A Zero-Knowledge Proof (ZKP) protocol allows a participant to prove the knowledge of some secret without revealing any information about it. While such protocols are typically executed by computers, there exists a lin...A Zero-Knowledge Proof (ZKP) protocol allows a participant to prove the knowledge of some secret without revealing any information about it. While such protocols are typically executed by computers, there exists a line of research proposing physical instances of ZKP protocols. Up to now, many card-based ZKP protocols for pen-and-pencil puzzles, like Sudoku, have been designed. Those games, mostly edited by Nikoli, have simple rules, yet designing them in card-based ZKP protocols is non-trivial. In this work, we propose a card-based ZKP protocol for Usowan, a Nikoli game. In Usowan, for each room of a puzzle instance, there is exactly one piece of false information. The goal of the game is to detect this wrong data amongst the correct data and also to satisfy the other rules. Designing a card-based ZKP protocol to deal with the property of detecting a liar has never been done. In some sense, we propose a physical ZKP for hiding of a liar. This work extends a previous paper appearing in Ref. [1]. In this extension, we propose two other protocols, for Herugolf and Five Cells. The puzzles are specifically chosen because each of those three puzzles shares a common constraint, connectivity. However, showing the connected configuration cannot be done with generic approach and brings new construction to the existing connectivity ZKP protocol. Indeed, in Herugolf, the connectivity is handled with a given length of cell which is decremental (i.e., the length of each connected cell decreases by one at each step). For Five Cells, there is an additional step in the setup allowing to encode all the information needed to ensure a valid ZKP protocol.展开更多
基金supported by the French ANR project ANR-18-CE39-0019(MobiS5)Other programs also fund to write this paper,namely the French government research program“Investissements d’Avenir”through the IDEX-ISITE initiative 16-IDEX-0001(CAP 20-25)+4 种基金the IMobS3 Laboratory of Excellence(No.ANR-10-LABX-16-01)Finally,the French ANR project DECRYPT(No.ANR-18-CE39-0007)SEVERITAS(No.ANR-20-CE39-0009)also subsidize this workThe first author was supported in part by Kayamori Foundation of Informational Science Advancement and JSPS KAKENHI(No.JP23H00479)The fourth author was supported in part by JSPS KAKENHI(Nos.JP21K11881 and JP23H00479).
文摘A Zero-Knowledge Proof (ZKP) protocol allows a participant to prove the knowledge of some secret without revealing any information about it. While such protocols are typically executed by computers, there exists a line of research proposing physical instances of ZKP protocols. Up to now, many card-based ZKP protocols for pen-and-pencil puzzles, like Sudoku, have been designed. Those games, mostly edited by Nikoli, have simple rules, yet designing them in card-based ZKP protocols is non-trivial. In this work, we propose a card-based ZKP protocol for Usowan, a Nikoli game. In Usowan, for each room of a puzzle instance, there is exactly one piece of false information. The goal of the game is to detect this wrong data amongst the correct data and also to satisfy the other rules. Designing a card-based ZKP protocol to deal with the property of detecting a liar has never been done. In some sense, we propose a physical ZKP for hiding of a liar. This work extends a previous paper appearing in Ref. [1]. In this extension, we propose two other protocols, for Herugolf and Five Cells. The puzzles are specifically chosen because each of those three puzzles shares a common constraint, connectivity. However, showing the connected configuration cannot be done with generic approach and brings new construction to the existing connectivity ZKP protocol. Indeed, in Herugolf, the connectivity is handled with a given length of cell which is decremental (i.e., the length of each connected cell decreases by one at each step). For Five Cells, there is an additional step in the setup allowing to encode all the information needed to ensure a valid ZKP protocol.
