## Cryptology ePrint Archive: Report 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 $f$ there exist polynomial algorithms that find
the vector space $A_d (f)$ of all annihilators of degree
$\leqslant d$. For CNF this problem is NP-hard. Nevertheless author
introduces one polynomial algorithm that constructs some subspace
of $A_d (f)$ having formula that represents $f$.

**Category / Keywords: **foundations / Boolean function, low degree annihilator, polynomial algorithm, recursive algorithm.

**Publication Info: **English version of the paper from Mathematics and Security of Information Technologies 2005

**Date: **received 12 Jan 2006

**Contact author: **vbayev at yandex ru

**Available format(s): **Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation

**Version: **20060127:180032 (All versions of this report)

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