Break-Resilient Codes for Forensic 3D Fingerprinting

3D printing brings about a revolution in consumption 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. While fingerprinting various forms of digital media (such as videos, images, etc.) has been studied extensively in the past, 3D printing is a relatively new medium which is exposed to different types of adversarial physical tampering that do not exist in the digital world. This paper focuses on one such 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. Notably, the problem bears some resemblance to the torn paper channel, which was recently studied for applications in DNA storage.