In vehicular ad hoc networks, establishing a secure channel between any two vehicles is fundamental. Authenticated key agreement is a useful mechanism, which can be used to negotiate a shared key for secure data transmission between authentic vehicles in vehicular ad hoc networks. Among the existing identity-based two-party authenticated key agreement protocols without pairings, there are only a few protocols that provide provable security in strong security models such as the extended Canetti-Krawczyk model. This article presents an efficient pairing-free identity-based one-round two-party authenticated key agreement protocol with provable security, which is more suitable for real-time application environments with highly dynamic topology such as vehicular ad hoc networks than the existing identity-based two-party authenticated key agreement protocols. The proposed protocol is proven secure under the passive and active adversaries in the extended Canetti-Krawczyk model based on the Gap Diffie-Hellman assumption. The proposed protocol can capture all essential security attributes including known-session key security, perfect forward secrecy, basic impersonation resistance, key compromise impersonation resistance, unknown key share resistance, no key control, and ephemeral secrets reveal resistance. Compared with the existing identity-based two-party authenticated key agreement protocols, the proposed protocol is superior in terms of computational cost and running time while providing higher security.

This paper presents a construction for a class of 1-resilient functions with optimal algebraic immunity on an even number of variables. The construction is based on the concatenation of two balanced functions in associative classes. For some n, a part of 1-resilient functions with maximum algebraic immunity constructed in the paper can achieve almost optimal nonlinearity. Apart from their high nonlinearity, the functions reach Siegenthaler's upper bound of algebraic degree. Also a class of 1-resilient functions on any number n > 2 of variables with at least sub-optimal algebraic immunity is provided.

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