CRT Steganography

C16: DRM patents. CC0.

CRT channels are algebraically independent. Replace D and K channels with secret data -- the remaining 4 channels (E,b,L,G) are untouched. The stego value is still a valid ring element. The secret is invisible to anyone who doesn't know which channels to read.

How It Works

CRT Steganographic Principle

Any ring element has 6 independent CRT residues. Modifying D (3 bits) and K (log2(9) bits) channels embeds ~7 bits per carrier value. The other 4 channels carry the original signal undistorted. CRT independence means the hidden data is algebraically invisible in the E,b,L,G subspace.

Channel hiding

CRT independence

Secret data replaces inner channels. Outer channels untouched.

Capacity

3+4 = 7 bits

D(3 bits) + K(~3.2 bits) per carrier value.

Invisibility

Algebraic orthogonality

E,b,L,G channels unchanged. No statistical distortion in 4/6 channels.

Extraction

Modular arithmetic

Read D and K channels. Reconstruct secret. Lossless.

Try It

Carrier value:

Secret range: 0-71 (D*K = 8*9 = 72 values). D carries low 3 bits, K carries high bits.

CRT Stego vs Traditional

Hiding methodLSB modification (fragile)CRT channel replacement (algebraic)DistortionAll bits slightly perturbedOnly D,K channels changed; E,b,L,G exactDetectionStatistical analysis can reveal4/6 channels have zero distortionExtractionBit masking (position-dependent)Modular arithmetic (position-free)Patent statusDRM/watermarking patentsCC0. Public domain. Forever.

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

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