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In this paper we introduce a concept of nearly totally disjoint spectra (NTDS) functions that slightly extends the notion of basic totally disjoint spectra functions. Novel construction methods of totally disjoint spectra (TDS) plateaued functions are proposed. We investigate the design of five-value spectrum functions with Walsh supports, the cardinalities of which are not a power of two. We also study the construction of TDS functions using NTDS functions. To acquire five-value spectrum functions in odd variables in practice, a succinct searching procedure using TDS functions designed in this paper is introduced finally. Experimental results show that such approach could yield plenty of desirable functions in odd-variable with few Walsh spectral values. [ABSTRACT FROM AUTHOR]

In this paper we put forward a method to construct balanced Boolean functions by modifying the Tang–Carlet–Tang functions with the help of functions in Generalized Maiorana–McFarland class. Essential cryptographic properties, for instance, nonlinearity, algebraic immunity and immunity to fast algebraic attacks are considered. A new lower bound on the nonlinearity of the functions that are contained in our construction is obtained. It is slightly better than the known result. Owing to a combinatorial fact, it can be demonstrated that the proposed functions have optimal algebraic immunity. Meanwhile, they also possess high nonlinearity and a moderate behavior against fast algebraic attacks. Apart from theoretical contributions, hardware implementation efficiency on the proposed functions is also analyzed. Since the participation of GMM class component, experimental results imply that functions constructed in this paper have a small implementation size and employ fewer logic gates compared with the construction containing an iterative structure. [ABSTRACT FROM AUTHOR]

Boolean functions play essential roles in certain symmetric cryptographic schemes and error-correcting codes. Apart from the cryptographic criteria satisfied by Boolean functions, constructions of functions with few Walsh spectral value are also of particular interests in cryptographic applications. Due to the problem that the five-value spectrum functions with duals being not basic plateaued functions remains to be answered, in this paper we intend to investigate the construction on non-basic plateaued duals of five-value spectrum functions. The issue of constructing non-basic totally disjoint spectra plateaued functions is dealt with from two aspects. We firstly address the characterization of non-basic plateaued functions corresponding to Walsh supports with unequal cardinality. Then the necessary and sufficient conditions of the spectral design of a partially non-basic five-value spectrum function are proposed. Meanwhile, we also provide the sufficient condition for constructing a valid five-value spectrum function whose duals are both defined on non-affine subspaces. Finally, the design of totally disjoint spectra functions on non-affine subspaces with equal cardinality is also studied. [ABSTRACT FROM AUTHOR]