randeval

A Python package for generating and evaluating random number sequences. Built for a masters thesis comparing classical PRNGs, CSPRNGs, TRNGs, and quantum random number generators.

• 32 generators across 4 categories (classical, CSPRNG, TRNG, quantum)
• 68 statistical tests (NIST SP 800-22, Dieharder, NIST SP 800-90B, information-theoretic, distribution, autocorrelation, novel)
• 27 randomness extractors across 6 families (debiasing, universal hashing, computational, practical, adaptive, CryptoMite)
• Strongly typed, PEP 561 compliant (py.typed)
• External sequences welcome — wrap any list[int], NDArray, or bytes

Install

cd randeval

# Core: classical + CSPRNG generators and the full statistical-test battery
uv sync

# Optional extras
uv sync --extra quantum      # Qiskit + IBM Quantum generators
uv sync --extra extractors   # CryptoMite extractor constructions
uv sync --extra rendering    # Mitsuba 3 + FLIP (rendering case study)
uv sync --extra dev          # pytest, mypy, nistrng (tests + validation)

# Everything at once
uv sync --all-extras

# Install from PyPI
pip install randeval                                      # core only
pip install "randeval[quantum,extractors,rendering,dev]"  # everything

# Editable install into another project
uv pip install -e .
uv pip install -e ".[quantum,extractors,rendering]"

Package Structure

src/randeval/
├── sequence.py              # RandomSequence — core data object
├── generators/
│   ├── base.py              # Generator ABC
│   ├── classical.py         # 11 classical PRNGs
│   ├── csprng.py            # 6 CSPRNGs
│   ├── trng.py              # 9 TRNGs (API, hardware, environmental)
│   └── quantum.py           # 6 quantum generators (optional)
├── extractors/
│   ├── base.py              # Extractor ABC
│   ├── debiasing.py         # Von Neumann, Peres, Elias, AMLS
│   ├── hashing.py           # 5 universal-hash extractors
│   ├── computational.py     # HMAC, SHA-256 conditioner
│   ├── practical.py         # 9 XOR / decimation-style extractors
│   ├── adaptive.py          # arithmetic coding, min-entropy, fuzzy
│   └── cryptomite_ext.py    # Toeplitz, Circulant, Dodis, Trevisan
├── tests_statistical/
│   ├── base.py              # StatisticalTest ABC, TestResult, Verdict
│   ├── nist.py              # 16 NIST SP 800-22 tests
│   ├── dieharder.py         # 18 Dieharder / Marsaglia tests
│   ├── sp800_90b.py         # 12 NIST SP 800-90B entropy estimators
│   ├── entropy.py           # 8 information-theoretic measures
│   ├── distribution.py      # 6 general statistical tests
│   ├── autocorrelation.py   # Lag-based autocorrelation
│   └── novel.py             # 7 novel tests
└── py.typed

Generators (32)

Classical PRNGs — generators/classical.py (11)

Class	Algorithm	Notes
LCG	Linear Congruential	glibc defaults, configurable bit extraction
MersenneTwister	MT19937	Python's random default
PCG64	Permuted Congruential	NumPy's default
Xorshift128Plus	Xorshift128+	Used in V8/WebKit JS engines
Xoshiro256StarStar	xoshiro256**	Blackman & Vigna, passes BigCrush
LFSR	Linear Feedback Shift Register	Configurable taps/width
MiddleSquare	Von Neumann (1946)	Historical, degenerates quickly
MiddleSquareWeyl	Middle Square Weyl Sequence	Widynski (2020), fixes original
Philox	Philox4x64 counter-based	Used in NumPy/TF/JAX, parallelisable
SFC64	Small Fast Chaotic 64	NumPy BitGenerator option
WichmannHill	Three combined LCGs	Python's pre-MT default

CSPRNGs — generators/csprng.py (6)

