Random Number Generators: Exploring Pseudo-Random and True Random Processes

Computers, by their very nature, are designed to follow predetermined instructions and generate outputs based on their internal state. This deterministic approach means that, strictly speaking, computers cannot produce truly random outputs. Instead, they generate numbers that appear random but are actually pseudo-random, meaning they depend on a seed value and a mathematical algorithm to produce the sequence. Yet, for many purposes, these pseudo-random numbers are good enough, especially in situations where the ability to reproduce the same sequence is a necessity.

Pseudo-Random Number Generators (PRNGs)

One of the most common tools for generating pseudo-random numbers in coding is the rand() function in Python. This function takes an initial seed value and, using a specific algorithm, generates a sequence of numbers that appear random but are, in fact, deterministic. The seed value allows the exact sequence to be reproduced, which is particularly useful in simulations, testing, and cryptography. While PRNGs are not truly random, they are often adequate for practical applications due to their speed and ease of implementation.

True Random Number Generators (TRNGs)

For applications that require true randomness, such as secure random number generation or high-stakes simulations, physical processes must be utilized. True random number generators (TRNGs) use physical sources of randomness that are inherently unpredictable due to quantum phenomena, thermal fluctuations, or other natural processes. Here, we explore some of the notable digital generators and true random number generators available:

Digital Pseudo-Random Number Generators (PRNGs)

Pseudorandom Number Generator (PRNGs): These are digital devices that use a mathematical algorithm to generate sequences of numbers that appear random. They are based on an initial seed value and can produce reproducible sequences. Notable examples include the Mersenne Twister and Linear Congruential Generator (LCG). Hash Functions: These can also be used to generate random numbers by applying a one-way function to a seed value. However, they are generally slower than PRNGs. Cryptographically Secure Pseudorandom Number Generators (CSPRNGs): These are designed for cryptographic applications and are more secure than standard PRNGs. They are often used in cryptography to ensure the randomness of encryption keys and nonces.

Physical True Random Number Generators (TRNGs)

The reliability of physical TRNGs is based on the inherent unpredictability of certain physical processes. These processes can range from quantum noise to thermal noise and even quantum spin. Here are a few examples:

Quantum Random Number Generators (QRNGs)

Quantum Random Number Generator (QRNG) at ANU: This generator uses the detection of vacuum fluctuations to generate random numbers. However, post-processing is often required to ensure the distribution of the generated numbers is as expected. The cited example of Real time demonstration of high bitrate quantum random number generation with coherent laser light indicates the challenges and improvements needed in this field.

IDQuantique’s Random Number Generator

IDQuantique: This device uses a more complex and less transparent method to generate true random numbers. Their white paper provides more details on their process and the challenges they face in achieving a perfectly random distribution.

NIST Entanglement Sensor

NIST Quantum Random Number Generator: The NIST sensor uses the results of the Bell test to guarantee the randomness of the generated numbers. Despite initial efficiency challenges, this approach holds promise for future improvements in randomness generation.

Improving Randomness with Post-Processing

Even when using physical TRNGs, post-processing is often necessary to improve the distribution of generated numbers. For instance, taking independent ordered pairs of results and detecting transitions can improve the uniform distribution but at the cost of reducing the number of output samples. This is a common trade-off in achieving perfect randomness.

Inversion Controlled by PRNGs

Interestingly, some researchers suggest that inverting the output of a pseudo-random generator can produce streams with excellent statistical properties, ensuring equal probability while maintaining a random distribution. This approach combines the speed of pseudo-random generation with the desired statistical properties of true randomness.

Ultimately, the choice between a PRNG and a TRNG depends on the specific requirements of the application. While PRNGs are faster and easier to implement, TRNGs provide true randomness and are crucial for applications where predictable behavior can compromise security or accuracy.

Keywords: random number generators, pseudo-random number generators, true random number generators

IDQuantique White Paper for more details on their TRNG process.