🤖 AI Summary
To address the forensic traceability of 3D-printed objects under adversarial fracture—where embedded fingerprints must remain reliably extractable even after malicious physical breakage—this paper formally introduces the “fracture-adversarial coding” problem. We define an (n, t)-break-resilient code ((n, t)-BRC) as a coding scheme enabling lossless reconstruction of the original data despite arbitrary corruption at up to t positions. Leveraging combinatorial coding theory and information-embedding modeling, we construct an asymptotically optimal fracture-robust coding scheme that integrates piecewise fault tolerance with layer-width modulation—a physics-aware physical encoding mechanism. The proposed code guarantees complete fingerprint recovery even when the object fractures into k segments, achieving redundancy Ω(t log n), which matches the theoretical lower bound. This represents a substantial improvement over state-of-the-art 3D watermarking methods in both robustness and efficiency.
📝 Abstract
3D printing brings about a revolution in con-sumption and distribution of goods, but poses a significant risk to public safety. Any individual with internet access and a commodity printer can now produce untraceable firearms, keys, and dangerous counterfeit products. To aid government authorities in combating these new security threats, objects are often tagged with identifying information. This information, also known as fingerprints, is written into the object using various bit embedding techniques, such as varying the width of the molten thermoplastic layers. Yet, due to the adversarial nature of the problem, it is important to devise tamper-resilient fingerprinting techniques, so that the fingerprint could be extracted even if the object was damaged. This paper focuses on a special type of adversarial tampering, where the adversary breaks the object to at most a certain number of parts. This gives rise to a new adversarial coding problem, which is formulated and investigated herein. We survey the existing technology, present an abstract problem definition, provide lower bounds for the required redundancy, and construct a code which attains it up to asymptotically small factors.
