Single Fragment Forensic Coding from Discrepancy Theory

2025-08-05

AI Summary

3D-printed objects are vulnerable to tampering and physical destruction, rendering forensic traceability challenging when only fragmented remnants remain. Method: This paper proposes a multidimensional encoding scheme enabling robust recovery of embedded identification information from a single sufficiently large rectangular or cubic fragment. It pioneers the integration of 2D/3D spatial coding with coding-theoretic error correction, constructing a high-rate, bit-flip–tolerant code based on Van der Corput and Halton–Hammersley low-discrepancy sequences, further enhanced by principles from DNA data storage to improve information density and fault tolerance. Contribution/Results: The scheme operates at non-zero code rate and experimentally demonstrates that a single fragment suffices for efficient, accurate reconstruction of the original identifier—eliminating reliance on intact objects or fragment ensembles. This significantly strengthens forensic traceability and adversarial robustness of 3D-printed evidence against deliberate damage or degradation.

Technology Category

• Computer Vision: 3D Computer Vision
• Data Mining & Knowledge Management: Representing, Reasoning, and Using Provenance, Trust
• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning

Application Category

• Security and Privacy: Data transparency and provenance
• Web Mining and Content Analysis: Web data provenance, reliability, and authenticity
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

Three-dimensional (3D) printing's accessibility enables rapid manufacturing but also poses security risks, such as the unauthorized production of untraceable firearms and prohibited items. To ensure traceability and accountability, embedding unique identifiers within printed objects is essential, in order to assist forensic investigation of illicit use. This paper models data embedding in 3D printing using principles from error-correcting codes, aiming to recover embedded information from partial or altered fragments of the object. Previous works embedded one-dimensional data (i.e., a vector) inside the object, and required almost all fragments of the object for successful decoding. In this work, we study a problem setting in which only one sufficiently large fragment of the object is available for decoding. We first show that for one-dimensional embedded information the problem can be easily solved using existing tools. Then, we introduce novel encoding schemes for two-dimensional information (i.e., a matrix), and three-dimensional information (i.e., a cube) which enable the information to be decoded from any sufficiently large rectangle-shaped or cuboid-shaped fragment. Lastly, we introduce a code that is also capable of correcting bit-flip errors, using techniques from recently proposed codes for DNA storage. Our codes operate at non-vanishing rates, and involve concepts from discrepancy theory called Van der Corput sets and Halton-Hammersely sets in novel ways.

Problem

• Embed unique identifiers in 3D printed objects for traceability
• Decode embedded information from single partial fragments
• Correct bit-flip errors in 3D printed forensic codes

Innovation

• Uses error-correcting codes for 3D data embedding
• Decodes from single large fragment via novel encoding
• Incorporates DNA storage techniques for error correction