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Designs, Codes and Cryptography

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20-02-2019

Hadamard matrices, d-linearly independent sets and correlation-immune Boolean functions with minimum Hamming weights

Author: Qichun Wang

Published in: Designs, Codes and Cryptography | Issue 10/2019

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Abstract

It is known that correlation-immune (CI) Boolean functions used in the framework of side channel attacks need to have low Hamming weights. In this paper, we study minimum Hamming weights of 3-CI Boolean functions, and prove that the Carlet-Chen conjecture is equivalent to the famous Hadamard conjecture. Moreover, we propose a method to construct low-weight n-variable CI functions through d-linearly independent sets, which can provide numerous minimum-weight d-CI functions. Particularly, we obtain some new values of the minimum Hamming weights of d-CI functions in n variables for \(n\le 13\).

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Title: Hadamard matrices, d-linearly independent sets and correlation-immune Boolean functions with minimum Hamming weights
Author: Qichun Wang
Publication date: 20-02-2019
Publisher: Springer US
Published in: Designs, Codes and Cryptography / Issue 10/2019
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-019-00620-1

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Hadamard matrices, d-linearly independent sets and correlation-immune Boolean functions with minimum Hamming weights

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