How We Bound 512-Bit Cryptographic Signatures to Non-Linear Sri Yantra Vector Geometry Inside Raw PDF Streams

Description and use

Marma‑Crypto embeds a 256‑bit cryptographic digest into PDF vector geometry, enabling lossless extraction and tamper detection with minimal overhead.

Problem

PDF documents signed with Qualified Electronic Signatures contain a visual stamp that is decorative and can be copied, while bitmap watermarks increase file size and degrade under scaling.

Outcome

The protocol embeds a 256‑bit cryptographic commitment into raw PDF vector geometry, enabling lossless extraction and tamper detection with minimal overhead.

Workflow

• 1. Build the 9‑triangle Sri Yantra geometry and pre‑compute 4,096 coupled configurations via L‑BFGS‑B optimization.
• 2. Compute a 256‑bit digest D256 by hashing GOST 34.311‑95, DSTU 7564:2014 Kupyna, and FIPS 180‑4 SHA‑256 over the document.
• 3. Quantize the digest into a 24‑bit geometric key (k0–k3) to select a base configuration, angular modulation, radial scaling, and micro‑phase shift.
• 4. Generate a 256‑bit bijective micro‑perturbation vector across 26 degrees of freedom of the inner vertices, encoding the digest into the SVG coordinates.
• 5. Inject the resulting ISO 32000‑1 PDF graphics operators (q … m l S Q) into the page content stream (~4.1 KB per page).
• 6. Seal the PDF locally using the CLI tool marma‑watermark or the browser web‑sealer.
• 7. Verify a sealed PDF by extracting the geometric commitment and comparing it to the original digest; a mismatch triggers a TAMPERED alert.

Evidence

When a PDF contract, court filing, or financial report is digitally signed with a Qualified Electronic Signature—such as European eIDAS (ETSI EN 319 142-1 PAdES-B-LTA) or Ukrainian DSTU 4145-2002—there is a fundamental disconnect between the binary cryptographic container and the visual representation of the page.

Source

Marma-Crypto turns raw PDF vector geometry into a 256-bit bijective carrier of the document's cryptographic digest.

Source

If an attacker alters even a single character in the PDF text—or modifies a single vertex coordinate by > 10^{-7} units—the recomputed digest D'_{256} diverges from the geometry-extracted vector, immediately triggering a TAMPERED alert.

Source