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The general principle for algebraic attack for multi-output stream ciphers was proposed by Courtois. Furthermore, Armknecht, and Krause gave a definition of algebraic immunity for multi-output Boolean functions in, and investigated some construction methods of multi-output Boolean functions with maximal algebraic immunity. In this paper, several new characterizations of algebraic immunity for multi-output Boolean functions are given, and some related invariants and their relations are also investigated. Some examples are given to illustrate the usefulness of these results.
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