Wireless Contact tracing has emerged as an important tool for managing the COVID-19 pandemic and relies on continuous broadcasting of a person's presence using Bluetooth Low Energy beacons . The limitation of current contact tracing systems in that a reception of a single beacon is sufficient to reveal the user identity, potentially exposing users to malicious trackers installed along the roads, passageways, and other infrastructure . In this paper, we propose a method based on Shamir secret sharing algorithm, which lets mobile nodes reveal their identity only after a certain predefined contact duration, remaining invisible to trackers with short or fleeting encounters . Through data-driven evaluation, using a dataset containing 18 million BLE sightings, we show that the method drastically reduces the privacy exposure . Finally, we implemented the approach on Android phones to demonstrate its feasibility and measure performance for various network densities.