Abstract
In this paper the possibilities of an iterative concatenation method towards construction of Boolean functions resistant to algebraic cryptanalysis are investigated. The notion of $\mathcal{AAR}$ (Algebraic Attack Resistant) function is introduced as a unified measure of protection against classical algebraic attacks as well as fast algebraic attacks. Then, it is shown that functions that posses the highest resistance to fast algebraic attacks are necessarily of maximum algebraic immunity, thus opposing a maximum resistance to algebraic cryptanalysis in general. The developed theoretical framework allows us to iteratively construct functions with maximum $\mathcal{AI}$ , and of almost optimized resistance to fast algebraic cryptanalysis. This infinite class for the first time, apart from almost optimal resistance to algebraic cryptanalysis, in addition generates functions that allow an extremely efficient hardware implementation, possess high nonlinearity and maximum algebraic degree; thus unifying most of the relevant cryptographic criteria.
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