CRT Hash

A7: Crypto patents. CC0.

CRT decomposition IS a hash function. Decompose into 6 independent channels, mix per-channel with primitive roots, fold through CRT reconstruction. 8 rounds. Pure ring arithmetic. No XOR, no bit shifts, no lookup tables.

How It Works

CRT Hash Principle
Every integer has a UNIQUE 6-dimensional CRT address in Z/8 x Z/9 x Z/25 x Z/49 x Z/11 x Z/13. Per-channel mixing with generators {3,2,2,3,2,2} creates nonlinearity. Cross-channel addition creates diffusion. CRT reconstruction folds channels back. After 8 rounds, no channel remembers the input alone.
6 parallel lanes
CRT decomposition
6 independent mixing networks. Each uses a different primitive root.
Cross diffusion
Neighbor injection
Each channel absorbs 2 neighbors per round. After 3 rounds, every channel influenced by every other.
CRT fold
Bijection breaker
Reconstruct to integer, multiply by 137 (ADDRESS), re-decompose.
8 rounds
Full diffusion
By round 8, each output depends on every input. Natural from algebraic independence.

Try It

Hash an integer (0-12612599):

Try: 42 vs 43 (avalanche), 137 (ADDRESS), 1576576 (OMEGA), 0 (void).

Batch Avalanche Test

Hash 100 consecutive pairs and measure average channel diffusion.

CRT Hash vs Traditional

StructureSHA-256: 64 rounds of bit manipulationCRT: 8 rounds of ring arithmetic over 6 channelsMixingXOR + rotate + shiftPrimitive root multiplicationOutput space2^256 (arbitrary)12,612,600 (structural)Patent statusVarious patents/NIST processCC0. Public domain. Forever.

This work is and will always be free.
No paywall. No copyright. No exceptions.

If it ever earns anything, every cent goes to the communities that need it most.

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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