CRT Digital Signature

RSA/ECDSA patents. CC0 alternative.

The 3+4 split IS a signature scheme. 7 CRT channels split into 3 data channels {mod 8, mod 25, mod 49} (private) and 4 parity channels {mod 9, mod 11, mod 13, mod 17} (public verification). Sign with data channels. Verify with parity channels. 4 parity channels detect any tampering in the full 7-channel signature. The algebra IS the cryptography.

How It Works

CRT Signature Principle (PROVED)
7 CRT channels partition into 3 data {mod 8, mod 25, mod 49} and 4 parity {mod 9, mod 11, mod 13, mod 17}. The signer transforms data channels using a private exponent. Parity channels pass through as public verification data. Verifier checks only parity channels -- needs no private key. 4 independent checks detect ANY tampering in the full 7-channel space.
3+4 split
Algebraic key separation
3 data channels = private key space. 4 parity channels = public verification.
4 independent checks
Parity verification
Parity channels detect full-ring tampering. Data channels invisible to verifier.
Key rotation
Carmichael period 1680
Private keys rotate naturally with the ring's Carmichael period.
Tamper detection
Per-channel check
Any modification changes parity residues. 4 independent checks.

Try It

Message (any integer):

Private key mod 1680 (Carmichael period). Red = data channels (private). Green = parity channels (public verification).

Batch Integrity Test

Sign 100 messages with key=137. Verify all. Then tamper each and check rejection.

Source code · Public domain (CC0)

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