Basic Theory in Construction of Boolean Functions with Maximum Possible Annihilator Immunity
Designs, Codes and Cryptography
Construction and analysis of boolean functions of 2t+1 variables with maximum algebraic immunity
ASIACRYPT'06 Proceedings of the 12th international conference on Theory and Application of Cryptology and Information Security
Constructing single- and multi-output boolean functions with maximal algebraic immunity
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
FSE'05 Proceedings of the 12th international conference on Fast Software Encryption
On the algebraic immunity of symmetric boolean functions
INDOCRYPT'05 Proceedings of the 6th international conference on Cryptology in India
Upper bounds on algebraic immunity of boolean power functions
FSE'06 Proceedings of the 13th international conference on Fast Software Encryption
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The algebraic immunity of a Boolean function is a parameter that characterizes the possibility to bound this function from above or below by a nonconstant Boolean function of a low algebraic degree. We obtain lower bounds on the algebraic immunity for a class of functions expressed through the inversion operation in the field GF(2 n ), as well as for larger classes of functions defined by their trace forms. In particular, for n 驴 5, the algebraic immunity of the function Tr n (x 驴1) has a lower bound 驴2驴n + 4驴 驴 4, which is close enough to the previously obtained upper bound 驴驴n驴 + 驴n/驴驴n驴驴 驴 2. We obtain a polynomial algorithm which, give a trace form of a Boolean function f, computes generating sets of functions of degree 驴 d for the following pair of spaces. Each function of the first (linear) space bounds f from below, and each function of the second (affine) space bounds f from above. Moreover, at the output of the algorithm, each function of a generating set is represented both as its trace form and as a polynomial of Boolean variables.