Zero-knowledge proofs (zkp) have been used to improve several blockchain limitations (e.g. privacy, scalability), and recent work proposed its usage to improve blockchain interoperability solutions in certain scenarios. However, more studies are needed to understand the full potential of zkp in this context. In particular, zkp may improve existing blockchain interoperability solutions, and help software architects and developers to reduce barriers for blockchain adoption. In this paper, we empirically analyse how zkp may improve a gateway-based interoperability solution. The results showed that it was possible to improve the selected solution and incorporate anonymous cross-chain authentication and private data exchange. A prototype was developed and evaluated using three strategies: 1) its application in a use case scenario, 2) performance tests, and 3) cost analysis. The evaluation showed that the approach is technically feasible, but not suitable for every use case. Furthermore, the private data exchange approach confirmed the results of other studies: zkp is not mature enough for some scenarios, and more work needs to be performed.