Spectral Domain Analysis of Correlation Immune and Resilient Boolean Functions

Palash Sarkar

Paper 2000/049

Spectral Domain Analysis of Correlation Immune and Resilient Boolean Functions

Palash Sarkar

Abstract

In this paper we prove a general result on the Walsh Transform of an arbitrary Boolean function. As a consequence, we obtain several divisibility results on the Walsh Transform of correlation immune and resilient Boolean functions. This allows us to improve upper bounds on the nonlinearity of correlation immune and resilient Boolean functions. Also we provide new necessary conditions on the algebraic normal form of correlation immune/resilient functions attaining the maximum possible nonlinearity.

Metadata

Available format(s): PS
Category: Secret-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: Boolean function correlation immunity resiliency nonlinearity Walsh Transform
Contact author(s): psarkar @ cacr math uwaterloo ca
History: 2000-09-26: received
Short URL: https://ia.cr/2000/049
License: CC BY

BibTeX

@misc{cryptoeprint:2000/049,
      author = {Palash Sarkar},
      title = {Spectral Domain Analysis of Correlation Immune and Resilient Boolean Functions},
      howpublished = {Cryptology {ePrint} Archive, Paper 2000/049},
      year = {2000},
      url = {https://eprint.iacr.org/2000/049}
}