The present invention provides one or more powered wireless transponders and/or one or more passive wireless transponder devices communicating with a reader/interrogator and the method of efficiently inventorying these devices without the risk of eavesdropping. A reader transmits a random number and transponders generate their own random number. The transponders whose random number matches all or a part of the random number responds. If a collision occurs, the reader's random number can be changed and retransmitted until almost one transponder response is verified in a tree search algorithm. Specifically, the invention concerns a method for inventorying wireless transponders providing anti-eavesdropping anti-collision.