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**2000/005**

**Title:**

On Resilient Boolean Functions with Maximal Possible Nonlinearity

**Authors:**
Yuriy Tarannikov

**Abstract:**

It is proved that the maximal possible nonlinearity of n-variable

m-resilient Boolean function is 2^{n-1}-2^{m+1} for

{2n-7\over 3}\le m\le n-2. This value can be achieved only for

optimized functions (i.~e. functions with an algebraic degree n-m-1).

For {2n-7\over 3}\le m\le n-\log_2{n-2\over 3}-2 it is suggested a method

to construct an n-variable m-resilient function with maximal possible

nonlinearity 2^{n-1}-2^{m+1} such that each variable presents in ANF of this

function in some term of maximal possible length n-m-1.

For n\equiv 2\pmod 3, m={2n-7\over 3},

it is given a scheme of hardware implementation for such function that

demands approximately 2n gates EXOR and (2/3)n gates AND.

**ePrint:**
https://eprint.iacr.org/2000/005

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