The recent pandemic of novel coronavirus produces a new challenge to balancing social welfare, the economy, and privacy while preventing contact among individuals. To reduce the reproduction rate without spoiling our economy, we need good incentive mechanisms to reduce the possibility of spreading the virus as well as good privacy enhancing techniques. Unfortunately, some of recent approaches in contact tracing are not successful due to privacy concerns and a lack of sufficient incentive mechanisms. In this paper, we provide a design using smart contracts as an incentive mechanism with enhanced privacy of user lo- cation information. We utilize encrypted data calculated from a set of network routing information, and plaintext equality test of a public key cryptosystem to estimate the time duration of staying at the same place. By staying at the same location longer, a user can obtain greater rewards. We have implemented a proof concept of this scheme to evaluate its ef- ficiency. We also discuss financial regulation and economic viewpoints.