On algebraic immunity and annihilators

Zhang, Xian-Mo, Pieprzyk, Josef, & Zheng, Yuliang (2006) On algebraic immunity and annihilators. Lecture Notes in Computer Science : Information Security and Cryptology, 4296, pp. 65-80.

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Abstract

Algebraic immunity AI(f) defined for a boolean function f measures the resistance of the function against algebraic attacks. Currently known algorithms for computing the optimal annihilator of f and AI(f) are inefficient. This work consists of two parts. In the first part, we extend the concept of algebraic immunity. In particular, we argue that a function f may be replaced by another boolean function f^c called the algebraic complement of f. This motivates us to examine AI(f ^c ). We define the extended algebraic immunity of f as AI *(f)= min {AI(f), AI(f^c )}. We prove that 0≤AI(f)–AI *(f)≤1. Since AI(f)–AI *(f)= 1 holds for a large number of cases, the difference between AI(f) and AI *(f) cannot be ignored in algebraic attacks. In the second part, we link boolean functions to hypergraphs so that we can apply known results in hypergraph theory to boolean functions. This not only allows us to find annihilators in a fast and simple way but also provides a good estimation of the upper bound on AI *(f).

Impact and interest:

11 citations in Scopus
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9 citations in Web of Science®

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ID Code: 74282
Item Type: Journal Article
Refereed: Yes
Additional Information: Proceedings of the 9th International Conference, Busan, Korea, November 30 - December 1, 2006.
DOI: 10.1007/11927587_8
ISSN: 0302-9743
Divisions: Current > QUT Faculties and Divisions > Science & Engineering Faculty
Deposited On: 23 Jul 2014 03:11
Last Modified: 25 Jul 2014 00:04

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