Finding Low Degree Annihilators for a Boolean Function Using Polynomial Algorithms

Vladimir Bayev

Paper 2006/027

Finding Low Degree Annihilators for a Boolean Function Using Polynomial Algorithms

Vladimir Bayev

Abstract

Low degree annihilators for Boolean functions are of great interest in cryptology because of algebraic attacks on LFSR-based stream ciphers. Several polynomial algorithms for construction of low degree annihilators are introduced in this paper. The existence of such algorithms is studied for the following forms of the function representation: algebraic normal form (ANF), disjunctive normal form (DNF), conjunctive normal form (CNF), and arbitrary formula with the Boolean operations of negation, conjunction, and disjunction. For ANF and DNF of a Boolean function there exist polynomial algorithms that find the vector space of all annihilators of degree . For CNF this problem is NP-hard. Nevertheless author introduces one polynomial algorithm that constructs some subspace of having formula that represents .

Metadata

Available format(s): PDF PS
Category: Foundations
Publication info: Published elsewhere. English version of the paper from Mathematics and Security of Information Technologies 2005
Keywords: Boolean function low degree annihilator polynomial algorithm recursive algorithm.
Contact author(s): vbayev @ yandex ru
History: 2006-01-27: received
Short URL: https://ia.cr/2006/027
License: CC BY

BibTeX

@misc{cryptoeprint:2006/027,
      author = {Vladimir Bayev},
      title = {Finding Low Degree Annihilators for a Boolean Function Using Polynomial Algorithms},
      howpublished = {Cryptology {ePrint} Archive, Paper 2006/027},
      year = {2006},
      url = {https://eprint.iacr.org/2006/027}
}