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SecureRolls

Description

This is an experimental project for educational purposes. It's a small script to collect randomness from dice rolls and estimate its entropy.

Entropy

Entropy is a measure of how unpredictable your random source is.

Why

I started this project to explore generating entropy from dice rolls at home. My goal is to produce a cryptographically secure amount of entropy — at least 128 bits — from dice rolls. In this script I assume a heavily biased die to test how much entropy can be extracted for different numbers of rolls and probability distributions.

Ultimately, my goal is to validate a methodology to generate the entropy needed to create Bitcoin wallets securely at home without relying solely on the system PRNG(pseudo-random number generators) or CSPRNG(cryptografically secure pseudo-random number generators).

Requirements

You will need Ruby installed. I recommend using rbenv.

Run

ruby generate_data.rb

Test

sudo apt-get install ent
sudo apt-get install dieharder

ent raw_entropy.bin
dieharder -a -f raw_entropy.bin

Quick guide to reading ent results

  • Entropy (bits per byte): range 0–8. Closer to 8 is better. Multiply by file size to get total bits (bits/byte × bytes). This is a Shannon-style estimate — useful but optimistic for cryptographic use.
  • Compression estimate: shows how much the file could be reduced. Large reduction (e.g., 80%+) means a lot of predictable structure — not good for cryptographic randomness.
  • Chi-square: tests whether byte frequencies match what we'd expect from truly random data. Very large values (and tiny p-values like <0.01%) indicate clear bias.
  • Arithmetic mean: should be near 127.5 for uniformly random bytes. Large deviation means bytes lean toward certain values.
  • Monte Carlo Pi: a rough uniformity test. Values far from 3.14159 mean non-uniform distribution.
  • Serial correlation: should be close to 0. Values far from 0 mean bytes depend on previous bytes (not independent).

How to judge validity (simple rules):

  • Small sample sizes (hundreds of bytes) are unreliable — collect much more data (thousand bytes to megabytes) before trusting results.
  • Passing ent tests does not guarantee cryptographic strength. ent shows statistical issues but does not prove min-entropy (the conservative measure cryptography needs).
  • If you see low entropy, large compression potential, high chi-square, mean far from 127.5, big Monte Carlo error, or strong serial correlation → your source is biased or dependent and not ready for seeding wallets.

Next steps

  • Run tests using large datasets(Kbs or MBs of data).
  • Use a conservative min-entropy estimator and assume the worst-case when counting usable bits.
  • Test vetted extractors (HMAC/HKDF-SHA256 or similar) to distill entropy — hashing helps extract but does not increase true entropy.
  • Test combination of raw results with CSPRNG.
  • Validate with larger test suites (NIST STS, Dieharder).