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中文摘要：
通过分析布尔函数的特征，建立了n元自对偶布尔函数和n-1元布尔函数之间的关系，根据此关系讨论了月元自对偶布尔函数的代数免疫度及其非线性度，得出自对偶布尔函数的非零次单项式个数为奇数，给出了n元n-1次自对偶布尔函数的个数和代数正规型表示的特征及其密码学陛质，对其代数次数为t的单项式个数提出了猜想，对其中两种特殊情况进行了证明。
英文摘要：
By analyzing character of Boolean function, the connection between n -variables self-dual Boolean function and n- 1 -vari- ables Boolean function is set up, and according to this connection the algebraic immunity and nonlinearity of n -variables self-dual Boolean function are discussed. It is also obtained that terms ofmonomials with algebraic degree nonzero are odd. The number, algebraic norm formation and cryptographical property of n -variables self-dual function with algebraic degree n- 1 are presented. A conjecture about terms ofmonomials with algebraic degree t is proposed, and two special cases are proved out.
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