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 fc called the algebraic complement of f. This motivates us to examine AI(fc). We define the extended algebraic immunity of f as AI*(f) = min[AI(f),AI(fc)}. 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).
Original language | English |
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Title of host publication | Information Security and Cryptology - ICISC 2006: 9th International Conference, Proceedings |
Editors | Min Surp Rhee, Byoungcheon Lee |
Place of Publication | Berlin; Heidelberg |
Publisher | Springer, Springer Nature |
Pages | 65-80 |
Number of pages | 16 |
Volume | 4296 LNCS |
ISBN (Print) | 3540491120, 9783540491125 |
Publication status | Published - 2006 |
Event | ICISC 2006: 9th International Conference on Information Security and Cryptology - Busan, Korea, Republic of Duration: 30 Nov 2006 → 1 Dec 2006 |
Other
Other | ICISC 2006: 9th International Conference on Information Security and Cryptology |
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Country/Territory | Korea, Republic of |
City | Busan |
Period | 30/11/06 → 1/12/06 |