Class	Algorithm	Notes
SystemRandom	OS entropy pool	os.urandom / secrets
ChaCha20	ChaCha20 stream cipher	Requires cryptography
AESCTR_DRBG	AES-256-CTR DRBG	Requires cryptography
HMAC_DRBG	HMAC-SHA256 DRBG	stdlib only
Hash_DRBG	SHA-256 DRBG	stdlib only
BlumBlumShub	x² mod pq	Validates p ≡ q ≡ 3 mod 4, coprime seed

TRNGs — generators/trng.py (9)

Class	Entropy Source	Requirements
RandomOrgGenerator	Atmospheric noise	requests, network
ANUQRNGGenerator	Quantum vacuum fluctuations	requests, network
HotBitsGenerator	Radioactive decay (Kr-85)	requests, network
RDRANDGenerator	CPU thermal noise (conditioned)	x86_64 only
RDSEEDGenerator	CPU raw entropy	x86_64 (Broadwell+/Zen+)
HWRNGDevice	Linux /dev/hwrng	Linux, read permission
TimingJitterGenerator	CPU timing jitter	None (quality varies)
AudioNoiseGenerator	Microphone ADC noise	sounddevice, microphone
CameraNoiseLavaRand	Camera sensor noise	opencv-python, camera

Quantum — generators/quantum.py (6, optional)

Class	Circuit	Notes
QiskitSimulator	1-qubit Hadamard	StatevectorSampler, 1 bit/shot
IBMQuantumBackend	1-qubit Hadamard	Real hardware, cloud queue
MultiQubitHadamard	N-qubit parallel H	N bits/shot, sim or real
EntanglementBasedQRNG	Bell pairs (EPR)	CHSH-verifiable quantumness
QuantumPhaseEstimationQRNG	QPE circuit	Multi-bit output per shot
RandomRotationQRNG	Ry(θ) + measure	Parametric bias for extractor testing

Quantum generators require pip install randeval[quantum] (Qiskit + IBM Runtime).

Statistical Tests (68)

NIST SP 800-22 — tests_statistical/nist.py (16)

Frequency, Block Frequency, Runs, Longest Run of Ones, Binary Matrix Rank, DFT Spectral, Non-overlapping Template, Overlapping Template, Maurer's Universal, Linear Complexity, Serial, Approximate Entropy, Cumulative Sums (fwd + bwd), Random Excursions, Random Excursions Variant.

Dieharder / Marsaglia — tests_statistical/dieharder.py (18)

Birthday Spacings, Overlapping Permutations, Parking Lot, Minimum Distance, 3D Spheres, Squeeze, Overlapping Sums, Craps, GCD, Gorilla, Coupon Collector, Gap, Poker, Collision, Bitstream, DNA, Count-the-1s (stream + byte).

NIST SP 800-90B — tests_statistical/sp800_90b.py (12)

Most Common Value, Collision, Markov, Compression, t-Tuple, LRS, Repetition Count, Adaptive Proportion, and the MultiMCW, Lag, MultiMMC and LZ78Y predictors.

Information-Theoretic — tests_statistical/entropy.py (8)

Shannon Entropy, Min-Entropy, Rényi Entropy, Compression Ratio, Lempel-Ziv Complexity, Conditional Entropy, Mutual Information, Permutation Entropy.

Distribution — tests_statistical/distribution.py (6)

Chi-Squared Uniformity, Kolmogorov-Smirnov, Anderson-Darling, Wald-Wolfowitz Runs, Mann-Kendall Trend, Turning Point.

Autocorrelation — tests_statistical/autocorrelation.py (1)

Lag-based autocorrelation test with configurable lag range.

Novel — tests_statistical/novel.py (7)

Running bias, bit-pattern spatial, weight distribution, close pairs, max-of-t, successive differences, byte runs.

