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**2000/054**

**Title:**

Correlation Immune Boolean Functions with Very High Nonlinearity

**Authors:**
Subhamoy Maitra

**Abstract:**

Here we provide a construction method for unbalanced, first order

correlation immune Boolean functions on even number of variables

n \geq 6. These functions achieve the currently best known

nonlinearity 2^{n-1} - 2^{\frac{n}{2}} + 2^{\frac{n}{2} - 2} .

Then we provide a simple modification of these functions to get

unbalanced correlation immune Boolean functions on even number of

variables n, with nonlinearity

2^{n-1} - 2^{\frac{n}{2}} + 2^{\frac{n}{2} - 2} - 2 and maximum

possible algebraic degree n-1. Moreover, we present a detailed

study on the Walsh spectra of these functions.

**ePrint:**
https://eprint.iacr.org/2000/054

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