On lower bounds on second-order nonliearities of bent functions obtained by using Niho power functions

Abstract. In this paper we find a lower bound of the second-order nonlinearities of Boolean bent functions of the form f(x) = Trn 1 (α1xd1 + α2xd2 ), where d1 and d2 are Niho exponents. A lower bound of the second-order nonlinearities of these Boolean functions can also be obtained by using a result proved by Li, Hu and Gao (eprint.iacr.org/2010 /009.pdf). It is demonstrated that for large values of n the lower bound obtained in this paper are better than the lower bound obtained by Li, Hu and Gao. Key words: Boolean function, derivative, Niho power function, Second-order nonlinearity, Walsh-spectrum.

• Type: Journal
• Year: 2011
• Where: IACR
• Authors: Manish Garg, Sugata Gangopadhyay
• Keywords: Boolean Functions, Eprint, IACR 2011, Lower Bound