Vehicle ad-hoc networks (VANETs) can offer numerous benefits, but also face many privacy and security issues. There exist the certificate management burden and key escrow issue in traditional public key infrastructure (PKI)-based and identity (ID)-based privacy-preserving authentication schemes, respectively. In addition, the security of some existing cryptographic schemes depends on strong assumptions about the ideal tamper-proof devices. To address these issues, a certificateless aggregate signature (CLAS) scheme for VANETs has been proposed, which was claimed provably unforgeable. However, we found that this scheme cannot resist collusion attacks, which means the equivalent validity of the aggregate signature would be broken. Therefore, this article proposes an improved CLAS scheme against collusion attacks for VANETs (CA-CLAS). Security and performance analyses show that the proposed CA-CLAS scheme not only offers privacy and security guarantees for VANETs, but also improves efficiency compared to existing authentication schemes.

The design of plateaued functions over GF(2)n, also known as 3-valued Walsh spectra functions (taking the values from the set {0,±2 ⌈ n+s/2 ⌉ }), has been commonly approached by specifying a suitable algebraic normal form which then induces this particular Walsh spectral characterization. In this article, we consider the reversed design method which specifies these functions in the spectral domain by specifying a suitable allocation of the nonzero spectral values and their signs. We analyze the properties of trivial and nontrivial plateaued functions (as affine inequivalent distinct subclasses), which are distinguished by their Walsh support Sf (the subset of GF(2)n having the nonzero spectral values) in terms of whether it is an affine subspace or not. The former class exactly corresponds to partially bent functions and admits linear structures, whereas the latter class may contain functions without linear structures. A simple sufficient condition on Sf , which ensures the nonexistence of linear structures, is derived and some generic design methods of nontrivial plateaued functions without linear structures are given. The extended affine equivalence of plateaued functions is also addressed using the concept of dual of plateaued functions. Furthermore, we solve the problem of specifying disjoint spectra (non)trivial plateaued functions of maximal cardinality whose concatenation can be used to construct bent functions in a generic manner. This approach may lead to new classes of bent functions due to large variety of possibilities to select underlying duals that define these disjoint spectra plateaued functions. An additional method of specifying affine inequivalent plateaued functions, obtained by applying a nonlinear transform to their input domain, is also given.

In this paper, we give an efficient method for constructing a large set of disjoint spectra functions without linear structures, which are not equivalent to partially linear functions. This positively answers the open problem [“how to construct a large set of disjoint spectra functions which are not (linearly equivalent to) partially linear functions” raised by Zhang and Xiao]. At the same time, this significantly extends a recent result of Zhang, where a method of specifying four disjoint spectra functions was given. It is demonstrated that such sets can be utilized in the design of highly nonlinear resilient functions. In the second part, based on a generalization of the indirect sum method, we give an alternative approach for designing sets of disjoint spectra functions of even larger cardinality than already given ones, but these functions then admit linear structures. In addition, it is shown that using suitable initial functions in the generalized indirect sum method we can specify highly nonlinear resilient Boolean functions (in odd number of input variables n) whose nonlinearity in many cases exceeds the current best known values. Moreover, we design some balanced functions (for odd n) that also achieve the highest nonlinearity known.

The problem of constructing bent-negabent functions that do not belong to the completed Maiorana-McFarland class emerges implicitly through a series of construction methods proposed recently. These approaches manage to optimize the algebraic degree of bent-negabent functions, but all of the constructed bent-negabent functions belong to the completed Maiorana-McFarland class. In this paper, we use the indirect sum construction (proposed by Carlet in 2004) for constructing the bent-negabent functions that are not provably contained in this class, which is the first significant attempt in this direction. To achieve this, we first provide a class of bent functions with certain desirable properties that does not belong to this class and demonstrate the existence of the class members. Then, embedding these functions in the framework of the indirect sum construction, we are able to specify sufficient conditions for bent-negabent functions not being contained in the completed Maiorana-McFarland class.

In the mid 1960s, Rothaus proposed the so-called “most general form” of constructing new bent functions by using three (initial) bent functions whose sum is again bent. In this paper, we utilize a special case of Rothaus construction when two of these three bent functions differ by a suitably chosen characteristic function of an n/2-dimensional subspace. This simplification allows us to treat the induced bent conditions more easily, also implying the possibility to specify the initial functions in the partial spread class and most notably to identify several instances of the so-called non-normal bent functions. Affine inequivalent bent functions within this class are then identified using a suitable selection of initial bent functions within the partial spread class (stemming from the complete Desarguesian spread). It is also shown that when the initial bent functions belong to the class D, then, under certain conditions, the constructed functions provably do not belong to the completed Maiorana-McFarland class. We conjecture that our method potentially generates an infinite class of non-normal bent functions (all tested ten-variable functions are non-normal but unfortunately they are weakly normal) though there are no efficient computational tools for confirming this.