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**2001/083**

**Title:**

On the Constructing of Highly Nonlinear Resilient Boolean Functions by Means of Special Matrices

**Authors:**
Maria Fedorova, Yuriy Tarannikov

**Abstract:**

In this paper we consider matrices of special form introduced in [11]

and used for the constructing of resilient functions with cryptographically

optimal parameters. For such matrices we establish lower bound

{1\over\log_2(\sqrt{5}+1)}=0.5902... for the important ratio

{t\over t+k} of its parameters and point out that there exists a

sequence of matrices for which the limit of ratio of its parameters

is equal to lower bound. By means of these matrices we construct

m-resilient n-variable functions with maximum possible nonlinearity

2^{n-1}-2^{m+1} for m=0.5902...n+O(\log_2 n). This result

supersedes the previous record.

**ePrint:**
https://eprint.iacr.org/2001/083

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