Paper 2000/054

Correlation Immune Boolean Functions with Very High Nonlinearity

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.

Metadata
Available format(s)
PS
Category
Secret-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Keywords
Boolean FunctionStream Cipher
Contact author(s)
subho @ isical ac in
History
2000-10-27: received
Short URL
https://ia.cr/2000/054
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2000/054,
      author = {Subhamoy Maitra},
      title = {Correlation Immune Boolean Functions with Very High Nonlinearity},
      howpublished = {Cryptology ePrint Archive, Paper 2000/054},
      year = {2000},
      note = {\url{https://eprint.iacr.org/2000/054}},
      url = {https://eprint.iacr.org/2000/054}
}
Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.