信息安全与通信保密
信息安全與通信保密
신식안전여통신보밀
CHINA INFORMATION SECURITY
2012年
6期
62-64
,共3页
H布尔函数%e-导数%导数%代数免疫%代数次数
H佈爾函數%e-導數%導數%代數免疫%代數次數
H포이함수%e-도수%도수%대수면역%대수차수
H Boolean function%e-derivative%derivative%algebraic immunity%algebraic degree
将导数和自定义的e-导数结合在一起作为新的研究工具，而这两者（导数和e-导数）结合在一起能直接明确反映布尔函数的重量，深入到布尔函数取值的内部结构中去，讨论相关免疫H布尔函数的代数免疫阶、代数次数等问题，即严格雪崩性质、相关免疫性、代数免疫性及最高代数次数的相容性问题，得出Hamming重量为2n－＋2n-2。这类H布尔函数的最低代数次数和最高代数次数、最优代数免疫等结果。同时，也给出了一些求布尔函数代数次数和最优代数免疫的方法。
將導數和自定義的e-導數結閤在一起作為新的研究工具，而這兩者（導數和e-導數）結閤在一起能直接明確反映佈爾函數的重量，深入到佈爾函數取值的內部結構中去，討論相關免疫H佈爾函數的代數免疫階、代數次數等問題，即嚴格雪崩性質、相關免疫性、代數免疫性及最高代數次數的相容性問題，得齣Hamming重量為2n－＋2n-2。這類H佈爾函數的最低代數次數和最高代數次數、最優代數免疫等結果。同時，也給齣瞭一些求佈爾函數代數次數和最優代數免疫的方法。
장도수화자정의적e-도수결합재일기작위신적연구공구，이저량자（도수화e-도수）결합재일기능직접명학반영포이함수적중량，심입도포이함수취치적내부결구중거，토론상관면역H포이함수적대수면역계、대수차수등문제，즉엄격설붕성질、상관면역성、대수면역성급최고대수차수적상용성문제，득출Hamming중량위2n－＋2n-2。저류H포이함수적최저대수차수화최고대수차수、최우대수면역등결과。동시，야급출료일사구포이함수대수차수화최우대수면역적방법。
The Boolean function derivative and self-defined e-derivative, combined together, could clearly characterize the weight of Boolean functions, and thus are taken as the tools for in-depth research of the internal structure of Boolean function value, and also for discussion of algebraic immunity and algebraic degree problem of correlation-immunity H Boolean function, that is, strict avalanche criterion, correlation- immunity, algebraic immunity and consistency of the highest algebraic degree. The lowest algebraic degree and the highest algebraic degree, optimal algebraic Immunity of H Boolean function with Hamming Weight 2n-1＋2n-2 are derived, and some methods for calculating algebraic degree of Boolean function and optimal algebraic immunity also given in this paper.
