Towards Verifying Physical Assumption in Card-Based Cryptography

Card-based cryptography realizes cryptographic tasks, such as secure computation, with a deck of physical cards. The primary research subjects for card-based cryptography are theoretical studies that, for example, propose efficient protocols regarding the number of required cards and procedures. However, almost all prior studies are based on the ideal physical assumption that the backs of all cards are indistinguishable without verification. This study addresses this assumption from a physical perspective to improve the security of card-based cryptography. In the first attempt, we assume a strong attacker who uses ink and a high-performance camera to distinguish the backs of the cards. We experimented with them and confirmed that such an attacker could identify the inked area of the back by analyzing an image captured by the camera. Based on our study, one can address another approach, such as using invisible oil and smartphone cameras to verify the physical assumption. This study is a seminal work that addresses this physical assumption. In addition to the verification, we study secret information that such a strong attacker can obtain during the execution of card-based protocols.