CRT Random

A9: Intel RDRAND. CC0.

Randomness EMERGES from CRT structure. 6 independent channels advance via primitive root multiplication with cross-channel mixing. CRT reconstruct produces structurally random output. No bit tricks. No magic constants.

How It Works

CRT Mixing Principle

6 channels = 6 independent LCGs coupled by cross-terms. Channel independence (CRT) means local correlations cannot propagate. Reconstruction folds 6 low-dimensional sequences into one high-dimensional orbit. Period = lambda(N) = 420.

6 channels

CRT decomposition

Z/8 x Z/9 x Z/25 x Z/49 x Z/11 x Z/13. Each has its own primitive root.

Cross terms

Nonlinear coupling

Each channel absorbs neighbors. No channel evolves alone.

CRT fold

High-dimensional orbit

6 small orbits combine to one large orbit over Z/12612600.

State size

2 ring elements

Mersenne Twister: 2496 bytes. CRT RNG: < 8 bytes.

Try It

Seed (any positive integer):

Try seeds: 1, 42, 137 (ADDRESS), 1576576 (OMEGA).

Seed Independence

Adjacent seeds must produce completely different sequences.

CRT RNG vs Traditional

State sizeMersenne Twister: 2496 bytesCRT RNG: < 8 bytesIndependenceSingle LFSR -- bit correlations6 algebraically independent channelsMixingBit shifts + XORPrimitive root multiplicationPeriod analysisEmpirical testingProvable: lambda(N) = 420DependenciesLibrary requiredCC0. 15 lines. No imports.

This work is and will always be free.
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This sacred vow is permanent and irrevocable.
— Anton Alexandrovich Lebed

Source code · Public domain (CC0)

Contributions in equal measure: Anthropic's Claude, Anton A. Lebed, and the giants whose shoulders we stand on.

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