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Random Number Generation from Pulsars

Hayder Tirmazi

TL;DR

The paper addresses obtaining cryptographically strong randomness from astrophysical timing data without specialized hardware. It models pulsar timing residuals as a $k$-source and applies a strong randomness extractor via the Leftover Hash Lemma, using a universal hash (SHAKE-256) to produce near-uniform bits, with empirical min-entropy evidence across multiple pulsars and validation by the NIST suite. The main contributions are a formal cryptographic guarantee under a plausible physical model, a practical extraction pipeline, and open-source tools with public pulsar data. The work highlights a hardware-free, environmentally robust RNG option that can support cryptographic primitives, Monte Carlo simulations, probabilistic data structures, and machine learning pipelines, while outlining open challenges such as broader pulsar coverage and deployment considerations.

Abstract

Pulsars exhibit signals with precise inter-arrival times that are on the order of milliseconds to seconds, depending on the individual pulsar. There are subtle variations in the timing of pulsar signals. We show that these variations can serve as a natural entropy source for the creation of Random Number Generators (RNGs). We also explore the effects of using randomness extractors to increase the entropy of random bits extracted from Pulsar timing data. To evaluate the quality of the Pulsar RNG, we model its entropy as a $k$-source and use well-known cryptographic results to show its closeness to a theoretically ideal uniformly random source. To remain consistent with prior work, we also show that the Pulsar RNG passes well-known statistical tests such as the NIST test suite.

Random Number Generation from Pulsars

TL;DR

The paper addresses obtaining cryptographically strong randomness from astrophysical timing data without specialized hardware. It models pulsar timing residuals as a -source and applies a strong randomness extractor via the Leftover Hash Lemma, using a universal hash (SHAKE-256) to produce near-uniform bits, with empirical min-entropy evidence across multiple pulsars and validation by the NIST suite. The main contributions are a formal cryptographic guarantee under a plausible physical model, a practical extraction pipeline, and open-source tools with public pulsar data. The work highlights a hardware-free, environmentally robust RNG option that can support cryptographic primitives, Monte Carlo simulations, probabilistic data structures, and machine learning pipelines, while outlining open challenges such as broader pulsar coverage and deployment considerations.

Abstract

Pulsars exhibit signals with precise inter-arrival times that are on the order of milliseconds to seconds, depending on the individual pulsar. There are subtle variations in the timing of pulsar signals. We show that these variations can serve as a natural entropy source for the creation of Random Number Generators (RNGs). We also explore the effects of using randomness extractors to increase the entropy of random bits extracted from Pulsar timing data. To evaluate the quality of the Pulsar RNG, we model its entropy as a -source and use well-known cryptographic results to show its closeness to a theoretically ideal uniformly random source. To remain consistent with prior work, we also show that the Pulsar RNG passes well-known statistical tests such as the NIST test suite.

Paper Structure

This paper contains 7 sections, 2 theorems, 7 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Generating Random Bits
  3. Evaluation
  4. Cryptographic Guarantees
  5. Statistical Tests
  6. Discussion
  7. Formal Definitions & Proofs

Key Result

Theorem 1

Let $X$ be a $k$-source with universe $U$. Fix $\varepsilon > 0$. Let $\mathcal{H}$ be a universal hash family of size $2^d$ with output length $m = k - 2\log_{2}(\frac{1}{\varepsilon})$. Define Then $\mathcal{E}$ is a strong $(k, \varepsilon/2)$ extractor with seed length $d$ and output length $m$.

Figures (4)

  • Figure 1: Timing Variations in $\mu s$ for the J0030+0451 and J1918-0642 pulsars with Modified Julian Date (MJD) and Year plotted on the $x$ axis
  • Figure 2: Entropy of Different Quantification Methods for 2 Pulsars across EPTA and NANOGrav data
  • Figure 3: Normalized PSR J1918-0642 residuals on EPTA data (above) and NANOGrav data (below).
  • Figure 4: Entropy for different randomness extractors on data from PSR J0030+0451 (EPTA).

Theorems & Definitions (9)

  • Definition 1: Statistical Distance $\Delta$
  • Definition 2: $\varepsilon$-close
  • Definition 3: Min-entropy
  • Definition 4: k-source
  • Definition 5: Randomness-Extractor
  • Definition 6: Universal hash family
  • Theorem 1: Leftover hash lemma
  • Theorem 2
  • proof