Improving the Lower Bound on the Higher Order Nonlinearity of Boolean Functions With Prescribed Algebraic Immunity

Abstract. The recent algebraic attacks have received a lot of attention in cryptographic literature. The algebraic immunity of a Boolean function quantifies its resistance to the standard algebraic attacks of the pseudo-random generators using it as a nonlinear filtering or combining function. Very few results have been found concerning its relation with the other cryptographic parameters or with the r-th order nonlinearity. As recalled by Carlet at Crypto'06, many papers have illustrated the importance of the rth-order nonlinearity profile (which includes the first-order nonlinearity). The role of this parameter relatively to the currently known attacks has been also shown for block ciphers. Recently, two lower bounds involving the algebraic immunity on the rth-order nonlinearity have been shown by Carlet et al. None of them improves upon the other one in all situations. In this paper, we prove a new lower bound on the rth-order nonlinearity profile of Boolean functions, given th...

• Type: Journal
• Year: 2008
• Where: TIT
• Authors: Sihem Mesnager
• Keywords: Algebraic Attack, Algebraic Immunity, Nonlinearity, TIT 2008