布爾函數(shù)擴(kuò)散性的矩陣刻畫
Matrix Description on Propagation Characteristic of Boolean Function
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摘要: 該文利用布爾函數(shù)的特征矩陣, 給出了n(3) 元布爾函數(shù)在sGFn(2) 滿足擴(kuò)散準(zhǔn)則的充分必要條件, 在此基礎(chǔ)上得到了布爾函數(shù)滿足嚴(yán)格雪崩準(zhǔn)則(SAC)的一個(gè)充分必要條件和n元平衡布爾函數(shù)滿足嚴(yán)格雪崩準(zhǔn)則、代數(shù)次數(shù)達(dá)到最大且不含有非零線性結(jié)構(gòu)的一個(gè)充分必要條件, 最后提出了平衡且滿足嚴(yán)格雪崩準(zhǔn)則的布爾函數(shù)的兩種特殊的遞補(bǔ)構(gòu)造法。Abstract: With characteristic matrix of Boolean function, a necessary and sufficient condition is given on a Boolean function satisfying the propagation criterion on vector sGFn(2), which provides n3. On the basis of it, the necessary and sufficient conditions are given on a Boolean function satisfying Strict Avalanche Criterion (SAC) and on a balanced SAC function which achieves the maximum degree and no nonzero linear structure. Finally, two special filling vacancies in the proper order methods of construction are presented.
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