CRT Random Number Generator

5 independent CRT channels mixed via ring arithmetic. CC0. No patents. No dependencies.

How It Works

Seed decomposes into 5 CRT channels: n mod {8, 9, 25, 49, 11}.

Each channel advances independently via multiplication by a primitive root.

Output = CRT reconstruction of mixed channels. The 5-way independence gives structural randomness.

Wide state: two 32-bit words (s0, s1). Period > 2^30.
step:
  1. xorshift on s0              -- standard bit mixing
  2. decompose s0 into 5 CRT channels (mod 8, 9, 25, 49, 11)
  3. nonlinear per-channel mixing -- each channel mixes with neighbors
  4. CRT reconstruct             -- the axiom's structural mixing
  5. advance s1 with CRT output  -- chains the two state words
output = (s0 XOR s1) mod 970200

Distribution (mod 256)

Chi-squared (uniform)

Period detected

Bit balance (0s vs 1s)

Serial correlation

2D Scatter (consecutive pairs)

Good RNG: uniform scatter. Bad RNG: visible patterns/lines.

Avalanche Test

Flip 1 bit of seed. How many output bits change?

Channel Independence

Each CRT channel should show independent statistics.