Contact tracing is an important measure to counter the COVID-19 pandemic. In the early phase, many countries employed manual contact tracing to contain the rate of disease spread, however it has many issues. The manual approach is cumbersome, time consuming and also requires active participation of a large number of people to realize it. In order to overcome these drawbacks, digital contact tracing has been proposed that typically involves deploying a contact tracing application on people's mobile devices which can track their movements and close social interactions. While studies suggest that digital contact tracing is more effective than manual contact tracing, it has been observed that higher adoption rates of the contact tracing app may result in a better controlled epidemic. This also increases the confidence in the accuracy of the collected data and the subsequent analytics. One key reason for low adoption rate of contact tracing applications is the concern about individual privacy. In fact, several studies report that contact tracing applications deployed in multiple countries are not privacy friendly and have potential to be used for mass surveillance by the concerned governments. Hence, privacy respecting contact tracing application is the need of the hour that can lead to highly effective, efficient contact tracing. As part of this study, we focus on various cryptographic techniques that can help in addressing the Private Set Intersection problem which lies at the heart of privacy respecting contact tracing. We analyze the computation and communication complexities of these techniques under the typical client-server architecture utilized by contact tracing applications. Further we evaluate those computation and communication complexity expressions for India scenario and thus identify cryptographic techniques that can be more suitably deployed there.