A Cryptographic Moving-Knife Cake-Cutting Protocol with High Social Surplus

This paper proposes a cake-cutting protocol using cryptography when the cake is a heterogeneous good that is represented by an interval on a real line. Although the Dubins-Spanier moving-knife protocol with one knife achieves simple fairness and truthfulness, all players must execute the protocol synchronously. Thus, the protocol cannot be executed on asynchronous networks such as the Internet. We show that the moving-knife protocol can be executed approximately but asynchronously by a discrete protocol using a secure auction protocol. The number of cuts is n − 1w heren is the number of players, which is the minimum. Sgall and Woeginger proposed another asynchronous protocol that satisfies simple fairness, truthfulness, and the minimum number of cuts. These two protocols are com- pared from the viewpoint of social surplus. The simulation result shows that the cryptographic moving-knife protocol is better than the Sgall-Woeginger protocol.