The COVID-19 pandemic has made the scientific community devise means to implement “contact tracing” mechanisms to mitigate the spread of the infection. The crucial idea is to scan and record close contacts between users using mobile device, in order to notify persons when their close contact(s) is diagnosed positive. First, the ability granted to service providers of the contact tracing systems to access user data violates user privacy, and attackers can fabricate identities and contact records in their devices, which harms the integrity of the system. Moreover, current contact tracing systems’ false-positive rate is too high to be practical as they do not filter scan results outside the range of infections, since the range of transmission for droplets is far less than the scanning range for Bluetooth Low Energy used by these systems. Furthermore, current systems neglect airborne transmission, a far cry from a tool against viruses suspended in the air. In this paper, we propose a cryptographic framework for contact tracing and provide a construction based on public key rerandomizable BLS signature, being capable of providing users of contact tracing with comprehensive privacy protection. Besides, we also implement a commitment scheme to prevent fabrication of identities and contact records. To prove the concept of our framework and to solve other problems mentioned above, we proposed a new contact tracing system, using environmental factors (temperature, humidity and airflow) to filter out results outside estimated effective transmission distance, and also take airborne transmission into consideration. Finally, we evaluate the performance of our design by implementing our algorithm on mobile devices with satisfactory results.