition will not hold for anything other than a uniform distribution.The concept of randomness has long been a topic that philosophers, scientists, statisticians, and other non-specialists have pondered. In all three cases, it is fine to use the word “random” and people will know what you mean from the context, but when it comes to making inferences from the underlying definitions, it is important to be clear. In Cryptography it is defined in terms of an adversary not being able to distinguish output of the RNG from what they would get from a truly uniform distribution. In Cryptography, we are back to unpredictability, but it is defined slightly differently. (Indeed, estimating distributions and parameters from a sample is a huge part of Statistics.) Underlyingly, Statistics uses definitions based on measure theory so that they work over real numbers. In Statistics you can talk about random variables of different distributions. The definition you quote is the “axiomatic unpredictability” one from Information Theory. I think that the question is the result of the collision and overlap of three different areas of mathematics. Even if they aren’t told up front that the distribution is normal, after enough input they will be able to compute good estimates of the distribution and its parameters. In your example of a normal distribution the adversary gets that advantage by picking values near the mode. If you have a non-uniform distribution the adversary will have an advantage when guessing. If your reading materials are leaving you with questions like these, maybe have a look at something more rigorous. Let $\ell$ be a polynomial and let $G$ be a deterministic polynomial-time algorithms such that for any $n$ and any input $ \in \$ For example in Katz & Lindell's textbook (2nd edition), Definition 3.14 (p. And in fact you should be able to conclude that your definition and interpretation implies that the output of a secure PRNG must be uniform.īut the definitions used in theoretical cryptography are much more precise than this. If we follow your logic strictly, then we have to conclude that your proposed attack on the normally-distributed output of $G$ would imply that $G$ is not in fact a secure PRNG by your definition and application thereof. You'd do well to review your readings to see if they stipulate somewhere earlier that when they say "random" they mean uniform random (equiprobable).īut even without such a stipulation that I'd say the definition as you've loosely formulated it and are interpreting it seems to imply equiprobability.
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