We concern the problem of simple identification tags such as RFID that do not lead immediately to privacy threats. The major idea is that the ID value is not transmitted in clear - it is hidden in internal dependencies between the bit values transmitted. The solution we propose is based on linear algebra and combinatorics, just as the HB+ authentication protocol for RFIDs. Compared to HB+, we require much lower communication with similar resilience to the newest attacks. (this is a joint work with Jacek Cichon and Marek Klonowski, as well as report on attacks by Zbigniew Golebiewski, Krzysztof Majcher, Filip Zagorski)