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Boolean functions used in stream ciphers should have large Algebraic Immunity (AI) in order to resist algebraic attacks. Constructing Boolean functions with the Maximum AI (MAI Boolean functions) and studying their cryptographic properties have been received attention for years. The existence of low degree multiples (or low degree annihilators) of Boolean functions is necessary for an efficient algebraic attack. Boolean functions with large AI can resist algebraic attacks since large AI guarantees the non-existence of low degree multiples.
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