Basic Theory in Construction of Boolean Functions with Maximum Possible Annihilator Immunity

Deepak Kumar Dalai; Subhamoy Maitra; Sumanta Sarkar

Paper 2005/229

Basic Theory in Construction of Boolean Functions with Maximum Possible Annihilator Immunity

Deepak Kumar Dalai, Subhamoy Maitra, and Sumanta Sarkar

Abstract

So far there is no systematic attempt to construct Boolean functions with maximum annihilator immunity. In this paper we present a construction keeping in mind the basic theory of annihilator immunity. This construction provides functions with the maximum possible annihilator immunity and the weight, nonlinearity and algebraic degree of the functions can be properly calculated under certain cases. The basic construction is that of symmetric Boolean functions and applying linear transformation on the input variables of these functions,one can get a large class of non-symmetric functions too. Moreover, we also study several other modifications on the basic symmetric functions to identify interesting non symmetric functions with maximum annihilator immunity. In the process we also present an algorithm to compute the Walsh spectra of a symmetric Boolean function with $O(n^2)$ time and $O(n)$ space complexity.

Metadata

Available format(s): PDF PS
Category: Secret-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: Algebraic Attack Algebraic Degree Algebraic Immunity
Contact author(s): subho @ isical ac in
History: 2005-07-20: received
Short URL: https://ia.cr/2005/229
License: CC BY

BibTeX

@misc{cryptoeprint:2005/229,
      author = {Deepak Kumar Dalai and Subhamoy Maitra and Sumanta Sarkar},
      title = {Basic Theory in Construction of Boolean Functions with Maximum Possible Annihilator Immunity},
      howpublished = {Cryptology {ePrint} Archive, Paper 2005/229},
      year = {2005},
      url = {https://eprint.iacr.org/2005/229}
}