Secondary constructions of Boolean functions with maximum algebraic immunity

Authors:
Konstantinos Limniotis;Nicholas Kolokotronis;Nicholas Kalouptsidis
Affiliations:
Hellenic Data Protection Authority, Athens, Greece and Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, Athens, Greece 15784;Department of Computer Science and Technology, University of Peloponnese, Tripolis, Greece 22100;Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, Athens, Greece 15784
Venue:
Cryptography and Communications
Year:
2013

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Abstract

The algebraic immunity of cryptographic Boolean functions with odd number of variables is studied in this paper. Proper modifications of functions with maximum algebraic immunity are proved that yield new functions whose algebraic immunity is also maximum. Several results are provided for both the multivariate and univariate representation, and their applicability is shown on known classes of Boolean functions. Moreover, new efficient algorithms to produce functions of guaranteed maximum algebraic immunity are developed, which further extend and generalize well-known constructions in this area. It is shown that high nonlinearity as well as good behavior against fast algebraic attacks are also achievable in several cases.