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What are the best ways to evaluate the quality of a random number generator?

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Random number generators (RNGs) are essential for many applications, such as cryptography, simulation, gaming, and statistical analysis. However, not all RNGs are equally reliable, and some may produce biased, correlated, or predictable outputs. Therefore, it is important to evaluate the quality of a RNG before using it for a specific purpose. In this article, you will learn about some of the best ways to test a RNG and how to interpret the results.

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Piyush Kumar

Software Development Engineer 2 @ Amazon | Artificial General Intelligence | Generative AI
Darshan Sharma

Full Stack Developer | React, Node.Js, GCP, AWS

1 Theoretical background

A RNG is a function or a device that produces a sequence of numbers that are seemingly random, meaning that they have no discernible pattern or regularity. There are two main types of RNGs: deterministic and non-deterministic. Deterministic RNGs, also known as pseudo-random number generators (PRNGs), use an algorithm and a seed value to generate the sequence. Non-deterministic RNGs, also known as true random number generators (TRNGs), rely on physical phenomena, such as quantum events, thermal noise, or atmospheric noise, to produce the sequence. Both types of RNGs have advantages and disadvantages, depending on the application and the required level of randomness.

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2 Randomness criteria

In order to evaluate the quality of a RNG, we need to define some criteria for randomness. John von Neumann proposed a framework in 1951 that consists of four levels of randomness. Level 0 means the numbers are not random and can be predicted or reproduced; Level 1 means they have a uniform distribution and are independent of each other; Level 2 means they are statistically random and unpredictable, even with knowledge of the algorithm or device used to generate them; and Level 3 means they are cryptographically random and irreproducible, even with the same algorithm or device. Depending on the application, a certain level of randomness may be necessary. For example, for simulation or gaming purposes, a level 1 RNG may suffice, but cryptography or security purposes may require a level 2 or 3 RNG.

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Piyush Kumar

Software Development Engineer 2 @ Amazon | Artificial General Intelligence | Generative AI
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Uniformity: Numbers should be distributed uniformly across the entire range, avoiding clusters or gaps that could compromise fairness in certain applications. Independence: Each generated number should be independent of the previous ones. The occurrence of a particular number should not influence or predict the next number in the sequence. Low Bias: The generator should minimize bias, ensuring that each number has an equal chance of being generated. Bias can lead to inaccurate simulations or skewed results.

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3 Randomness tests

To test whether a RNG meets a certain level of randomness, we can use various methods and tools that measure different aspects of the output sequence. The frequency test checks if numbers are uniformly distributed, the runs test checks for independent numbers, and the autocorrelation test measures the similarity between the sequence and a shifted version of itself. Additionally, there is a statistical test suite which covers multiple aspects of randomness, such as frequency, runs, autocorrelation, complexity, entropy, etc. Examples of these suites include the NIST Statistical Test Suite, the DIEHARDER Test Suite, and the TestU01 Test Suite.

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Piyush Kumar

Software Development Engineer 2 @ Amazon | Artificial General Intelligence | Generative AI
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Statistical Tests: The sequence should pass rigorous statistical tests for randomness, such as frequency tests, correlation tests, and uniformity tests, to validate its reliability in diverse contexts. Security: In cryptographic applications, the generator should withstand attempts to predict or manipulate the sequence. It should meet specific criteria to ensure a high level of unpredictability and resistance to attacks.

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4 Randomness results

To interpret the results of the randomness tests, we need to consider several factors, such as the sample size, the significance level, the p-value, and the pass/fail criteria. The sample size is the number of numbers generated by the RNG and used for the tests; generally, the larger the sample size, the more reliable the results. The significance level is the probability of rejecting the null hypothesis when it is true; typically, this is set to 0.01 or 0.05. The p-value is the probability of obtaining a test result at least as extreme as the observed one, assuming that the null hypothesis is true; a smaller p-value indicates more evidence against the null hypothesis. Finally, pass/fail criteria are rules for deciding whether a RNG passes or fails a test or a test suite based on the p-value and significance level.

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5 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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Darshan Sharma

Full Stack Developer | React, Node.Js, GCP, AWS
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A primary difficulty in RNGs lies in guaranteeing genuine randomness, particularly in PRNGs, given that they may ultimately cycle through their number sequence or turn foreseeable.

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What are the best ways to evaluate the quality of a random number generator?

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1 Theoretical background

2 Randomness criteria

3 Randomness tests

4 Randomness results

5 Here’s what else to consider

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What are the best ways to evaluate the quality of a random number generator?

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1 Theoretical background

2 Randomness criteria

3 Randomness tests

4 Randomness results

5 Here’s what else to consider

Algorithms

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