On the Security of Non-Linear HB (NLHB) Protocol against Passive Attack

As a variant of the HB authentication protocol for RFID systems, which relies on the complexity of decoding linear codes against passive attacks, Madhavan et al. presented Non-Linear HB(NLHB) protocol. In contrast to HB, NLHB relies on the complexity of decoding a class of non-linear codes to render the passive attacks proposed against HB ineffective. Based on the fact that there has been no passive solution for the problem of decoding a random non-linear code, the authors have claimed that NLHB's security margin is very close to its key size. In this paper, we show that passive attacks against HB protocol can still be applicable to NLHB and this protocol does not provide the desired security margin. In our attack, we first linearize the non-linear part of NLHB to obtain a HB equivalent for NLHB, and then exploit the passive attack techniques proposed for the HB to evaluate the security margin of NLHB. The results show that although NLHB's security margin is relatively higher than HB against similar passive attack techniques, it has been overestimated and, in contrary to what is claimed, NLHB is vulnerable to passive attacks against HB, especially when the noise vector in the protocol has a low weight.