Construction and Analysis of Boolean Functions of 2t+1 Variables with Maximum Algebraic Immunity
In this paper, we study the construction of (2t+1)-variable Boolean functions with maximum algebraic immunity, and we also analyze some other cryptographic properties of this kind of functions, such as nonlinearity, resilience. We first identify several classes of this kind of functions. Further, some necessary conditions of this kind of functions which also have higher nonlinearity are obtained. In this way, a modified construction method is proposed to possibly obtain (2t+1)-variable Boolean functions which have maximum algebraic immunity and higher nonlinearity, and a class of such functions is also obtained. Finally, we present a sufficient and necessary condition of (2t+1)-variable Boolean functions with maximum algebraic immunity which are also 1-resilient.
KeywordsAlgebraic attack algebraic immunity Boolean functions balancedness nonlinearity resilience
- 4.Carlet, C.: A method of construction of balanced functions with optimum algebraic immunity (2006), Available at: http://eprint.iacr.org/2006/149
- 10.Dalai, D.K., Maitra, S.: Reducing the Number of Homogeneous Linear Equations in Finding Annihilators (2006), Available at: http://eprint.iacr.org/2006/032
- 13.Li, N., Qi, W.F.: Construction and count of Boolean functions of an odd number of variables with maximum algebraic immunity, Available at: http://arxiv.org/abs/cs.CR/0605139
- 14.Lobanov, M.: Tight bound between nonlinearity and algebraic immunity (2005), Available at: http://eprint.iacr.org/2005/441