Battery helpers

from randeval.tests_statistical import (
    nist_battery,        # 16 NIST SP 800-22 tests
    dieharder_battery,   # 18 Dieharder tests
    sp800_90b_battery,   # 12 NIST SP 800-90B estimators
    entropy_battery,     # 8 entropy tests
    distribution_battery,# 6 distribution tests
    novel_battery,       # 7 novel tests
    full_battery,        # all 68 above combined (+ autocorrelation)
)

Extractors

27 extractors across 6 families:

Family	Count	Examples
Debiasing	4	Von Neumann, Peres, Elias, AMLS
Universal hashing	5	Toeplitz, linear, inner-product, LHL, polynomial
Computational	2	HMAC, SHA-256 conditioner
Practical	9	XOR, block parity, bit decimation, CRC32, subsampling, …
Adaptive	3	arithmetic coding, min-entropy, fuzzy extractor
CryptoMite	4	Toeplitz, Circulant, Dodis, Trevisan

Implement the Extractor ABC to add more.

The CryptoMite constructions (Toeplitz, Circulant, Dodis, Trevisan) require uv sync --extra extractors.

Intrusive Generator Warnings

Generators that access peripherals, network, or cloud services emit a UserWarning on instantiation:

Generator	Warning
RandomOrgGenerator	HTTPS to api.random.org
ANUQRNGGenerator	HTTPS to qrng.anu.edu.au
HotBitsGenerator	HTTPS to fourmilab.ch
TimingJitterGenerator	CPU busy-loop
AudioNoiseGenerator	Microphone access
CameraNoiseLavaRand	Camera access, LED activates
IBMQuantumBackend	IBM cloud queue, token transmitted
MultiQubitHadamard	IBM cloud queue (when use_real_backend=True)

Suppress with warnings.filterwarnings("ignore", category=UserWarning).

Quick Usage

from randeval import RandomSequence
from randeval.generators.classical import LCG
from randeval.tests_statistical import full_battery, nist_battery
from randeval.tests_statistical.nist import FrequencyTest

# Generate from a generator
seq = RandomSequence.from_generator(LCG(seed=42), n=10_000)

# Or wrap externally-produced bits
import numpy as np
seq = RandomSequence(np.array([0, 1, 1, 0, 1], dtype=np.uint8))

# Or from raw bytes
seq = RandomSequence(b"\xaf\x3c\x01")

# Run a single test
result = seq.test(FrequencyTest())
print(result)  # TestResult('NIST 1: Frequency (Monobit)', p=0.7342, pass)

# Run the full NIST battery
results = seq.test_suite(nist_battery())

# Run all 68 battery tests
results = seq.test_suite(full_battery())

# Apply an extractor then re-test
from randeval.extractors.von_neumann import VonNeumannExtractor
clean = seq.extract(VonNeumannExtractor())
clean_results = clean.test_suite(nist_battery())

Extending

Implement Generator, Extractor, or StatisticalTest to add new components:

from randeval.generators.base import Generator
import numpy as np
from numpy.typing import NDArray

class MyGenerator(Generator):
    @property
    def name(self) -> str:
        return "MyGenerator"

    def generate(self, n: int) -> NDArray[np.uint8]:
        # Return array of n bits (0s and 1s)
        ...

Testing & Validation

uv run --extra dev pytest tests -q          # full suite (extractors + statistical-test validation)
uv run --extra dev pytest tests/statistical -q   # just the statistical-test validation
uv run --extra dev mypy --strict src/       # type-check (clean under strict mode)

tests/statistical/ validates the statistical tests against ground truth:

• test_nist_kat.py — known-answer tests against NIST SP 800-22 Rev 1a worked examples (the 100-bit pi sequence and the vendored data.e/data.pi reference files in fixtures/).
• test_null_calibration.py — confirms tests reject good random data at ~alpha and produce ~Uniform(0,1) p-values.
• test_cross_impl.py — cross-checks against nistrng (optional dev dep).
• test_sanity.py — good data passes the battery, broken data is flagged.
• run_calibration.py — heavier 200-stream tiered calibration sweep (uv run --extra dev python -m tests.statistical.run_calibration).