Due to their frequent use in unattended and hostile deployment environments, the security in wireless sensor networks (WSNs) has attracted much interest in the past two decades. However, it remains a challenge to design a lightweight authentication protocol for WSNs because the designers are confronted with a series of desirable security requirements, e.g., user anonymity, perfect forward secrecy, resistance to de-synchronization attack. Recently, the authors presented two authentication schemes that attempt to provide user anonymity and to resist various known attacks. Unfortunately, in this work we shall show that user anonymity of the two schemes is achieved at the price of an impractical search operation—the gateway node may search for every possible value. Besides this defect, they are also prone to smart card loss attacks and have no provision for perfect forward secrecy. As our main contribution, a lightweight anonymous authentication scheme with perfect forward secrecy is designed, and what we believe the most interesting feature is that user anonymity, perfect forward secrecy, and resistance to de-synchronization attack can be achieved at the same time. As far as we know, it is extremely difficult to meet these security features simultaneously only using the lightweight operations, such as symmetric encryption/decryption and hash functions.

In order to evaluate the goodness of frequency hopping (FH) sequence design, the periodic Hamming correlation function is used as an important measure. Aperiodic Hamming correlation of FH sequences matters in real applications, while it received little attraction in the literature compared with periodic Hamming correlation. In this paper, an upper bound on the family size of FH sequences, with respect to the size of the frequency slot set, the sequence length, the maximum aperiodic Hamming correlation is established. Further, a construction of optimal FH sequence sets under aperiodic Hamming correlation from Reed-Solomon codes is presented, whose parameters meet the upper bound with equality. From generalized $m$ sequences (GM sequences) and generalized Gordon-Mills-Welch sequences (GGMW sequences), two classes of optimal FH sequence sets under aperiodic Hamming correlation are also presented, whose parameters meet the upper bound with equality.

In practice, when a frequency-hopping sequence (FHS) set is applied in a frequency-hopping multiple-access (FHMA) system, its periodic partial Hamming correlation (PPHC) rather than its periodic Hamming correlation (PHC) within the whole period is used to evaluate the system performance. Moreover, FHS sets with low hit zone (LHZ) can be well applied in quasi-synchronous (QS) FHMA systems in which some relative time delay among different users within a zone around the origin can be allowed. Therefore, it is very urgent to conduct research on LHZ FHS sets with optimal PPHC property in depth. In this paper, we first derive a new tighter lower bound on the maximum PPHC of an LHZ FHS set. Then we present a new class of optimal one-coincidence FHS sets. Finally we have a construction of LHZ FHS sets which can be optimal with respect to our new lower bound.